When an author of one of the pieces that I mock shows up, I try to bump them up to the top of the queue. No matter how crackpotty they are, I think that if they’ve gone to the trouble to come and defend their theories, they deserve a modicum of respect, and giving them a fair chance to get people to see their defense is the least I can do.
A couple of years ago, I wrote about the Cognitive Theoretic Model of the Universe. Yesterday, the author of that piece showed up in the comments. It’s a two-year-old post, which was originally written back at ScienceBlogs – so a discussion in the comments there isn’t going to get noticed by anyone. So I’m reposting it here, with some revisions.
Stripped down to its basics, the CTMU is just yet another postmodern “perception defines the universe” idea. Nothing unusual about it on that level. What makes it interesting is that it tries to take a set-theoretic approach to doing it. (Although, to be a tiny bit fair, he claims that he’s not taking a set theoretic approach, but rather demonstrating why a set theoretic approach won’t work. Either way, I’d argue that it’s more of a word-game than a real theory, but whatever…)
The real universe has always been theoretically treated as an object, and specifically as the composite type of object known as a set. But an object or set exists in space and time, and reality does not. Because the real universe by definition contains all that is real, there is no “external reality” (or space, or time) in which it can exist or have been “created”. We can talk about lesser regions of the real universe in such a light, but not about the real universe as a whole. Nor, for identical reasons, can we think of the universe as the sum of its parts, for these parts exist solely within a spacetime manifold identified with the whole and cannot explain the manifold itself. This rules out pluralistic explanations of reality, forcing us to seek an explanation at once monic (because nonpluralistic) and holistic (because the basic conditions for existence are embodied in the manifold, which equals the whole). Obviously, the first step towards such an explanation is to bring monism and holism into coincidence.
Right from the start, we can see the beginnings of how he’s going to use a supposedly set-theoretic notion, in a very peculiar way. I don’t know anyone who seriously thinks that the universe is a set. Sets are a tool that we use to construct abstract models that describe things. The universe isn’t a set; it’s the universe. And yet a huge part of his argument is, ultimately, based on “disproving” the idea that the universe is a set, based on silly word-games.
And also, right from the beginning, we can see exactly the kind of semantic games he’s going to play. He manages to say pretty much nothing about the universe – all he’s doing is playing with the semantics of the words “Universe”, “real”, “holistic”, etc.
I particularly love this next bit.
When theorizing about an all-inclusive reality, the first and most important principle is containment, which simply tells us what we should and should not be considering. Containment principles, already well known in cosmology, generally take the form of tautologies; e.g., “The physical universe contains all and only that which is physical.” The predicate “physical”, like all predicates, here corresponds to a structured set, “the physical universe” (because the universe has structure and contains objects, it is a structured set). But this usage of tautology is somewhat loose, for it technically amounts to a predicate-logical equivalent of propositional tautology called autology, meaning self-description. Specifically, the predicate physical is being defined on topological containment in the physical universe, which is tacitly defined on and descriptively contained in the predicate physical, so that the self-definition of “physical” is a two-step operation involving both topological and descriptive containment. While this principle, which we might regard as a statement of “physicalism”, is often confused with materialism on the grounds that “physical” equals “material”, the material may in fact be only a part of what makes up the physical. Similarly, the physical may only be a part of what makes up the real. Because the content of reality is a matter of science as opposed to mere semantics, this issue can be resolved only by rational or empirical evidence, not by assumption alone.
After a particularly egregious exercise in english semantics, in which he does nothing but play with word meanings, coming nowhere near actually saying anything, but using lots of impressive-looking words, he concludes that it “is a matter of science as opposed to mere semantics”. Rich!
He spends some more time rambling about semantics of words like “physicalism”, “materialism”, and “containment”, before finally getting to the part that’s got any math content at all.
Now for a brief word on sets. Mathematicians view set theory as fundamental. Anything can be considered an object, even a space or a process, and wherever there are objects, there is a set to contain them. This “something” may be a relation, a space or an algebraic system, but it is also a set; its relational, spatial or algebraic structure simply makes it a structured set. So mathematicians view sets, broadly including null, singleton, finite and infinite sets, as fundamental objects basic to meaningful descriptions of reality. It follows that reality itself should be a set…in fact, the largest set of all. But every set, even the largest one, has a powerset which contains it, and that which contains it must be larger (a contradiction). The obvious solution: define an extension of set theory incorporating two senses of “containment” which work together in such a way that the largest set can be defined as “containing” its powerset in one sense while being contained by its powerset in the other. Thus, it topologically includes itself in the act of descriptively including itself in the act of topologically including itself…, and so on, in the course of which it obviously becomes more than just a set.
First – he gets the definition of set wrong. He’s talking about naive set theory, which we know is unsound. And in fact, he’s talking about exactly the kinds of inclusion issues that lead to the unsoundness of naive set theory!
Then he uses semantic word-games to argue that the universe can’t be a set according to set theory, because the universe is the largest thing there is, but set theory says that you can always create something larger by taking a powerset. What does he conclude from this pointless exercise? That playing word-games doesn’t tell you anything about the universe? No, that makes too much sense. That naive set theory perhaps isn’t a great model for the physical universe? No, still too much sense. No, he concludes that this problem of word-games means that set theory is wrong, and must be expanded to include the contradiction of the largest thing being both smaller than its powerset and larger than its powerset.
Yes, the solution is to take an unsound mathematical theory, and make it doubly unsound.
In the Cognitive-Theoretic Model of the Universe or CTMU, the set of all sets, and the real universe to which it corresponds, take the name (SCSPL) of the required extension of set theory. SCSPL, which stands for Self-Configuring Self-Processing Language, is just a totally intrinsic, i.e. completely self-contained, language that is comprehensively and coherently (self-distributively) self-descriptive, and can thus be model-theoretically identified as its own universe or referent domain. Theory and object go by the same name because unlike conventional ZF or NBG set theory, SCSPL hologically infuses sets and their elements with the distributed (syntactic, metalogical) component of the theoretical framework containing and governing them, namely SCSPL syntax itself, replacing ordinary set-theoretic objects with SCSPL syntactic operators. The CTMU is so-named because the SCSPL universe, like the set of all sets, distributively embodies the logical syntax of its own descriptive mathematical language. It is thus not only self-descriptive in nature; where logic denotes the rules of cognition (reasoning, inference), it is self-cognitive as well. (The terms “SCSPL” and “hology” are explained further below; to skip immediately to the explanations, just click on the above links.)
(His text refers to “the above links”, but in fact, the document doesn’t contain any links.)
Now… on the one hand, he claims that I’ve misrepresented him by saying that he’s talking about the universe using a set-theoretic framework. And yet, what is this but an extremely ill-defined variation of naive set theory?
This is pure muddle. It’s hard to figure out what he even thinks he’s doing. It’s clear that he believes he’s inventing a new kind of set theory, which he calls a “self-processing language”, and he goes on to get very muddled about the differences between syntax and semantics, and between a model and what it models. I have no idea what he means by “replacing set-theoretic objects with syntactic operators” – but I do know that what he wrote makes no sense – it’s sort of like saying “I’m going to fix the sink in my bathroom by replacing the leaky washer with the color blue”, or “I’m going to fly to the moon by correctly spelling my left leg.”
From there who moves to adding a notion of time, which he seems to believe can be done using nothing but set theory. Unfortunately, that makes no sense at all: he wants to somehow say that sets have time properties, without modifying the sets, modeling the time property, or in fact anything at all – once again, he just throws around lots of terminology in meaningless ways:
An act is a temporal process, and self-inclusion is a spatial relation. The act of self-inclusion is thus “where time becomes space”; for the set of all sets, there can be no more fundamental process. No matter what else happens in the evolving universe, it must be temporally embedded in this dualistic self-inclusion operation. In the CTMU, the self-inclusion process is known as conspansion and occurs at the distributed, Lorentz-invariant conspansion rate c, a time-space conversion factor already familiar as the speed of light in vacuo (conspansion consists of two alternative phases accounting for the wave and particle properties of matter and affording a logical explanation for accelerating cosmic expansion). When we imagine a dynamic self-including set, we think of a set growing larger and larger in order to engulf itself from without. But since there is no “without” relative to the real universe, external growth or reference is not an option; there can be no external set or external descriptor. Instead, self-inclusion and self-description must occur inwardly as the universe stratifies into a temporal sequence of states, each state topologically and computationally contained in the one preceding it (where the conventionally limited term computation is understood to refer to a more powerful SCSPL-based concept, protocomputation, involving spatiotemporal parallelism). On the present level of discourse, this inward self-inclusion is the conspansive basis of what we call spacetime.
I can’t make head or tails out of this. It’s just word-games, trying to throw in as many fancy-sounding terms as possible. What on earth does Lorentz invariance have to do with this muddle? LI means something quite specific, and he’s done nothing to connect any of this rubbish to it. He’s just throwing around words: “conspansion”, “lorentz invariance”, “protocomputation”.
But it gets worse. We get yet more of his confusion about just what “syntax” means:
Every object in spacetime includes the entirety of spacetime as a state-transition syntax according to which its next state is created. This guarantees the mutual consistency of states and the overall unity of the dynamic entity the real universe. And because the sole real interpretation of the set-theoretic entity “the set of all sets” is the entire real universe, the associated foundational paradoxes are resolved in kind (by attributing mathematical structure like that of the universe to the pure, uninterpreted set-theoretic version of the set of all sets). Concisely, resolving the set-of-all-sets paradox requires that (1) an endomorphism or self-similarity mapping D:S–>rÎS be defined for the set of all sets S and its internal points r; (2) there exist two complementary senses of inclusion, one topological [S Ét D(S)] and one predicative [D(S) Éd S], that allow the set to descriptively “include itself” from within, i.e. from a state of topological self-inclusion (where Ét denotes topological or set-theoretic inclusion and Éd denotes descriptive inclusion, e.g. the inclusion in a language of its referents); and (3) the input S of D be global and structural, while the output D(S) = (r Éd S) be internal to S and play a syntactic role. In short, the set-theoretic and cosmological embodiments of the self-inclusion paradox are resolved by properly relating the self-inclusive object to the descriptive syntax in terms of which it is necessarily expressed, thus effecting true self-containment: “the universe (set of all sets) is that which topologically contains that which descriptively contains the universe (set of all sets).”
Yes, lucky us, more wordplay!
The thing to notice here is right in the first sentence: “Every object in spacetime includes the entirety of spacetime as a state-transition syntax“. Spacetime isn’t a syntax. Like I said before, it’s like talking about spelling your leg. An object can’t be a syntax. A syntax is a method of writing down a sequence of symbols that expresses some logical statement. An object in spacetime can’t “include the universe as a state transition syntax”.
What I think he’s trying to say here is that we can describe objects in the universe as state transition systems, in which the state of an object plus the state of the universe can be used to compute the next state of the object. But he doesn’t understand that a syntax and a system are different things. And he seems to think that the idea of describing the universe as a state transition system is somehow profound and original. It’s not. I’ve read papers proposing state-transition semantics for the universe dating back to the 1950s, and I’d be surprised if people like von Neumann hadn’t though of it even earlier than that.
The rest of that paragraph is yet more of his silly word-games, trying to cope with the self-created paradox of inclusion and size in his mangled set theory.
At this point, I’m going to stop bothering to quote any more of his stuff. The basic point of his argument, and the basic problems that pervade it are all abundantly clear after this much, and you’ve already experienced as much fun as your going to by laughing at his foolishness.
To recap: this “theory” of his has three problems, each of which is individually enough to discard it; with the three of them together, it’s a virtual masterpiece of crap.
- The “theory” consists mostly of word-games – arguing about the meanings of words like “universe” and “inclusion”, without actually explaining anything about how the universe works. It’s a theory with no predictive or descriptive value.
- The “theory” is defined by creating a new version of set theory, whose axioms are never stated, and whose specific goal guarantees that it will be an unsound theory. Unsound mathematical theories are useless: every possible statement is provable in an unsound theory.
- The author doesn’t understand the difference between syntax and semantics, between objects and models, or between statements and facts – and because of that, the basic statements in his theory are utterly meaningless.
Could he be trying to pull a reverse-Sokal on us?
http://en.wikipedia.org/wiki/Sokal_affair
This doesn’t sound like relatvism, it sounds more like logical positivism to me.
Well, it really sounds most like the gobbledigook Sokal made fun of, but if I pretend for the moment that there is some actual meaning behind the words, that meaning is more like a version of positivism than it is relativism. He’s trying to construct some perfect (mathematical) language with a vocabulary that, in some undefinable way, has a one-to-one relationship with things in reality. There is also no indication (at least in these excerpts) that he thinks reality can be manipulated by people in the way that typically characterizes strong forms of relativism. So he’s missing one of the ‘red flags.’
Final thought – it seems distinctly odd for someone so obsessed with the idea of sets to claim right out of the gate to reject reductionism in favor of ‘monism.’ When you model some subject as a set, you are almost by definition doing a form of reductionism.
Good grief. And here I was hoping we could leave it on a semi-pleasant note.
Unfortunately, instead of retiring to write something vaguely constructive, Mark has now created a third rudely-titled “crank” page for me where previously there were only two, and without my original responses (in which I roughly explained what I was actually trying to convey). Instead, I’m now invited to start over from scratch in “defending my theory”.
It’s an old game, and everybody knows it all too well. The target is supposed to enhance the reputation of the critic by pretending that the critic is legitimate while bumping up the critic’s hit count with his “defense”, despite the obvious lack of any willingness on the part of the critic to give an inch under any circumstances, even if somebody puts a blueberry-math pie in his face.
This, of course, leaves me with no rational alternative but to point out that Mark is not a legitimate critic. In fact, Mark is incompetent. Thus, instead of defending myself against Mark, the most appropriate course of action in the present instance is to invite Mark to defend himself.
Let me explain what I mean by “incompetent”.
There are a lot of ideas floating around out there. Some are good; others are bad; others aren’t so attractive to the naked eye, but improve under magnification (many of the best ideas have come in this form, and sometimes the magnification process is not complete until long after publication).
A three-way partition can also be applied to Internet pundits, e.g. Mark, who entertain themselves and their readers by evaluating the ideas of others. Some are good at it, others are not so good, and others are a complete waste of time and bandwidth.
The value criteria for distinguishing among good and bad ideas are fairly cut and dried:
(1) Syntactic consistency: Is the idea well-formed and logically consistent? (Y/N)
(2) Semantic consistency: Is the idea consistently applied to its universe? (Y/N)
(3) Relevance: Is the idea relevant to its purported content or the problem to be solved? (Y/N)
The competency criteria for distinguishing among evaluators, e.g. Mark, are equally obvious:
(1) Comprehension: The evaluator makes sure he fully understands the ideas he evaluates and refrains from attaching extraneous constructions, speculative interpretations, or inappropriate conceptual models (even in the face of uncertainty regarding the proper interpretation).
(2) Discernment: The evaluator possesses the willingness, the knowledge, and the intelligence to properly and thoroughly apply value criteria 1-3.
(3) Neutrality: The evaluator limits his judgments to value criteria 1-3, and withholds final judgment on ideas to which he is unable to apply criteria 1-3 with reasonable certainty (e.g., in fields outside his areas of expertise, or where he bumps up against his intellectual ceiling).
In scholarly discourse, evaluators are required to justify their judgments. Those who display inadequate comprehension, discernment, or neutrality in their judgments, having failed one or more competency criteria, are by definition incompetent. Among incompetent evaluators, the worst-of-breed are obviously those who chronically fail all three competency criteria.
With regard to my essay, Mark fails all three competency criteria. Indeed, he readily admits to it. This renders Mark incompetent, by his own admission, to do what he’s trying to do here. Accordingly, he fails to qualify as a legitimate “debunker”, “crank fighter” or whatever it is that he likes to call himself, instead constituting a mere pain in the neck and leaving me nothing sufficiently coherent to “defend” against.
In fact, it’s a bit worse than that. This is because Mark sometimes seems to choose the ideas he attacks *because* he fails to comprehend them. In other words, it’s not just that Mark randomly encounters ideas he’s unfit to evaluate, and then does so anyway just to be a pain in the neck; it’s that for Mark, personal incomprehension almost seems to be an irresistible evaluation-stimulus.
Of course, in keeping with his overall incompetence as an evaluator, Mark doesn’t understand this. Instead, he pulls a cognitive switcheroo of which he is seemingly not consciously aware, automatically confusing his own incomprehension with incomprehensibility. In fact, “incomprehensibility” seems to be his main critique of my essay.
In other words, Mark has switched a judgment on his own subjective mental state (incomprehension) for a purportedly objective attribute of the idea he’s trying to evaluate (incomprehensibility), thus making the distinction “good math | bad math” effectively equivalent to “math that Mark is capable of understanding, and therefore likes | math-like content that Mark is incapable of understanding, and therefore hates!”
Now, if Mark were as smart as he evidently thinks he is, he’d be less aggressive. He wouldn’t immediately stick his neck out to upchuck all over ideas he doesn’t understand. Instead, finding himself unable to locate obvious falsehoods in the target of his derision, he’d wait until he has more data on what’s really going on with it. After all, that’s what reasonable people do.
But Mark isn’t always reasonable, or all that smart either, at least when he lets his characteristic irascibility get the better of him. In fact, as we’ve already established, he can be an incompetent little pain in the neck. In fact, he often appears to wallow in irrationality with what appears to be near-demonic relish.
Remember, the value and competency criteria listed above are objective in nature. This isn’t just an opinion; it’s a rock-solid indictment of Mark’s incompetence as an evaluator of ideas that he considers sufficiently “mathematical” to merit his special attention, but about which he actually can’t tell his ass from his elbow.
This doesn’t necessarily mean that nothing Mark says makes sense; some of what he says obviously does make sense. But some does not, and that’s where Mark tumbles into incompetency. Obviously, as the very first order of business here, Mark needs to mend his incompetent ways.
(I hope we’ve managed to avoid any problems with English comprehension this time around.)
Chris, you want us to believe you, you’re going to have to defend your theory rather than getting on the offensive. From what I’ve read over the past half hour, in this blog and on your own site, I can’t make out anything solid that you’re trying to convey. A summary here might at least enlighten us to your goals
‘Now, if Mark were as smart as he evidently thinks he is, he’d be less aggressive’
Where’s that kettle? I want to yell at it…
Dude, that stuff is from the INTRO page on your own website talking about CTMU. If you’re going to do an introduction to something and expect people to understand what you’re talking about, explain in simpler terms first. And if you don’t want people to understand what you’re talking about, then you’re being the classic internet elitist jackass. PRESUMING you want people to understand what this stuff’s about, you should probably elaborate in simpler terms.
Your FIRST SENTENCE doesn’t make sense to me, and I’ve had training in set theory. A set is a logical device used for talking about things. It’s not actually the things it’s talking about. And you say a set “exists in space and time”. Where in “space and time” is the set of real numbers between 0 and 1? What you’re describing is not a set as has ever been described in any set theory studies I’ve done. If you’re moving away from accepted terms and using different definitions for something as basic as sets, you really should define your terms.
I’ve slammed Mark CC a few times before. But you know what? He at least speaks with content, possibly true, possibly false, so there’s always a target thought to work with. You, in contrast, are just gibbering, outputting a cuckoo word salad whose high point is that it is grammatical and has some spiffy vocabulary in it now and then.
But Mark is treating you very gently in merely pointing out that you’re a crackpot and spelling out how you don’t make any sense repeatedly. Me? I suspect you couldn’t pass a Turing test. The difference between you and a program that cuts and pastes from Knol™ is you have the MGonz add-in. You’d be more entertaining, at least, if you threw in some Time Cube trash or Neal Adams quality artwork. As it is, you’re just a crackpot and complete bore.
You see, your theory, and your defenses of it, are 100% content-free. Telling us, for example, that some parts of what Mark wrote makes sense, and some parts do not, without giving any hints as to which is which, is all you can do to defend yourself. Rather telling, except to you.
As a minor nit, Mark’s comment that space-time is not syntactical might be correct, but it might not. It is certainly not known to be syntactical in any model yet proposed, but it could conceivably be. (Wheeler for a while thought this hope might go somewhere, but nothing came of it.)
Ad hominem through and through. Textbook.
Your defense does not apply here. Let’s see why. To be able to competently evaluate Mark’s criticism, you should
1) Comprehension: I believe you don’t understand what Mark is saying, but in any case it doesn’t matter, because you are trying to refute what Mark says without referring to what Mark says.
2) Discernment: You are obviously not willing to apply your whole criteria for evaluation.
3) Neutrality: do I really need to address this point?
Now, can we focus on your theory? We are not discussing about you, but your theory, and you are in a prime position to teach us. We are willing to learn and think. Can you give as any guiding idea?
Reads like someone who has gotten lost in his own abstractions and become convinced of their independent reality.
I hate when that happens.
It looks to me like he starts out with naive set theory and a conflation of “subset of” and “element of” in the term “containment”, follows this up with the idea of a theory (in the model theoretic sense of the term) which serves as a model for itself (which I admit is an interesting idea) and which somehow serves as a language for itself as well, despite never defining the symbols or syntax in use. Next he seems to try resolving Russel’s paradox by positing a temporally-couched version of Russel’s hierarchy of sets, in which each instantaneous slice of the universe “contains” the previous instantaneous slice, while somehow maintaining identification of each slice with the next. Then, referring back to his self-interpreting model, he identifies syntax and semantics while trying to keep “containment” in the language separate from “containment” in the meta-language, still not realizing his initial equivocation on the word “containment”.
How he gets to the idea that each piece of the universe “contains” the universe as a whole (i.e. the holographic universe idea) from there, I have no idea, unless he’s moved silently from sets to multisets, in which case he could simply have begun by defining the universe to be the multiset whose elements consist exactly of however many copies of itself he wants, since he is clearly ignoring the axiom of regularity from the beginning.
Indeed. Langan fails to grasp the fact that real physical things aren’t and cannot be sets, i.e. that Mark and the singleton set that only has Mark as a member are two completely different things, and that the universe and the set of all things in the universe (and, for that matter, the set that has the universe as a member) are completely different things.
What he actually seems to be doing – if I am charitable – is a kind of mereology, Lesniewski-style, or perhaps trying to replace set-theory by a completely nominalistic mereology. He doesn’t seem to be aware that this is what he is doing, however, and continues to use the language of set theory. Besides, most of the questions he is asking and claims he is making would make no sense in mereology.
Trivia: Langan contributed a chapter to Dembski’s anthology “Uncommon Dissent”. Make of that what you want.
For example certain properties of the reflexive self-contained language of reality that it is syntactically self-distributed self-reading and coherently self-configuring and self-processing respectively correspond to the traditional theological properties omnipresence omniscience and omnipotence. While the kind of theology that this entails neither requires nor supports the intercession of any supernatural being external to the real universe itself it does support the existence of a supraphysical being the SCSPL global operator-designer capable of bringing more to bear on localized physical contexts than meets the casual eye.
Hey Chris, who is on first bud?
LOL! I tried reading through the CTMU, and got the exact same feeling as some others … complete semantics. I was expecting it to be about math, physics, or something a little more solid. It seems to me to be at least 85% fluff and word-games. Too bad, one would hope the ‘smartest man in america’ would have something to contribute to the world rather than CTMU and Intelligent Design.
A high IQ is a necessary, but not sufficient, condition for understanding advanced mathematics. Like Vos Savant, Langan has attempted to understand mathematics with his intellectual gifts alone, skipping over the thousands of hours of arduous study necessary for true comprehension.
I recommend Mr. Langan start here.
Your comment is so condescending the spittle flying from your mouth feels like rain.
How in hell does your statement make any sense? How does condescension have anything to do with spit or its qualities?
As an internet pundit once said (paraphrased), “If you can’t count to metathree, you shouldn’t be using metaphors.”
Holy shit, Chris Langan is here in the comments! Y’all might not realize it, but he has an incredibly high IQ. Unfortunately, he is also pretty much incapable of making himself understood — a form of low social intelligence. Malcolm Gladwell relates in Outliers that Langan taught himself calculus at a young age; when he attended his first calculus class in university, he went to speak to the professor after the lecture to offer criticisms of the pedagogy. The professor thought Langan was complaining that the material was too difficult — Langan was unable to convey the fact that he understood the material perfectly and had for years.
Mr. Langan, please take my advice. I have a Ph.D., and yet I recognize that, in terms of raw intelligence, relative to you I am mentally handicapped. My advice is this: you have got to figure out how to get your ideas understood as much as possible by people whose intelligence does not compare to yours! Experiment! Try new things! Test your progress in this task!If you’re so smart, how can you consistently fail over and over at this one skill? This is the most important thing one can possibly learn that you haven’t taught yourself already.
I think you’re too charitable. Mr. Langan is certainly intelligent. But being intelligent isn’t enough – you also have to know stuff. You cannot just figure out set theory and mathematical logic on your own, no matter how intelligent you are (because no matter how intelligent you are, you won’t match the intelligence of Frege, Russell, Church, Hilbert and so on combined). Not only do you need to know stuff, you also need to correct misunderstandings everyone does make in teaching themselves the fundamentals. High intelligence doesn’t help against psychological biases (confirmation bias and so on), but may help you create a huge, bizarre and confused framework based on misunderstanding without helping you weed out those misunderstandings (because you are just trying to make everything else you do work as well as possible with the misconstruals).
The point of this piece of hobby-psychology is that I don’t for a moment think Langan’s primary problem is to make himself understood. His problem is that he is thoroughly confused; the fundamental concepts and their application are misunderstood – and that means that he not only uses the wrong words; the questions he tries to solve are meaningless. His nonsense ideas probably stem from some fundamental understanding somewhere; the precise differences between syntax and semantics, and between sets and their elements, are my guess – every crucial distinction in set theory, mathematics, logic and physics is meshed together in an incoherent jumble. Langan might think it makes sense, and it may seem as if it makes sense to himself, and he may use his high intelligence to interpret everything in ways that seems to make sense to himself; but it doesn’t make sense. There is no way to just clarify the passages above; they are wrong and usually not even wrong.
I don’t disagree with what you wrote; I just think that Langan is so mired in his own skewed frame of thought that he won’t be able get free without an actual attempt to communicate with other people (instead of jockeying for status, as he does in his reply to MarkCC).
What is Eric Hart up to these days?
Wow. Spinoza would shake his head in disappointment at how his philosophy got hijacked for something like this. He had his share of word-mixups (and honestly, that tends to be a common problem with rationalists that start working from the top down), but at least he was fairly clear in meaning *most* of the time.
OK, I think we’ve waited about long enough for Mark to defend himself from the charge of incompetence.
You know, it never looks good when the proprietor of a highly contentious web site hides behind his commentators. It tends to destroy the forum as an appropriate setting for serious intellectual discussions. So I trust that Mark has merely been busy, or better yet, that he recognizes the futility of trying to defend his indefensible behavior.
In any case, I’ll go ahead and pave the way to a final resolution of the situation by dispelling any remaining doubt that Mark is incompetent to evaluate the essay he’s been attacking here. Fortunately, an analysis of the first “substantive” paragraph of his critique will be sufficient for that purpose.
Here’s the paragraph:
“Right from the start, we can see the beginnings of how he’s going to use a supposedly set-theoretic notion, in a very peculiar way. I don’t know anyone who seriously thinks that the universe is a set. Sets are a tool that we use to construct abstract models that describe things. The universe isn’t a set; it’s the universe. And yet a huge part of his argument is, ultimately, based on “disproving” the idea that the universe is a set, based on silly word-games.”
Let’s have a look the above paragraph sentence by sentence.
Sentence 1: “Right from the start, we can see the beginnings of how he’s going to use a supposedly set-theoretic notion, in a very peculiar way.”
I don’t know what this means; it’s “geek” to me. It’s probably an error, but in the spirit of evaluative competence, I’ll withhold judgment.
Sentence 2: “I don’t know anyone who seriously thinks that the universe is a set.”
Error 1: That’s vanishingly unlikely. Materialists think that the universe is a set of material objects (e.g., atoms and subatomic particles in various combinations) on which all else can be secondarily defined and/or causally supervened. Any assertion by Mark that he doesn’t know at least one person subscribing to such a viewpoint is simply incredible, especially given the atheist-materialist circles in which he runs. (Mark describes himself as a “religious, theistic, reconstructionist Jew,” but that’s beside the point; merely that he attended a modern university is enough to tell us that he has rubbed elbows with many atheistic materialists.)
But materialism is almost beside the point; all we need here is the scientific method. With its unrelenting emphasis on observation of, and experimentation on, material objects including the measurement devices thereby affected, the scientific method demands that everything in science be related to observables and the objects to which they are attached, which, being individually discernable, qualify as elements of sets (with all appropriate distinctions applied; e.g., sets of physical objects or events are countable, while sets of points in a continuum are uncountable).
In search of counterexamples, one may be tempted to point to such things as time and process, “empty space”, various kinds of potential, forces, fields, waves, energy, causality, the spacetime manifold, quantum wave functions, “laws of nature”, “the mathematical structure of physical reality,” and so on as “non-material components of the universe”, but these are predicates whose physical relevance utterly depends on observation of the material content of the universe. To cut them loose from the elements of observational sets would be to deprive them of observational content and empty them of all physical meaning.
Sentence 3: “Sets are a tool that we use to construct abstract models that describe things. “
Error 2: More accurately, the concept “set” is a formal entity into which real content may be mapped by description or definition. To preclude content is to sever the mapping and render the “tool” descriptively useless.
Everything discernable (directly perceptible) within the physical universe, including the universe itself (as a coherent singleton), can be directly mapped into the set concept; only thusly are secondary concepts endowed with physical content. One ends up with sets, and elements of sets, to which various otherwise-empty concepts are attached. Unfortunately, in standard theory, this attachment is reminiscent of sessile mollusks which have glued themselves to foreign bodies, and this is a problem for set theory as a descriptive language for the universe (or as a foundational language of the mathematical formalisms applied to the universe by science), as it is subject to a crippling form of dualism which separates functions from the sets they relate. But while set concept is obviously necessary – these other concepts are rendered physically meaningless without it – this in no way implies its sufficiency on any scale of reference.
Sentence 4: “The universe isn’t a set; it’s the universe.”
Error 3: This is an instance of logical negation amounting to an absolute distinction between “set” and “the universe”. It asserts the nonexistence of structural overlap between “universe” and “set” on all levels of reference, thus precluding shared structure.
Let’s take a closer look. Mark isn’t just saying
4a. “The universe is *in part* a set, but ultimately *more than* just a set (of objects, events, etc.)”;
he’s saying
4b. “The universe is *not* a set, period.”
These statements are mathematically distinct. Mark’s statement, 4b, implies that the universe is nowhere a set, i.e., that neither it nor any of its contents can be mapped into a collection or aggregation of objects, elements, points, or any other discernable entities as content. But this is completely absurd.
Indeed, if the “set” concept is free of physical content, then this precludes the use of any measurement device for observation or experimentation, and in fact, reference to anything that is observationally discernable and quantifiable in number, as this would provide physical content for the “set” concept. Whoops, no more science!
Obviously, the universe IS a (structured) set, but not MERELY a set in the context of any established version of set theory. Its description requires a more powerful mathematical language incorporating the “set” concept within a more capacious formal entity (which, of course, was largely the point of my little essay, which was written back before “everybody knew” that standard set theory could not be rehabilitated as a foundational language). Hello, CTMU, and hello, SCSPL!
In short, the author of Sentence 4 (i.e., Mark) is either mathematically illiterate, or he’s trying a bit clumsily to agree with me in all essential respects, but doesn’t quite know it due to the depth of his own incomprehension.
Sentence 5: “And yet a huge part of his argument is, ultimately, based on ‘disproving’ the idea that the universe is a set, based on silly word-games.”
Error 4: This statement consists of two parts:
5a: “His argument is based on ‘disproving’ the idea that the universe is a set” (I’ll be charitable and assume that Mark knows what proof actually entails in mathematics);
5b: “This attempted disproof, and the argument based on it, are silly word games.”
Quibbles aside, statement 5a is close to accurate; I do, after all, maintain that the universe is not merely a set, but something with greater expressive capacity (properly including that inherent in the set concept itself). However, statement 5b amounts to an accusatory misconstruction of the writer’s personal incomprehension, for which there is no excuse.
And that’s just one little paragraph. Its completely erroneous character conclusively establishes that Mark’s critique fails value criteria 1-3 enumerated above, and that Mark himself fails all three adjoining competency criteria … which, somewhat to his credit, he freely admits.
Summary: Explaining the errors made by Mark at the very beginning of his critique requires more space than is occupied by Mark’s statements themselves. Mark actually generates errors at roughly the same rate, and arguably faster than the rate, at which he writes about the “errors” of others!
Even though this may not seem like serious business to some readers, it certainly is. If Mark does not desist in his nonsense, it may well turn out to be something he regrets for the rest of his life. This is not because he is merely wrong; we all live and learn. It is because Mark often lacks any clue regarding the wrong turns he has taken, and in order to distract himself from his frustration, habitually lashes out at the sources of his confusion like a vindictive child. Any failure of comprehension precipitates him into a fit of pique, at which point he disastrously (for him) attempts to damage the understanding and the reputations of others without just cause.
I’m sure it would be a relief for all concerned if this were the end of my participation here. So I hope that’s the case…all the more so because if it is not, then one way or another, things will only go further downhill for Mark.
Chris:
What a load of ad-hominem ridden bullshit.
The universe isn’t a set. A set is a mathematical construct defined axiomatically. That can sound like doublespeak, but it actually captures an extremely important distinction – one which you still don’t seem to understand.
In math, we build mathematical models of things in order to study and understand them. The mathematical model is an abstract description that’s useful for developing an understanding of the thing that it models – but the model is not the thing that it models.
A set is a mathematical model that’s useful for describing many things. There are many things in the universe that can be modeled very well using set theory. But that’s entirely different from saying that the universe, or that anything in the universe is a set. A mathematical model is not the thing that it models.
There are also many things in the universe that cannot be modeled very well using set theory. (For example, try to put together a meaningful set-theoretic model of vacuum fluctuation and hawking radiation based on the set of particles in the universe. It really doesn’t fit well.)
Does the existence of things in the universe which can’t me modeled nicely in set theory mean that set theory is something wrong? No. Because the universe isn’t a set. The universe and a mathematical model of the universe are very different things. There are many different possible mathematical models of the universe. Even taking set theory as a basis, there are numerous different set-theoretic mathematical models of the universe. The universe isn’t any of those mathematical models; those models are mathematical constructions that we use to try to understand it.
The lack of understanding of this distinction – the difference between a model and the thing that it models – runs throughout your writing. It’s part of why you try to talk about “syntax” in your model in a way that doesn’t make any sense to people who know what syntax means in math and logic. Because you muddle important distinctions. Syntax and semantics are very different things in a mathematical model. But if you insist that the mathematical model is indistinguishable from the thing that it models… then the syntax of an object is the object, the semantics of an object are the object, and therefore the syntax and semantics of the object are exactly the same thing – because they both are the object.
As I’ve frequently said on this blog: the worst math is no math. And that’s a pretty good description of your writing. There are lots of mathematical words, but they’re used in ways that just make no sense. They look impressive, but when you try to burrow down to get to their meaning, they don’t make sense. They muddle together fundamental concepts in nonsensical ways; they blur the distinctions between things that are necessarily distinct.
Worse, even if you ignore much of the muddled reasoning, you still can’t make this stuff work. If you actually take the word salad and try to render it as math, what you get is something very much like naive set theory. Unfortunately, naive set theory doesn’t work: it’s inconsistent. And your system, which by definition embeds itself, necessarily includes all of the inconsistencies of naive set theory.
Of course, you won’t actually address any of these problems. You’ll just wave your hands around and insult me some more. I remain uncertain of just how it is that doing that somehow defends the validity of your theory, but that’s probably just because I’m not as smart as you.
Well, lets see. It is not difficult to disprove this wanna-be-a-proof-by-verbosity.
The core of your “proof” is
>“The universe is *not* a set, period.”
>These statements are mathematically distinct. Mark’s statement, 4b, implies that the universe is nowhere a set, i.e., that neither it nor any of its contents can be mapped into a collection or aggregation of objects, elements, points, or any other discernable entities as content. But this is completely absurd.
Lets recall the mathematical definition of a (naive, not to be too hard on our friend) set. A set is more or less any collection into a whole of definite, distinct objects m (which are called the “elements” of M) of out perception or of our thought. Credits go to wikipedia.
Then you say: the universe is an aggregation of objects. Well, as you which. But, are they DISTINCT?
I don’t know, and you neither. Maybe you have not thought about it, but you don’t know.
Consider two identical particles, like two electrons, or two atoms in precisely the same quantum state. If you know something about Physics (elementary Physics), you will know that these particles can not be differentiated, and that they behave in a very particular way. They are completely indistinguishable. Are they different objects?
You can not trace them by their trayectories: there are no trayectories in the quantum World.
If you see two electrons orbiting an atom, and you look an instant later, you can not tell which particle is which. Are the ultimate elementary particles distict? Sorry, you don’t know. If it is so, no set for you.
Particles are created and destroyed. They exists now but not then. Are they distinct?
Particles can be entangled. Two particles behave like one entity. Are they distinct? Stand a moment to think. Maybe all particles are entangled in some way (this is a very real possibility). Are they distinct?
When you throw electrons agains a screen, you observe particles. But they are guided by a guiding wave function. But wait, a whole system can be described by only one quantum wave function! Are their particles distinct? The whole universe can be described by a (little bit complicated) wave function. In quantum mechanics you loose locality, so you loose individual particles. Are they distinct?
I see a shadow of reasonable doubt.
From my point of view, you declare the universe a set, and you base this conclusion in your assumption that the universe is a set. Not very good logic.
You could model the universe as a set. But that will be your (somewhat outdated) model. But it is not something obvious. I don’t believe it you could tell a person “mathematically illiterate” for not thinking the idea is a tautology.
Of course, you now can always play word games and say you were speaking of an informal set, in everyday language. Maybe you can save face that way. Or by saying that the Universe is the set of one element, the Real Universe.
PS: You should consider reading http://en.wikipedia.org/wiki/Fallacy. You used practically all of the fallacies listed there.
You’re still jockeying for status. The thing is, you’re not good at it, so your words are lowering your own status.
The posts listed in A Human’s Guide to Words on the Less Wrong Wiki would be useful to you.
“You know, it never looks good when the proprietor of a highly contentious web site hides behind his commentators. ”
Chris, I don’t think that the most people consider Good Math, Bad Math to be a “highly contentious website”. Note also that the claim here is simple wrong. Whether Mark or someone else responds to comments is utterly irrelevant to determining if Mark’s comments are correct. There are in this thread, aside from Mark, multiple mathematicians and physicists commenting. The fact that they all agree with Mark should cause you to wonder if maybe, just maybe, you are mistaken.
While Chris points out the obvious, I’ll just add one curious detail:
Langan says: “Materialists think that the universe is a set of material objects”.
No. In fact, it is incompatible with materialism to assume that the universe is a set of material objects, since sets are not material objects. Materialists think that the universe consist of only material objects. The fact that sets are not material objects is precisely why nominalists like Lesniewski and Goodman developed mereology, as a substitute for set theory that satisfied their nominalist inclinations. And nominalistic mereology is what Langan seems to be sliding into when he talks about collections and aggregations of objects at some point in the above rant.
Of course, mathematical objects are generally not considered very problematic by materialists unless they are also nominalists (especially given the revival of logicism).
To get a feeling for how deep this misunderstanding runs, consider:
“Indeed, if the “set” concept is free of physical content, then this precludes the use of any measurement device for observation or experimentation”
Yes, you cannot physically measure or observe a set. A set is a mathematical object. But you can of course physically measure and observe the universe. Therefore, the universe is not a set. You can also use set theory as a tool when you describe the universe and make models of it.
The number of fallacies committed in the above post is actually staggering. Just look at:
“This is an instance of logical negation amounting to an absolute distinction between “set” and “the universe”. It asserts the nonexistence of structural overlap between “universe” and “set” on all levels of reference, thus precluding shared structure.”
But of course, saying that the universe and a set of the universe are distinct things does in absolutely no way “assert the non-existence of structural overlap”, if Langan uses “structural overlap” or “shared structure” (i.e. isomorphism or partial isomorphism). Would Langan also deny, I wonder, that there can be any “shared structure” between a map and the terrain it is a map of?
“It is because Mark often lacks any clue regarding the wrong turns he has taken”
That one blows the irony meters. Langan must be one of the most spectacular examples there is of Dunning-Kruger in action.
That should be “While Mark points out the obvious”. Sorry
There are links in his text, but they are visually indistinguishable from the surrounding text.
So I did some reading on Chris, and it’s interesting seems to be a really “smart” guy, if you define smart as being mental horsepower.
Let me explain. I’m sort of familiar with this, because I’m a little bit like Chris, though not nearly to the same virtuoso level. I find that I have a tremendous amount of mental horsepower, in that I am able to grasp new concepts very quickly, do fairly complicated mental calculations without having to practice the feat very much, have excellent recall (though I’ll be damned if I can remember appointments…), things like that. But in terms of creativity, inventiveness, etc., well, I’m probably a little above average if I am being honest rather than humble, but it’s not nearly to the same level. And worse than that, I’m a little sloppy and have a scandalous lack of persistence and ambition. And in terms of strategizing, and discerning good ideas from bad, I think I’m pretty much dead-on average.
So the upshot is that I score pretty highly on IQ tests, and in certain arenas I can come across as scary-smart — but overall in my career I’m just doing fairly well. Oh, I have a master’s degree and a good job in an R&D dep’t, but it’s nothing to write a book about. I’m almost certainly not ever going to have papers published in high impact journals, or invent the Next Big Thing, or anything like that. And — here’s the thing — I know people with less mental horsepower than me are doing those things, because they excel in other talents that are more crucial to academic success. Just to take an example from my work, it’s no good if I can read and digest other people’s patents much more rapidly than most, if I don’t have any (well, many) damn patents myself. Mental horsepower is useful, but above a certain point it’s not much more than a party trick.
I get the feeling Chris is a bit like that, only with an absurd, almost inconceivable amount of mental horsepower. He can think through all of this stuff blindingly fast — but in terms of discerning whether any of it is a good idea… not so much. 🙂
Reading some of the comments above, I realize Chris is doing another thing I am prone to doing. I have a tendency to reinvent the wheel, and/or to make awkward probings into what turns out to be established territory. I think it comes from having a very high ratio at a) skill at seeing connections and synthesizing concepts from what knowledge you had, to b) desire and ability for seeking out previously established work. To be clear: You can still be pretty good at (b), but if you are way better at (a), you (like me) will have a tendency to reinvent the wheel — it may not be that you don’t care to look up what has already been done, but you start running away with all the shit you can figure out yourself based on what you already know… which by the way is way more fun than looking up what other people have done… and you wind up making forays into areas that it turns out other people have already covered exhaustively.
Seems like Chris is doing that in regards to deciphering the problems in applying set theory to the real world. There’s a certain brilliance in that he identified many of the problems in naive set theory by himself — how many of you could do that? — but it’s all for naught of dozens of other thinkers have been there before and already have more refined solutions to the problem.
Reading your comments, I think, helps me understand a bit better how someone smart can fuck up badly.
Thanks, dude.
Heh. Like the time in the early 80’s I was messing with polyrhythms, thinking I was being so clever, then hearing King Crimson’s “Discipline”. Holy shit.
It’s should be noted that Langan himself has not brought up his intelligence; it’s the other commentators who seem all too willing to make that into the subject of discussion. I think that is what he means by ” I would merely advise you not to leap so readily to what seem to be your highly standardized conclusions regarding me,” since half the people on this forum have already subscribed to the “Oh Chris is smart, but he should really learn to interact with other people” stereotype. The other half thinks that’s he’s a stuck-up intelligent prick. Why would he even want to talk to any of us under these conditions?
Totally off-topic, Mark, but was that your wife who appeared briefly as part of the Watson team at IBM, on this week’s Jeopardy? Is there anything about Watson’s inner workings that you would be free to talk about on the blog? Because that would be a heck of a lot more interesting than the current topic of discussion.
Alright, then. At this point, I think it’s safe to say that Mark has no intention of trying to defend himself against the charge of evaluative incompetence.
In repeatedly failing to defend himself against the charge of evaluative incompetence, Mark has now exhausted his last chance to prove that he has the intellectual standing to criticize my work. (Lest this be misinterpreted, “intellectual standing” refers not to Mark’s intelligence, but merely to his highly deficient knowledge state, on which I think he could greatly improve by freeing himself from various irrational prejudices and unnecessary cognitive bottlenecks.)
As I’ve already observed, Mark generates errors faster than he writes. This makes it quite tedious to rebut him, as it is far easier for him to dash off a few paragraphs of ill-considered pseudomathematical gobbledygook than it is for me to explain all of his errors in detail. But just so as not to waste an opportunity for instruction, I’ll do it one more time anyway.
Mark: “What a load of ad-hominem ridden bullshit.”
Comment: It was Mark who first resorted to personalized invective in this exchange. Anyone who doubts this need merely look at the titles of both of his Langan/CTMU critiques, including this one.
Mark: “The universe isn’t a set. A set is a mathematical construct defined axiomatically. That can sound like doublespeak, but it actually captures an extremely important distinction – one which you still don’t seem to understand.”
Error 1: A set is not a “mathematical construct defined axiomatically”. That would be set *theory*. While set *theories* are indeed defined axiomatically, the set concept itself is defined in a very basic and general way, which is precisely why it supports multiple versions of set theory incorporating different axioms.
Everybody around here seems to like Wikipedia. Well, here’s how Wikipedia defines “set”: “A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics” (… sufficiently fundamental, in fact, to nucleate different axiomatic theories and play an indispensable role throughout mathematics).
This definition is qualified and restricted by various strains of set theory, but it remains essentially intact as theoretical context varies. More advanced versions of set theory improve on naïve set theory only by adding distinctions and restrictions; for example, NBG adds the concept of classes, while ZF proscribes self-inclusion. Such advanced theories do nothing to expand the expressive capacity of the basic “set” concept.
Error 2: Because the universe fulfills the definitive criteria of the “set” concept (and more), it is at least in part a (structured) set. Mark seems to believe that “set”, being a concept or formal entity, cannot possibly describe the universe; after all, the universe is not a mere concept, but something objective to which concepts are attached as descriptive “tools”. But to the extent that concepts truly describe their arguments, they are properties thereof. The entire function of the formal entities used in science and mathematics is to describe, i.e. serve as descriptive properties of, the universe.
Obviously, not all formal entities qualify as properties of the things to which they are attributed. E.g., the formula “abracadabra, X, shazam!” is just a nonsense formula in which X has been written without attention to fact, and can hardly be described as a “property of X”. However, when a form duly reflects the actual structure of X – e.g., when it is an isomorphism or a model of X which attributes to X the distinguishable, observationally replicable structure we actually observe when we look at X – it indeed defines a property of X, at least for scientific purposes. For example, where X is actually green (reflects green light), the form “X is green” ascribes the property “greenness” to X. Similarly, because the formal entity “set”, meaning “collection of distinct objects”, actually describes the structure of the universe – which is in fact a collection of distinct objects, plus additional structure – the property of “being a set” is a factual property of the universe, and this permits us to say “the universe is a set”.
Error 3: Previously, Mark was caught substituting CTMU “incomprehensibility” for his own personal incomprehension regarding the CTMU. Here he goes a step further, substituting *my* alleged incomprehension for the alleged CTMU “incomprehensibility” that he originally substituted for his own personal incomprehension of the CTMU. Instead of standing pat on his own personal confusion, he wanders ever farther afield, from his own mental state to an allegedly objective attribute of a theory to another mental state … this time, somebody else’s. This is not how sound mathematical reasoning is conducted.
Mark: “In math, we build mathematical models of things in order to study and understand them. The mathematical model is an abstract description that’s useful for developing an understanding of the thing that it models – but the model is not the thing that it models. A set is a mathematical model that’s useful for describing many things. There are many things in the universe that can be modeled very well using set theory. But that’s entirely different from saying that the universe, or that anything in the universe is a set. A mathematical model is not the thing that it models.”
Error: Mark is having a terrible problem distinguishing “set” from “set theory”. As I’ve just pointed out, “being a set” is in fact a property of the universe. That’s because “set” is defined as “a collection of distinct objects”, and the universe is in fact a collection of distinct objects (and more). The definition of “set” correctly, if only partially, describes the structure of the universe, and nothing can be separated from its structure. Remove it from its structure, and it becomes indistinguishable as an object and inaccessible to coherent reference.
I also get the impression that Mark is confused regarding the definition of “model”, which comes in two strengths. In logic, a model is a valid interpretative mapping, i.e., an interpretation of a formula A or class of formulae A* under which A, or every formula of the class A*, is true. The argument is generally a mathematical language with its own formal structure, while the image is anything that “makes the argument true” by virtue of identical structure “up to isomorphism” (of course, this situation is symmetrical; just as content instantiates a language, the language describes its content, and where validity is given, we have a “model” in either direction). The model includes both ends of the mapping, argument and image, in the form of shared structure.
So much for logic. In less formal contexts, the term “model” may be used in a less exacting way; the validity criterion of the mapping may be relaxed. The model can then be structurally non-identical to the argument, as when a scientist tentatively applies some mathematical description to a phenomenon without being sure that the description is correct, e.g., because inobvious features of the argument and/or image may be irreconcilable with the explicit part of the mapping. In this case, the model is not a legitimate property of the object thereby modeled, and can thus be separated from it without depriving the argument of structure. This is the sense in which Marks seems to be using the term.
Unfortunately, it is not the sense in which *I* usually employ the term, i.e. the logical sense, and it is my work that Mark has been criticizing.
Mark: ”There are also many things in the universe that cannot be modeled very well using set theory. (For example, try to put together a meaningful set-theoretic model of vacuum fluctuation and hawking radiation based on the set of particles in the universe. It really doesn’t fit well.)”
Comment: Although he seems unaware of it, Mark is not actually disagreeing with me here. Simply that the universe can be partially characterized as “a set of particles” does not imply the existence of a “meaningful set-theoretic model of vacuum fluctuation and hawking radiation”. In fact, this is a large part of what my essay actually says (a pity that Mark doesn’t appear to understand this). Once again, a key distinction is that between “set” and “set theory”; although any version of the latter contains more formal structure than the unadorned “set” concept, it is insufficient to describe or model the universe in its entirety.
Mark: ”Does the existence of things in the universe which can’t me modeled nicely in set theory mean that set theory is something wrong? No. Because the universe isn’t a set. The universe and a mathematical model of the universe are very different things. There are many different possible mathematical models of the universe. Even taking set theory as a basis, there are numerous different set-theoretic mathematical models of the universe. The universe isn’t any of those mathematical models; those models are mathematical constructions that we use to try to understand it.”
Error: For the umpteenth time, “set” does not equal “set theory” (any version), and the property “being a set” isn’t something one can slap onto the universe, or not, at whim. It is synonymous with “being a collection of distinct objects”, which accurately reflects the observed structure of the universe. This makes it an actual property of the universe.
If the universe does not possess the property “being a set” – or if one prefers, “being valid content of the formal entity ‘set’” – then the set concept cannot be properly applied to the universe even as a tool. But then the natural and mathematical languages to which the set concept is fundamental cannot be properly applied to the universe either, and science is impossible. (This is called “reductio ad absurdum”; it consists in the derivation of an absurdity or contradiction from Mark’s initial premise that “the universe is not a set”.)
Mark: ”The lack of understanding of this distinction – the difference between a model and the thing that it models – runs throughout your writing.”
Error: In logic, a model is an interpretation (interpretative mapping) of a formula A or class of formulae A* under which A, or every formula of the class A*, is true. That is, it is a valid interpretative mapping. Because it is valid, it is an actual property of the thing modeled. Just as Mark can construct a verbal model of himself which factually represents his actual properties (“The person named Mark corresponds to the formal entity ‘a software engineer who is also a religious, theistic, Reconstructionist Jew’”), he can start with the model and then apply it to himself as a compound property: “Mark IS a software engineer AND a religious, theistic, Reconstructionist Jew.” The model reflects one or more actual properties displayed by Mark.
Mark: ”It’s part of why you try to talk about “syntax” in your model in a way that doesn’t make any sense to people who know what syntax means in math and logic. Because you muddle important distinctions. Syntax and semantics are very different things in a mathematical model. But if you insist that the mathematical model is indistinguishable from the thing that it models… then the syntax of an object is the object, the semantics of an object are the object, and therefore the syntax and semantics of the object are exactly the same thing – because they both are the object.”
Error: In logic, “syntax” describes the intrinsic structure of formulae and systems thereof, while ”semantics” additionally accounts for the meaning, interpretation, or descriptive content of formulae. Essentially, the syntax-semantics distinction is as simple as the form-content distinction on which it is based. I’ve made it very clear in my writings that by “syntax”, which I naturally define with respect to SCSPL, I mean “the formal (structural and grammatical) invariants of SCSPL”. By using a functional definition of syntax, one can avoid the necessity of enumerating its specific ingredients (functional definition is definition in terms of function; one specifies the definiendum in terms of its functionality in the overall system in which it exists, independently of content, at any desired level of generality).
Not, mind you, that I can’t enumerate the ingredients of SCSPL syntax at least in part, or that I haven’t actually done so. But a full extensional definition is not necessary for the purposes of this essay. Mark clearly has no business taking exception to my usage, as the CTMU is not his theory, but mine. If Mark wants to use his own preferred definition of syntax (and I can only imagine what that might be, if not the typographical structure of a programming language), then Mark needs to write his own theory.
There is one little respect in which Mark is right, however: the CTMU does indeed couple syntax and semantics in a new and profoundly different way, and has done so for the last couple of decades or more. Perhaps someday, Mark will come to understand what this means. But for now, it is 100% certain, by his own admission, that he does not.
Mark: “As I’ve frequently said on this blog: the worst math is no math. And that’s a pretty good description of your writing. There are lots of mathematical words, but they’re used in ways that just make no sense. They look impressive, but when you try to burrow down to get to their meaning, they don’t make sense. They muddle together fundamental concepts in nonsensical ways; they blur the distinctions between things that are necessarily distinct.”
Error 1: When Mark says that the mathematical words I use “do not make sense”, he again oversteps his bounds. The most he is actually entitled to say is that they do not make sense *to him*. We have now ascertained that the reason for this is Mark’s severe incomprehension regarding my usage of certain terms, and in some cases, regarding their conventional meanings as well.
Error 2: Mark should not keep assuming that there is “no math” underlying the CTMU and my various descriptions of it, especially after he has been caught making errors of mathematical comprehension in connection with it. As Mark observes, there is plenty of mathematical terminology in this essay, and it has indeed been correctly and relevantly employed. Like it or not, that’s mathematical content. The most Mark can say is that he disputes this content, dismisses it as irrelevant or inconsequential, or doesn’t understand it (which, in any case, we already know beyond any shadow of doubt).
Error 3: Mark says that my essay blurs the distinction between certain fundamental concepts. In the present context, one may assume that he has two specific distinctions in mind: model | universe and syntax | semantics. But as we have already seen, it is Mark who does not understand these distinctions, at least in the context of the work he is criticizing.
Mark :”Worse, even if you ignore much of the muddled reasoning, you still can’t make this stuff work. If you actually take the word salad and try to render it as math, what you get is something very much like naive set theory. Unfortunately, naive set theory doesn’t work: it’s inconsistent. And your system, which by definition embeds itself, necessarily includes all of the inconsistencies of naive set theory.”
Error 1: Again, Mark is attempting to impute the muddled character of his own mental state to the reasoning in my essay. This is evaluative incompetency plain and simple (see the value and competency criteria enumerated above). In view of his personal befuddlement, it is simply impossible for him to say whether or not the CTMU can “work”.
Error 2: Again, while I am employing the basic “set” concept in my reasoning, I am not employing “naïve set theory”. Nor am I employing any more advanced version of set theory; such versions improve on naïve set theory only by adjoining extra distinctions and restrictions that do nothing to expand the expressive capacity of the “set” concept, or any other concept general enough to suffice as an ultimate reductive entity.
Mark: “Of course, you won’t actually address any of these problems. You’ll just wave your hands around and insult me some more.”
Comment: It is not my responsibility to solve problems which are functions of Mark’s personal incomprehension rather than anything actually relevant to my work. And my goal here has not been to “insult” Mark, but merely to get to the bottom of his incomprehension and establish that he has no business flinging insults like “crank” around when he clearly doesn’t understand who or what he’s attacking.
Mark: “I remain uncertain of just how it is that doing that somehow defends the validity of your theory, but that’s probably just because I’m not as smart as you.”
I have not considered whether I’m “smarter than” Mark or vice versa. That’s because such a judgment would detract from the content of the discussion. Even though I do find him deficient in the kind of knowledge he’d actually need to properly read my work, I actually think he’s probably pretty smart, all considered. I just think that he’s verbally incontinent and incompetent as an evaluator of my work.
Bottom line: Philosophically and mathematically speaking, Mark is what one would call a “hardcore dualist”. This is because he makes a hard and uncompromising distinction between form (e.g., “set”; “model”) and content (e.g., “universe”). As we have seen, Mark cannot possibly justify this form of dualism, as it has the effect of separating the universe from the structural properties in terms of which we scientifically identify it and reason about it at any stage and on any level.
Mark is obviously a decent computer programmer; this is implied by the fact that he’s a senior software engineer for Google. But just as obviously, he is neither a mathematician nor a philosopher. Writing good code is not easy, and Mark deserves respect for his evident ability to do it. But he should either stow the “math” blog, or trim his sails and try to stay closer to home. He is simply not up to going toe-to-toe with all of those on whom he targets his uncontrollable resentment.
Regarding Mark’s commentators, thanks for your participation. Some of you have offered, amidst the noise, what almost seems to be intended as constructive and well-meant advice. To the extent that this is actually the case, your efforts are appreciated. I would merely advise you not to leap so readily to what seem to be your highly standardized conclusions regarding me, my level of knowledge, and the originality and profundity of my writing, lest you end up disappointed and embarrassed as a result.
If I pop in here again, it will be strictly as an undeserved favor. Good day to all of you.
What the hell is ZF?
This is such an unbelievably strange response. What kind of a person:
a) writes an incoherent argument ostensibly directed at the general public;
b) receives said critique from the public; and them
c) repeatedly insinuates that said evaluator is “incompetent” to critique the work?
The answer, it seems to me, is the Bill Dembskis of the world — the people who write not to edify but to confuse; the “if you can’t blind ’em with brilliance, baffle ’em with bullshit” crowd who prefers to use two pages of mathematics to say what you could say in two sentences, and then proclaims it something pompous like “the Law of Conservation of Information.”
Chris: you were advised earlier in this thread to visit Eliezer Yudkowsky’s posts on the English language at Less Wrong. I’d second that advice. Read Yudkowsky; he’s a smart guy who can actually communicate his thoughts to others. You might learn something.
I haven’t read all the comments/diatribes, but given the context, I’m guessing ZF is the Zermelo-Fraenkel axioms of set theory.
You can take your ‘undeserved favor’ and shove it right up your ass. You could be the smartest man on the planet, but if you put your brainpower into being a pretentious, condescending ass, you’ll be putting it to complete waste.
Don’t center your fustration on Mark, please. There are more people here. In fact, there is a lot of people outside this little forum who do not seem to be very interested on your theory, neither.
Ok, so you admit that you are not calling “set” to anything a mathematician would call a “set”. Of course, you are free to define Lagan’s set theory. But it has to be:
a) interesting and justified for people to take the work to learn, use and teach it
b) more strict than naive set theory, because simply calling “a collection of distinct ‘things'” a set does not work very well. The collection of all sets is not a set, and if it is, it would lead to contradictions. So you have to impose some restrictions.
c) informative. What are the elements of the “set” Universe? You evade the question. Calling something a set explaining that you understand by set something vague and without giving any idea what the elements are is not very useful. I would call that a sentence free of meaning.
I can call the Universe “the stuff”, composed of “zitirione”. Yes, I can, for some definition of “the stuff”, but it is not very useful. We understand you can start with a vaguely defined theory, and go refining it, working on it. But you have a very vague idea of what a set is and try to force people to accept real Universe is one.
Yes, our Universe is “the stuff”. And, what is “the stuff”? Something very expressive to be what our Universe is. And if someone say the opposite, the hell with him, he is an ignorant.
That’s a bad actitude. You are probably discovering how little people (that counts) are interested in your theory. Of course, you can think it’s because they are all ignorant. Don’t be fooled.
But please, stop doing that. Stop assuming the Universe is a set to prove it is a set, and writing one million words saying “as we proved”, “we saw that”, and things to sound like a mathematician. You have not proved anything. By maintaining your concept of set open enough you can evade criticism for a while, but by the same measure you maintain your theory content free. Circular logic and vagueness would carry you nowhere.
Remember: it is not a Mark’s mental state. Have you find anyone (seriously) interested in your theory? (Family members doesn’t count).
I still think the real Universe can be unmodelable as a set because you could not differentiate one entity from other. At quantum level, there is no individual particles. You have no locality, you have entanglement, you have wave functions filling all the space that adds together, you have no trajectories, you have a different number of particles each time, you have multiple paths… I would find it difficult to say what a “distinct element” is. You didn’t even have tried.
Wave functions (any function really) can be described using sets. A function f : X -> Y can be seen as a subset of X*Y (its graph.) This can be extended to multiple particles and possibly even the ‘wave function of the universe’ or some such thing. This set is something completely different from the ‘set’ containing all the particles (or whatever) of the universe though.
Wow. That’s creative! But you’re very right, Robert.
In any case, you know, that’s not what I mean. A wave function is a _model_ of the Universe, and not a complete model. Considering a wave function as a set is only “modeling a model” as a set.
One can show all our current models can be expressed as a set and still not be allowed to say that the Universe is a set.
What I say is that we can never know if a model completely reflects reality, which it is a necessary step to make that identification, the model as the reality. There is a lot of things we don’t know. A lot.
That’s why Phycisist still have a job.
But very clever, Robert. Very good observation.
A minor point, but the set of all sets is a set. There’s no contradiction there.
The contradiction comes when someone introduces the set of all sets that are not members of themselves. Then ask whether that set is a member of itself. It is if and only if it isn’t.
Bertrand Russell tried to work around this by redefining terms so that a set cannot be a member of itself, but his approach is not universally accepted. (If I recall correctly, it produces different levels, so a set at level 0 can be a member of a class at level 1, but not of another level-0 set.)
From what I understand the set of all sets is a contradiction since axiomatically if X is any set, then {x in X: “some condition”} is also a set. So if the set of all sets is a set then Russel’s paradox follows.
You’re right. The Universal set is problematic only in some theories, but not in all. And you rightly pointed out an alternative problem.
Thanks.
Yeah, Russell tried to do leveled sets, so that you had first-order sets, whose members were atoms; second-order sets, whose members were first order sets; third order sets whose members were second-order sets, and so on.
Gödel showed that it didn’t work, because you could embedding the first-order sets into representations as atomic values, and then use those to create first order sets whose members could be interpreted as first-order sets, allowing you to formulate purely first-order predicates that weren’t really first-order.
The most common solution these days is the set/class distinction, which is similar to a single-step version of Russell’s hierarchy: there are sets, and there are classes; you can do things with sets that you can’t do with classes. A set can’t contain itself, because of the constraints on what can be in a set; and you can’t express predicates on classes that would allow you to create paradoxical sets.
Why shouldn’t he center “his frustrations on Mark”? Mark is the one with the front page post “Another Crank Comes to Visit”. Right from the start this forum is biased into thinking of Chris as a crank which turns this “discussion” into a many vs one situation.
I don’t agree with you, allOrNothing.
I mean, I hold responsibility for my opinions. If I am biased by Mark’s writing, it is entirely my fault, not his. I find it wrong for Langan to blame Mark for my opinions.
I also believe you misinterpreted the origin of the many versus one situation. Langan has very peculiar ideas. Regardless of the their validity, when someone has non-common ideas it will always be a many vs one situation. They can be true, or they can be false, but initially it will be that many vs one. (That’s the reason why they have to explain them).
@John Fringe
I should explain the “many vs one” in more detail. I’m not just talking about the “crank bias”, I also mean the very mode of discussion. How is Langan supposed to get anything done when new people keep popping up like weeds, each with different objections? It’s like a media blitz. So “centering his frustrations on Mark” is, at it’s simplest, a practical choice.
When Langan showed up here, his primary goal was to talk to Mark, not the unknown number of varied commentators.
@allOrNothing
Well, yes, it is impossible for one person to cope with so much comments in a blog. (I believe this is a common problem). From this point of view, yes, it may be the only sensible thing to do, to talk only to Mark. I didn’t thought of your comment this way.
(Then he may have choosen the wrong media, but I understand he wanted to answer the thread).
One thing on which Mr. Langan and I clearly agree is that there is a distinction to be drawn between “set theory” and “set”.
However, Mr. Langan seems to think that the various formal “set theories” which exist throughout the mathematical community are all formalizations (i.e. formal descriptions of the structural nature) of the same concept of “set”. To be sure, there is an overlap between these theories in which respect they do represent formalizations of the same concept, however each “set theory” gives rise to a subtly different corresponding concept of “set”, likewise each concept of “set” corresponds to a distinct “set theory”.
The basic concept of “set” corresponds precisely to what is referred to as “naive set theory”, which I believe is aptly named since it is the “set theory” developed by simply ignoring formalization entirely in favour of the simplicity of the concept of “set” which is understood by even the most naive.
Mr. Langan is also quite correct that mathematical “set theories” do nothing to enhance the expressive power of the basic concept of “set”. In fact “set theories” restrict that expressive power and this is the very purpose for which they have been developed.
The expressive power of the basic concept of “set” led to contradictions when instantiated into “naive set theory” in a mathematical context, demonstrating its inconsistency as a mathematical structure. (For those who may not be familiar, within classical or intuitionist logic, one can derive any statement from a contradiction making every contradiction equal and maximal in expressive power.) In order to make use of the basic concept of “set” within a mathematical context in a consistent manner therefore, it is necessary to reduce its expressive power by making subtle changes to it, i.e. to use the concept of “set” functionally defined by one of the existing “set theories” (or by some new one, also formally defined, which avoids those contradictions currently known in “naive set theory”).
In short, one cannot use the “basic concept of ‘set'” in a mathematical context while dismissing the quirks introduced by whichever formalization of “set” is in use in the background, and such a formalization must be present in order to be consistent.
This definition is qualified and restricted by various strains of set theory, but it remains essentially intact as theoretical context varies. More advanced versions of set theory improve on naïve set theory only by adding distinctions and restrictions; for example, NBG adds the concept of classes, while ZF proscribes self-inclusion. Such advanced theories do nothing to expand the expressive capacity of the basic “set” concept.
This is wrong. First of all, naive set theory is not logically consistent. That’s a pretty big difference. The claim about “more advanced theories” is also wrong in so far as it is well-defined. Consider for example, ZF with anti-Foundation replacing Foundation. Or ZF with a large cardinal axiom.
There is one little respect in which Mark is right, however: the CTMU does indeed couple syntax and semantics in a new and profoundly different way, and has done so for the last couple of decades or more. Perhaps someday, Mark will come to understand what this means. But for now, it is 100% certain, by his own admission, that he does not.
Well, here’s news for you: no one else understands it at all either. So try explaining in it more simply, or using different language.
It is not my responsibility to solve problems which are functions of Mark’s personal incomprehension rather than anything actually relevant to my work.
If you want anyone to understand your work, then the fact that people with relevant expertise don’t understand what you are saying should be relevant.
: Philosophically and mathematically speaking, Mark is what one would call a “hardcore dualist”. This is because he makes a hard and uncompromising distinction between form (e.g., “set”; “model”) and content (e.g., “universe”).
You are using language in a non-standard fashion again. This isn’t what dualism is generally taken to mean.
Mark is obviously a decent computer programmer; this is implied by the fact that he’s a senior software engineer for Google. But just as obviously, he is neither a mathematician nor a philosopher. Writing good code is not easy, and Mark deserves respect for his evident ability to do it. But he should either stow the “math” blog, or trim his sails and try to stay closer to home. He is simply not up to going toe-to-toe with all of those on whom he targets his uncontrollable resentment.
Wha? I don’t even… are you fucking kidding? Mark has a large amount of math background as should be pretty clear from reading his blog on a regular basis. The fact is that what you’ve done doesn’t include any substantial math and the math you do have is either ill-defined or just wrong. There are multiple professional mathematicians in this thread. They’ve all agreed that Mark is spot on. Maybe, just maybe, you should consider that Mark is correct and that your ideas really don’t make sense. (It seems to me remotely possible that you are just explaining yourself very poorly and using language in non-standard ways, but if so, that’s not our problem. That’s something that can only be remedied by you.)
Chris:
First off, the point of promoting this whole thing to a new post, rather than leaving it hidden in a discussion on a two-year-old post that had been migrated from my old site was, actually, intended as a gesture of respect. I may think you’re a jackass, but I genuinely believe that if an author goes to the trouble of coming to my site and responding, that they deserve to have those responses made visible. It was not intended as a gesture of spite, or a “none dare cross MarkCC”.
And you’ve done a remarkable job of demonstrating exactly why I say that your theory is rubbish, in the following two paragraphs.
Naive set theory is inconsistent. That’s not a trivial matter. That means that using naive set theory, you can “prove” every statement that can be expressed in terms of set theory. Naive set theory is ill-founded and ultimately useless, because no proof, no implication, no inference based on naive set theory is valid – because the fundamental axiomatic basis of naive set theory is invalid.
The only sense in which NBG and ZF don’t “expand the expressive capacity” of naive set theory – that is, of “the basic set concept” – is that naive set theory has no expressive capacity, because it’s inconsistent.
Any argument that you make about set theory, or about anything built on set theory, is only as valid as the underlying theory. There are lots of different axiomatizations of set theory. NBG and ZFC are the most well-known, but they’re far from the only ones. And you’re certainly able to define your own. But you need to have some axiomatization, or you’re not doing math. You don’t have your own axiomatization of sets in your theory, and you don’t appear to be using any valid axiomatization. But you expect people to accept that you’re using a consistent, valid definition.
This circles back to my most fundamental critique of your “theory”. It’s word salad. It doesn’t define its terms in any meaningful way. It pretends to be talking about math – but it doesn’t actually use mathematical reasoning. It pretends to be talking about sets in a mathematical way – but you refuse to specify just what you mean by sets, and you don’t even seem to understand why that’s a problem.
You redefine the words syntax and semantics, but you don’t bother to give your definition of them. In fact, I’m not actually sure that you actually understand the meaning of the distinction between syntax and semantics in logic. There’s no good way for me to be sure, because you never actually demonstrate just what you mean by syntax. You just spew out a bunch of garbled word-salad.
Mark, when I look at your writing, it’s like trying to decode gibberish.
I’m not just saying that; I really mean it. You claim you can’t understand a word I write, but for me it’s the other way around. I’ve already tried repeatedly to tell you, your ditto-heads, and other commentators in plain English that my essay nowhere relies on naïve set theory, and in fact can be construed as a condemnation of naïve set theory for philosophical purposes. Yet here you go again, behaving as though I said the exact opposite. Your only possible justifications are (1) that I’m lying about not using naïve set theory; or (2) that I’m so asleep that I don’t know when I’m relying on naïve set theory and when I’m not. But to my way of looking at it, both of those claims are absurd. I feel like I walked into a seedy diner and ordered the “fresh garden salad” only to have the proprietor hand me a day-old corn dog with a couple of bites missing and a check that reads “1 salad plus tax (no credit).”
In fact, I’m reminded of a sad old joke. Somewhere in the Deep South of yore, a bus containing a Black gospel choir was on its way to a revival. Suddenly, a car stopped on the shoulder of the road pulled out directly in front of the bus. Panicked, the driver cranked the wheel as hard as he could, veering directly into the path of an oncoming semi. Unable to stop, the fast-moving semi ripped open the midsection of the bus, strewing the highway with dead or injured passengers, some moaning in pain. A minute or two later, an archetypal redneck and his woman drove up in a pickup truck. Seeing the carnage, the hillbilly stopped, got out of the truck, and sauntered among the bodies for a minute or two. Then he returned to the pickup, and without saying a word, resumed driving in the same direction as before. “But Billy-Bob,” said his incredulous damsel, “ain’t summa them people still alive?” The redneck snorted contemptuously and used his teeth to pop open a can of beer. “Wayull, Lurleen,” he drawled after a long and satisfying gulp, “some of ‘em *SAYud* they was. But you know how them @#$$%&s lie!” (Ring a bell?)
On a more serious note, I think I know what your problem is. As soon as I mentioned the words “self-including set” in the essay, a little warning buzzer went off in your head. What you should have said to yourself at that point was “He’s right – if the universe is a set, and if the universe actually implements self-inclusion in any way – after all, he has explicitly stated that when it comes to the universe, there’s ultimately nothing external to contain it or serve as a medium or background for it – then really what we’d have is something at least reminiscent of a self-inclusive set. But since that’s a violation of logic associated with naïve set theory, which everyone knows doesn’t work, this guy must be trying to describe, or at least pointing in the general direction of, a new way of eliminating the contradiction. So maybe I’d better try a little harder to get the message. Even if I can’t quite get it right, at least I won’t be guilty of getting it all wrong.”
Instead, what you evidently said to yourself was more like this: “Oh man, this fool is absolutely out to lunch! ‘Self-including set’ indeed – when I get done with him, this crank is going to be sorry he ever dared to open his mouth! No doubt about it – he’ll rue the day he ever heard the glorious name of Mark Chu-Carroll (which probably hasn’t happened yet, but thanks to my thousands of hits and my faithful legion of anti-crank warriors, soon will)! Why, with my superior math skills, this guy and everyone like him is totally at my mercy, cannon fodder for my unbelievably excellent anti-crank blog! Good Math (my opinion) trumps Bad Math (any conflicting opinion) every time, so everybody better hunker down and get ready for some more of that trademark supercilious Chu-Carroll wit! Oh, joy – life is fine when you’re a crank-fighting internet hero like me, myself, and I!!”
While you might see the latter self-dialogue as a bit over the top, your subsequent behavior shows that it accurately reflects your basic attitude. And whether or not you’re capable of recognizing it, this makes you incompetent to evaluate the essay you’ve been trying to evaluate, to the extent that at this point, I no longer think that you (and some of your fans) are capable of understanding anything that I say on the subject, mathematical or otherwise. So why not do yourself a favor, stop giving yourself so much undeserved credit as an all-purpose authority on all things mathematical, and learn to withhold judgment on that which you don’t understand? You’ll probably live a longer and happier life if you do.
Just a piece of friendly advice to someone who seems desperately in need of it.
Chris:
Even if we stipulate that Mark completely misunderstands your theory, that in itself doesn’t make the theory correct.
If you want people to accept your theory, you need to present it in ways that they can understand, and convince them that it is correct. If you are the only person alive who can understand it, and it makes no testable predictions different from current theory, either you’re out of luck, or you need to find ways to explain it to people.
It’s not sufficient to say “study this, this, and this for three years, and then you will see my theory is valid” unless people already have reason to think you are right. Or at least that you’re probably right. Unfortunately, you are hardly the only person who is presenting what he believes to be a revolutionary new theory. Not all of those theories are correct (because they contradict each other). You need something beyond “I am very intelligent” to prove your theory. Even very intelligent people make mistakes.
I’d go so far as to say very intelligent people make the big mistakes more often because they’re so used to being correct, they’re not used to being challenged or needing to question their own workings.
That’s my excuse and I’m sticking to it.
to: Chris Langan
1) How is your theory falsifiable?
2) What use is it? For example, the heliocentric theory of the solar system was useful in that it simplified computations. The fact that is also represented the observable universe was simply a bonus. So, what utility does your theory provide?
How does one measure the utility of being able to condescend to the entire world? If Mr. Langan is a Benthamite, that’s probably a fairly high number on the hedonic calculus….
I can’t speak on behalf of Langan, but…
1) I don’t think the theory is intended to be falsifiable. It’s intended to be the truth, independent of context and beyond falsification. This doesn’t work, and the reason why is explained here.
2) If the theory would work, the concept of telic recursion could be used to construct a satisfactory concept of epistemologic relevance, which in turn could be used to solve the problem of induction.
I have to agree with allOrNothing, and in fact I’d go further: it seems that so far Mr. Langan has had the better of his exchange with Mr. Chu-Carroll, not to mention some of the less knowledgeable commenters. Those chiming to question the reference to ZF (entirely on point and reasonable shorthand in Langan’s remark) or objecting that items in the universe may not count as “distinct” (which seems to me trivial to work around – any two non-distinct objects are one object, no?) or objections that parts of Langan’s remarks are mathematical, and parts are not, but dare to use the term “proof” — they seem to be grasping at straws with which to feebly flail Mr. Langan. Others have pointed accusatory fingers at Mr. Langan, declaring him guilty of ad hominem attacks (mostly falsely, in my opinion) for merely having questioned Mr. Carroll’s competence in this particular subject) in a post that starts out, *in its title*, labelling Mr. Langan a crank! In fact, despite provocation, Mr. Langan has not descended to personal attacks or name calling, and has confined his judgment to Mr. Chu-Carroll’s competence to evaluate the particular essay under consideration. I think the worst insult he issued was to call Mr. Chu-Carroll “verbally incontinent”; this seems to me to be a mild slide from decorum in response to having been called “a crank”. He also made remarks that showed that he respects Mr. Chu-Carroll”s obvious high achievements and learning in those areas where he is really an expert.
I trust that Mr. Chu-Carroll really thought Mr. Langan’s work full of fallacies and deficiencies, and sincerely tried to explain that, though in a harsh and insulting tone. But so far Mr. Langan appears to me to have successfully defended himself against at least his selected set of Mr. Chu-Carroll’s criticisms, and made a plausible case (to the uninformed, such as me) that Mr. Carroll may be the one who misunderstood.
I enjoy Good Math Bad Math frequently. I often learn from it. But these occasional exercises in derision, and subsequent group efforts in condemnation, only detract from that. I know that comments on blogs are notorious for such chauvinism, but perhaps this need not be the case here.
I don’t know if Mr. Langan has any serious contribution to make to humanity’s knowledge, or not. Most people don’t, so it would be no surprise if his ideas fall short. Regardless, I wish these critical discussions of wrong ideas did not take the form of a group effort in condemnation — it does not improve anyone’s understanding of matters, I judge.
> “or objecting that items in the universe may not count as “distinct” (which seems to me trivial to work around – any two non-distinct objects are one object, no?)”
Yes, of course. You can trivially say that any two non-distinct objects are one object. That’s completely right. You can go aggregating entities until you have only one. Strictly right.
Because reality is one, and the division into “objects” is simplification of our models.
So yes, you can say at least you’ve got the set of one element, the real Universe. This is strictly true. But, let me say, it is also completely useless. It’s a completely void idea.
By that treatment, everything is a set. Not a mathematical set, but some kind of aggregation of some stuff. At least one, the thing. And he is fighting for this idea! If everything (everything, think of it) is a set, then that does not carry any information.
That is why I explicitly said (yes, I said it first!) that he always could save face by saying “that the Universe is the set of one element, the Real Universe”.
And something. The universe is also something. You will not find me fighting for the “something” idea.
By the way. Have you read http://megafoundation.org/CTMU/Articles/IntroCTMU.htm ?
I had a look at it, and began reading, more than once, up to the point that I was sure I didn’t know what he was talking about.
Because I think Mr. Chu-Carroll is a good-to-outstanding explicator of things he does understand, and because I know he knows a lot about some relevant topics, I would ordinarily consider him a good guide to this stuff. But when Mr. Langan, apparently correctly, points out errors in Mr. Chu-Carroll’s criticism, and when that criticism obviously strays into speculation and slam, I need to reserve judgement.
Some of Mr. Langan’s claims sound pretty grandiose to me. They may be wrong for any number of reasons, from a few simple errors to large-scale self-delusion. Exercises in condemnation of his ideas do not help me (or, I think, anyone) to understand that. Unfortunately, too much of this post and the ensuing comments takes that tack, rather than careful criticism.
Everything is in the Simpsons:
– Newspaper Tour Guide: And each paper contains a certain percentage of recycled paper.
– Lisa: What percentage is that?
– Newspaper Tour Guide: Zero. Zero is a percent, isn’t it?
First of all, why is not a collection of objects a “mathematical set”?
The last time I encountered any set theory in a formal context, it was over two decades ago, in the course of learning about other topics, so I am sincerely asking here: what distinguishes a “mathematical set” from a correct application of the set concept to non-mathematical objects? From what I can find in quick researches on the web (admittedly, a very poor reference source) a set is an “undefined primitive”, with certain axiomatic properties. As long as the sets Mr. Langan considers fit the basic set concept (regardless of what they contain as elements) and exhibit the properties stipulated by the axioms, they are mathematical sets, right?
Second, it seems to me there is some choice of the level of concern at which we view entities as distinct. Two things may be the same in some respects and different in others. But it would be valid to reason about them either way, as long as we establish the context correctly. In fact, from skimming through Mr. Langan’s writing, it seems this question is a large part of what he discusses.
I cannot judge if he has done this well or poorly, coherently or incoherently, in part because I lack the background, in part because I have been stymied by some of his new nomenclature, and in part because some of his reasoning is unclear to me. But I think he has grappled with this question.
> “Two things may be the same in some respects and different in others. But it would be valid to reason about them either way, as long as we establish the context correctly.”
That’s is exactly the point. That is exactly what we are talking about.
The “establishing the context correctly” is what we call “defining a model”.
You have a reality. As it is impossible to comprehend, one “models” it, one builds a model of it, selecting the interesting features (for oneself) and ignoring the rest.
Of course, one can build different models of reality, depending on what is of interest in every moment.
Then you have mathematics, which are a good language to build models of reality. One of their tools is the concept of set. You can MODEL reality as a set.
When you are building your model, you can decide if some perception is modeled as an object, as two objects, or as many as you want.
But what you are not able do is to mistake the model for reality. It is your model that is a set, not reality.
You’ve got the perception of two things. From some perspectives they look the same, from others they do not. And you can assume there are unknown perspectives to you. So you evaluate and you decide if you model them by one entity or two. That’s up to you.
If you read Langan comments you’ll see he is defending the Universe is a set, not his model of it. He is doing this because he pretends not to be discussing a model for the Universe, which could be more or less appropiate and would be refutable, but the Universe itself. This is what is profoundly wrong and is highly antiscientific.
Of course we understand you can model the Universe as a set. But that is not what Langan is saying.
I can see two possible ways that you mabe wrong here:
1. First of all, let us suppose that there could be a completely correct, exhaustive “model” of the universe. Such a model would have to account for *all* valid contexts and possible perceptions, because the people having the perceptions — you, me, everyone — are themselves part of that universe. Earlier you suggested that the model might amount to a one-element set, because none of the things in it might be truly distinct. And this, then, has no explanatory power: we’re left with a set of the universe. All we have, essentially, is something pointing at the universe and saying “there it is”.
But if this is so, in what way can it be a complete, successful model of the universe? The universe actually exhibits manifold aspects, which may be observed as its distinct features or parts, or objects contained in it. If the model can only model it as a singular entity, then it is not an exhaustive model.
So any successful, complete model actually would not be such a singleton set, and would instead have to have many elements.
2. I may be wrong here, but it seems to me you are restating Mr. Chu-Carroll’s claim, which Mr. Langan attributed to “hard-core dualism”, that a set is always a model which is distinct from the thing modelled. I found Mr. Langan’s reply thought-provoking and plausible — that an isomorphic model may actually define the properties of attributes of the real entity under consideration, and in that sense “being a set” is one such property.
I have searched, in vain, for some guidance on the web as to whether it is valid to think, from a mathematical perspective, of real objects as being contained in a set. If I define the set of my steak knives — which I’m looking at across my kitchen right now — does mathematics have anything to say about whether the real, six physical Henckel knives are actually “a set”, or whether the set is a “model” for them that exists only in my (and now others’) minds? If so, I’d sincerely like to see a reference to such a discussion.
@James Wetterau
I don’t see why point 1 will make me wrong.
I don’t agree with your proof, believing it is wrong. But anyway, let suppose it is right: you would have proved that if a completely correct model exists then it would be a set. You would still have to prove that this model exists. That’s very metaphysical! And not obvious at all.
I mean: (A implies B) does not prove B. We need to know if A is true.
(I don’t believe the proof is right for several reasons: for example, the Universe can exhibit deterministic behaviour without being deterministic. The fact that you perceive some aspects does not mean they are real).
With respect to 2, “a set is always a model which is distinct from the thing modelled”, while I agree with that, I don’t need that.
I agree because, well, yes, you see your knives, and you think they are a set. But at certain level the model falls down: the knives are made of atoms. Some atoms are separated from the blade, and mix with air. Some atoms go, some arrive. Some are interchanged between the blades. Do reality equal your mental set of six knives? I don’t think so. Yes, you can go for another model, an atomic one. But that’s another model, which is too of limited application. Not to mention that a mathematical set is a “static” entity, and the knives will not exists forever. The model is not the thing. Again, you could consider a temporal model. Got it?
But that is irrelevant, so I will not go into any deep. The key is this: a model can not be identified with the modeled reality because we can never know if the modeled reality will always behave as our model.
That’s a deep idea, but a simple one.
You can not identify a model of the Universe with the Universe because you certainly don’t completely know the Universe, and you should not be surprised if tomorrow you see something unexpected in its behavior.
How can you be sure your model completely fit the reality? You can not, and so you can not mistake one thing for the other.
@John Fringe, For some reason the website is not allowing me to reply to your reply to my reply, so I’m replying to your comment to which I earlier replied, to which you replied on February 19, 2011 1:14pm.
I am not claiming to have proven anything — I’m just trying to show that your earlier rejection of the idea that the universe could be a set on a priori grounds was mistaken. I think that was accomplished, at least according to your reply.
As to the fact that we may perceive things that are not real — yes, of course. But the *perceptions* are real, and need to be in the model.
I think your take on the steak knives question is a non-starter. It is not the case that the definition of the knives is identical to a particular collection of atoms. The definition of the knives is what an intelligence can recognize as the knives.
> “I’m just trying to show that your earlier rejection of the idea that the universe could be a set on a priori grounds was mistaken”
The only problem with that is I never said that. That “earlier rejection” is a supposition of yours. You are assuming I said things I didn’t said. I said Langan can not say the Universe is a set because he don’t know, and he was assuming it was a set to show it was a set. Reread my comments, please.
> “But the *perceptions* are real, and need to be in the model.”
Perceptions are real, yet I don’t see why that makes the Universe a set. If you want to model perceptions, feel free to use a set.
> “The definition of the knives is what an intelligence can recognize as the knives.”
Yes, and the definition is not the Universe, but a model for your perception of a real knife.
You have the universe (a real knife), you model your perception of it, and as you can model it by a set, you say I was mistaken telling maybe the Universe is not a set. I’m really not able to follow you on this. I don’t see the connection. You are not arguing with me, but you believe you are.I was talking about Langan views and you are arguing about models of our perception.
@John Fringe —
Again, I can only reply to your earlier comment.
Sets are, by definition, collections of objects. Sets are not “models” for those objects — they are groups of objects. In our universe, perceptions are, by observation, among the objects that we find. They are not unreal — they are real perceptions. That means they are among the distinct things in the universe. If all perceptions, thoughts, etc. of any entity at any time are among the things in the universe, there is no contradiction between one persepective or another being in the set — they *all* belong in the set. This is not a model — it’s more like a list.
You are correct and I was wrong about your point to Mr. Langan; I misremembered your earlier remark and did not go back and re-read the entire thread. However, it still seems to me that your attempted refutation that the universe is set — because it may not be made up of distinct objects — is invalid. There are clearly many distinctions between objects, e.g. the perceptions we were just talking about. If you want to argue that none of those distinctions are “real”, or real enough to warrant creating a set, then it seems to me that you believe the set concept cannot apply in any way to reality, because there would always be this doubt, which makes it useless.
I’m specially in disagreement with this sentence of yours: “it seems to me that you believe the set concept cannot apply in any way to reality, because there would always be this doubt, which makes it useless.”
I think a model (and therefore a set) can be useful despite that “doubt”, and that the concept of set can be applied in a very specific (but indirect) way to reality.
You build a model for the Universe, and you use concepts such as sets. The set is useful in the building of the model. Then you use the model to explain your perceptions and to make predictions. If the predictions are in agreement with the observations you conclude the model is a good model for the Universe, under the limitations of the observations. Then you can make predictions with your model and be confident in the results. This way, the model is useful for you, and, transitively, the concept of set is useful. But you can never know if the model if completely correct. There is the “doubt”.
How can you ever tell if a model is completely valid? I believe you’ll agree with me: you can’t. The doubt is always there, you can not evade it. But even in this way a model can be useful to make predictions, and so the concept of set.
Yes, set are, by definition, collections of objects. Sets are not “models” for those objects. I agree with this. But, what is an object? I believe any definition of an object is in the realm of a model. So yes, a set is a collection of objects, but an object is an abstraction.
I believe you will not agree with me on this. I’ll ask: what is, for example, a knife? For me, a knife is an abstraction, a classification. You’ll take a “real knife” and will tell me: no, a knife is this. Would you be able to say if something is a small sword or a big knife? You’ll probably say the intention of the manifacturer makes the difference. Is a knife too rusty to work still a knife? For me, “a knife” is an abstraction.
You’ll say (I’m making up your dialogue, you’ll probably say more intelligent comments; sorry for that) you can call it a knife or a sword, a rusty knife or a rusty piece of metal, but it is definitely an object. I’ll respond: well, no, it’s a lot of objects, a lot of atoms. Or maybe not. Because the atoms are changing. Is it an objects or a lot of them? Is a collection of atoms? In what instant? For me, an object is an abstraction, not a real thing.
In fact any though you can have is about models in your head. A lot of times I can not say where a perception ends and where the next starts; nor I can say if two perceptions (thunder and lighting) are one objects or two. A lot of time a can not say if I’m having one perception or two (smell and taste). Language is about abstractions, not reality (directly).
So, in my mental models of reality, I’m not sure of anything. I’m always testing (and of course in science) my models agains my perceptions. But I still find the concept of set very useful. I can make predictions with them.
Anyway, all these are my opinions, which seem very natural to me. You have your own, which I respect and find interesting. I think they pose some problems, but neither of them have been refuted (I don’t think they can) so I accept the two can coexists.
But precisely as we both have different perspectives Langan can not say the Universe is a set. At least without explaining why my perspective (that which I find so natural) is wrong. He could always assume it is a set and create a theory from that assumption. No problem, all theories make assumptions. But he was taking the fact as a truth, and when asked for clariffication he answer what a somewhat flawed logic: the Universe is a set because it is a set, and if you don’t see this you’re wrong.
@John Fringe:
I don’t want to go into all the philosophical questions you have raised here, but I do think we have some that are matters of difference of opinion. To take just one example, for me the important thing is not to recognize all knives (vs. swords, etc.), but to be able to recognize particular knives for a particular duration of time. Do philosophical questions remain about being able to do so? I suppose they probably do (e.g. what if a knife falls and breaks into two parts — what is “the knife” now?), but I do think one could build a coherent idea of a set of real objects regardless. I admit this is just my strong intuition; not something I can prove.
You have made me question (a little bit) what seemed transparently obvious to me at the outset: that the universe is, in a real sense, composed of many different objects, and it is legitimate, therefore, to call it a set, but not only a set. Perhaps I should have confined myself to that point, and not got onto the side issues. I do respect your different perspective, but I must admit it’s hard for me to imagine holding that point of view.
It seems to me that the difference in our point of view comes down to your saying that even in assigning identity to things there is an act of modelling which may be wrong. My point of view is that as long as the assignments are done according to some repeatable algorithm based on real perceptions, then there is no real doubt that the assignment is capturing something real about the universe. My argument would be pretty close to Langan’s remarks about greenness being a real property of the thing that reflects green light. Perhaps that is a philosophical point of view, after all.
I want to correct my remark: re-reading, I see that Mr. Langan did use some harsher language in his first reply than he used in his later replies. He did throw around some ad hominem stuff, mixed in with valid atttemps at rebuttal. All in all, no one in this exchange fought entirely on the level of ideas; there was some invective on both sides.
That said, I still think that the condemnation pile-on amounts to an outpouring of bias.
I’m actually too busy for this right now, but I see that given the apparent harshness of my first response in this thread – the primary purpose of which was to provide simple criteria by which conceptual value and evaluative competence can be objectively rated – a little background might be in order.
1. Mark originally critiqued my essay in February, 2008 at ScienceBlogs.
2. Just a week or two ago, somebody brought Mark’s critique to my attention. Here’s the link provided in that email:
http://scienceblogs.com/goodmath/2008/02/two_for_one_crackpot_physics_a.php
3. Noting that Mark had titled his critique in an extremely deprecating manner, I thought it advisable to respond. However, I found that because Mark had moved his blog to Scientopia, it would be impossible to enter a response at ScienceBlogs. Therefore, I proceeded to the analogous entry at Mark’s new blog site. Here’s that link:
http://scientopia.org/blogs/goodmath/2008/02/21/two-for-one-crackpot-physics-and-crackpot-set-theory/
4. I entered what I thought, under the circumstances, was a friendly and moderately informative response. I’m sure that my impatience was evident, but bear in mind that I had just discovered that Mark had been insulting me and my work with impunity for the last several years.
5. Mark responded in a highly aggressive and insulting way. So I entered another comment to make sure that everyone understood the problem. I hoped that this would be the end of the matter.
6. Unfortunately, it was not the end of the matter. Mark moved a slightly updated version of his critique to the current front page of his blog, under an arguably even more insulting heading, in an apparent effort to teach me the following lesson:
“Hey @#$%&, you don’t mess with Mark Chu-Carroll, except at your peril!”
(The wording is my own; I’m merely trying to approximate what seemed to be the message that Mark was sending by renewing his critique under the heading he chose.)
If one thinks about it a little, this may at least begin to explain the harshness of my tone. While I understand that some people might find my language excessive, I’m afraid I can’t agree. In fact, I think that my language has been quite controlled under the circumstances.
Thanks for your attention.
I like how you are utterly unable to talk about math instead of your rather large ego and insults to it. It would have been much more effective had you simply addressed the criticism against you rather than ignored it (and raised several points that had already been dealt with) and talked about MarkCC instead.
Consider that even if Mark was a complete idiot, it would still be possible for him to point out a flaw in what you are saying. Defending yourself by saying that he isn’t qualified is therefore your own logical mistake, and not a very hard one to see either.
Lily, I can’t help but feel you are missing the point. It’s not that Chris was calling Mark an idiot, but merely pointing out that Mark is devoid of certain knowledge about the claims his theory makes about particular mathematical structures. For example, let us say that everyone’s understanding of physics largely rests on key assumptions of classical physics – namely, absolute space. If these people wanted to explain why the surface of the water in a bucket curves when the water rotates, they will explain this phenomenon as the effect of the motion of the water with respect to absolute space.
Now let us say someone comes along and says that this phenomenon is not due to the absolute circular motion of the water, but is actually due to the relative motion of the water with respect to the local gravitational field. Getting the point: are 100 “hardcore Newtonians” whose assumptions about motion resting on absolute space “qualified” to critique the assumptions of 1 relativist? No, because they’re judgments will always be based on certain assumptions that simply don’t apply in the relativistic domain.
Am I trying to compare relativity to Chris’s theory? Certainly not. The point is: there are certain assumptions about the nature of mathematics that people around here carry that may not apply to Chris’s theory. How merely pointing this out renders him the biggest jerk on the planet is beyond me. This is not my concern however: my concern is that the people on here simply do not know how to be civil in a debate. People complain about Chris’s “ad hominem BS”, but then people mindlessly attack him by throwing every name in the book. People try to critique his theory, but they haven’t bothered to read his paper, and don’t even ask him questions to clarify.
As I said, the content of the theory is important, but you can’t discuss the content in any manner conducive to productive discussion if this is the way you go about it. If you think there is an aspect of the theory that is objectionable, ask questions to clarify. If you think something he said was unfair, explicate why you feel that way in a polite manner. Overall, actually have a discussion rather than just making these increasingly incoherent statements along with the name calling.
– John
It’s not like Chris’s ideas are well known to the point that someone being unaware of the specific assumptions he is using is somehow a point against him.
If Chris had pointed out that he was using different assumptions and then proceeded to explain the differences that would have been perfectly reasonable. But he didn’t.
I’m not trying to be contrived but it seems to me that we agree that information about the author of a theory should play no part in the discussion of that theory. That was the goal of pointing out that Chris was bringing Mark the person into it rather than defending his ideas.
I’m probably taking a few steps back from the current discussion here in saying this, but I think that Chris’ requirement that Mark “comprehend” the object of his intended critique prior to embarking on such a critique is inappropriate given the nature of some of Mark’s arguments against CTMU. Specifically, Mark’s charge that certain assertions made by Chris are nonsensical cannot be properly evaluated with reference to a criterion of comprehension because any meaningless statement necessarily defies comprehension. Using Mark’s example of someone saying “I’m going to fly to the moon by correctly spelling my left leg,” it becomes evident that requiring someone to comprehend such an assertion before they can legitimately criticize it is unreasonable. The very fact that such a statement is incomprehensible counts against its coherency.
I know Chris separately addressed a supposed disconnect between Mark’s failing to comprehend something and that thing’s being incomprehensible. However, this seems to fail to counter my above point, tangential to the overall discussion as it may be.
But if people really believe the theory is meaningless then why are they even bothering to raise objections? Why would you object to something that says precisely nothing? If you are raising objections, you have to assume he is trying to convey something, don’t you?
He is most certainly trying to convey something. I didn’t intend to imply anything to the contrary. Rather what I meant is that Mark’s charge is that Chris, while trying to convey something, is failing to do so precisely because his assertions, as formulated in his essay, are nonsensical. This is not an uncommon (or pointless) charge especially when it comes to evaluating metaphysical theories. For example, logical positivists claim that metaphysical claims are meaningless by virtue of their being unverifiable, and various theorists of meaning have thought that sentences whose subject lacks a referent are meaningless (e.g. ‘Sherlock Holmes is a detective’). I don’t necessarily endorse these particular claims but I certainly think it is a legitimate move to criticize a theory/assertion on the grounds that it is in whole or in part, nonsensical.
Since no one has pointed it out, I may as well. Langan’s 17. February post at least makes one of his fundamental problems very clear.
Langan says “A set is not a “mathematical construct defined axiomatically”. That would be set *theory*. While set *theories* are indeed defined axiomatically, the set concept itself is defined in a very basic and general way, which is precisely why it supports multiple versions of set theory incorporating different axioms.”
Yes, the intuitive concept of a set (or at least “collection of elements”) can be incorporated into many frameworks, from extensional mereology to ZF and beyond. In mereology, one can talk about the universe itself as a collection of objects (or mereological sums). In naive set theory or ZFC, the universe cannot be a set since the set of the entities comprising the universe and the universe itself are different things (by definition). In order to derive any problems for set theory or our conception of the universe, Langan has to decide which framework he is using. He never explicitly does that, but jumps back and forth between mereology and naive set theory. But he hasn’t given us any problems for the mereological conception of collections/sums (he doesn’t even display any hint that he is aware of this branch of philosophy (not mathematics)). In naive set theory (which is inconsistent anyway) or ZFC none of his purported problems even arise, since in these systems the universe cannot be viewed as a set – rather, the structured set consisting of all the elements in the universe is itself an abstract, mathematical object (as is the singleton with the universe as a member) with physical entities as members – and the only thing he provides is some feeble nonsense about how, if we distinguish our mathematical models of reality from the physical phenomena they model, science becomes impossible and we are saddled with ontological dualism.
Well, there are indeed philosophical questions that arise from accepting abstract objects, but they have nothing to do with what Langan discusses. If you do think that accepting abstract objects entails an untenable form of dualism (but it is a problem for nominalism rather than materialism, and those are not the same positions), I suggest adopting some kind of constructivist or even formalist view of mathematics. A lot of work, to put it mildly, has gone into developing such approaches, none of which Langan even mentions (removing the sharp distinction between syntax and semantics and the need for model theory has been a defining characteristic for many logicist approaches, for instance, although they do retain the difference between mathematical language and the reality the language is about, of course; it is not so obvious that Langan does).
I’m still befuddled by anyone — even if they are the self-proclaimed next Marilyn vos Savant — who offers up a theory for public consumption and then, rather than defend his own theory, spends his time attacking the critic for ostensibly being “unqualified.”
I’ll say it again: Chris, when you’re trying to communicate with the public, it’s YOUR obligation to make your points clear. Attacking Mark isn’t an ad hominem (I’m sort of surprised you’re not aware of that); but it *is* a non sequitur.
It seems to me that the problem is very clear when Chris says “A set is not a ‘mathematical construct defined axiomatically’.” Sure, the word ‘set’ has a basic meaning that is probably understood by many, without reference to axioms, and there are several set theory axiomatising that concept. But as long as we’re not dealing with axiomatic definitions, we’re not doing mathematics, just playing with words.
On one level, it doesn’t really matter whether you say a set is a model or being a set is a possible property of the universe – you still need to work with some sort of definition, and if we’re doing mathematics, axioms get involved.
Obviously, if we’re determined to hold on to our assumptions this might eventually create some problems one way or another, but without axioms we are just playing word-games. Using mathematical words doesn’t create mathematical content. This is the biggest issue with Chris’s essay – even the parts that seem most plausibly open to mathematical resolution don’t actually contain any mathematics.
On a related note, it is claimed that things like syntax and semantics are coupled in a new and profoundly different way. Since this is not actually described, why wouldn’t a reader conclude that there is simply confusion, rather than profound absent content? The same goes for the “extension” of set theory, which must involve a restriction of the naive set theory that the definitions appear to invoke, even if there is also additional structure involved.
Finally, I don’t think anyone has been bothered by Chris’s tone – the problem is that his responses, particularly the first, did not at all address the issue of his essay. This is what everyone else is talking about, qualified or otherwise. Focussing on what you are actually saying, rather than finding a reason to simply dismiss a criticism, also (although not always) tends to make it easier to deal with a “many-to-one” converstion.
@Jonathan D — “But as long as we’re not dealing with axiomatic definitions, we’re not doing mathematics, just playing with words.”
That is not the case — there are primitive notions in mathematics that are not derived from any axiom. They, themselves, have a status like axioms.
http://en.wikipedia.org/wiki/Primitive_notion
The thing about primitive notions is that you can’t reason with them mathematically — the role of axioms is to permit such reasoning. If you’re saying that Langan is working with the primitive notion directly, well, then it’s no wonder that he’s not making himself understood.
@Cyan, can you support that with a reference?
The wikipedia link (admittedly a poor reference, which I would be happy to learn better about) describes primitive notions as “undefined” terms that are expected to be immediately understandable, and that are “analagous” to axioms. It further quotes Tarski saying that:
“the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expression of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION,…”
This seems to me to be saying that we do indeed use (“employ”) them in mathematical reasoning, though in _conjunction_ with other axioms. This does not make them invalid for use in axiomatic theories.
Have I misunderstood? Can you cite another authority to explain where I go wrong in this?
I have no reference beyond your own pointer to the Wikipedia article. My understanding of formal systems comes from Godel, Escher, Bach; when I put that together with “In mathematics, logic, and formal systems, a primitive notion is an undefined concept,” and “When an axiomatic system begins with its axioms, the primitive notions may be forgotten,” I come to the conclusion I stated in my previous comment.
I would say that one constructs axioms to try to capture the primitive notion, but once the axioms and rules of inference are chosen, the primitive notion has no more role to play. The essence of mathematical proof is the application of the rules of inference to the axioms; nowhere does the primitive notion that the mathematician was trying to capture play a role.
Maybe it is Wittengenstein’s Tractatus Ladder. You know, you understand Chris and in so doing you recognize him as senseless and hence, throw out the CAT.
In any case, a useful theory ultimately has to connect the ‘rubber to the road’ with regard to describing a range of expected observations or relationships. And hopefully, the logical chain behind a theory should be validated by more than one person.
Precisely! And maybe this is the antithesis and anathema to the postmodernist and why you get nothing but obfuscation and rhetoric from that camp.
“The real universe has always been theoretically treated as an object, and specifically as the composite type of object known as a set.”
P.S.
One needs to realize that the Universe has never been treated as a set but more as a complex. After all, do we treat a library as a set? No, we treat it as a complex, i.e. a whole that comprehends a number of intricate parts, especially one with interconnected or mutually related parts and a set is nothing more than a collection of distinct objects, considered as an object in its own right.
So, in the end it appears the basic premise is flawed outside of any “attempt” to add rhetorical scaffolding.
I’d like to make an observation and raise a question. My observation has to do with the quality of the article and posts on this blog. My question is motivated by the desire to see whether any of you can clarify my thoughts on a philosophical question I’ve been pondering.
The writing on this blog, it seems to me, suffers from a lack of self-editing. Most of the writing displays deep and thoughtful consideration of interesting issues. However, the ideas are often not well expressed, leading to misunderstanding and personal attacks. “What we have here . . . is failure to communicate.” (Cool Hand Luke)
One fundamental way to improve written communication is to self-edit. In particular, I would recommend that, after writing a first draft of a post, take a coffee break, come back, and reread your post, asking yourself, “What am I really trying to say here?” Then edit and reorganize your writing in something like the following template:
Introduction
1) Explain in a sentence why we should care about what you are about to say.
2) Enumerate briefly your main points.
Body
Go through each point in order and methodically. When transitioning from one point to the next, explicitly state any temporal, logical, or other connection between the point you just finished and the next point.
Conclusion
Summarize what you think you just said. Call for whatever action you want from the readers.
I’ll finish this topic with a quote from Ann Lamotte: “I know some very great writers, writers you love who write beautifully and have made a great deal of money, and not one of them . . . writes elegant first drafts. All right, one of them does, but we do not like her very much.”
OK. Now for the question. In the evolution of my world-view, I have decided that I believe that everything in the world exists and is material. In particular, given what I have read about modern neuroscience, I have come to the view that ideas, thoughts, and emotions exist in a material form, in particular, as electrical signals and chemical combinations in the brain.
I would be interested in your thoughts on this matter. With regard to the original issues raised by this post, in my formulation, the concept of a set, whether naive or not, has an existence in this universe as a pattern of physical events occurring in each of our brains when we consider the concept. Of course, it is probably the case that patterns are slightly different for each individual. Nonetheless, perhaps when we are communicating effectively, our use of the term and concept is recognized by the reader as sufficiently close to his or her concept that the communication can be understood.
To conclude, and to follow my own template, I think I have said that self-editing, and in particular, reorganization would improve the quality of communication on this blog and I encourage you all to try it. I have also asked for your opinion on my philosophical ruminations. I would enjoy reading your response, whether it takes the form of references to materials I might be interested in, general thoughts on my concept of materialism, or your answer to the question, How does the idea that all concepts, including the concept of a set, have a physical presence affect the idea of the universe as a set?
I realize I’m coming into this late, but maybe there’ll be a response or two anyway.
I started reading Chris Langan’s CTMU intro and understood a lot of it; then I reached a point where I couldn’t understand anymore. I assumed that there were some concepts that he was making reference to that I just hadn’t yet learned. I feel a little bit better now that I realize that he’s just using terminology in a non-standard way, and that I’m not the only one confused.
There were a few things that I got from it that, somewhere between Chris’s angry responses and Mark’s initial criticisms about terminology, got completely lost. So I thought I’d take my interpretation of what I think Chris is saying and put it out there in plain English, and if Chris is still reading maybe he can confirm whether or not I got the point. Or if any of you folks are still reading you can feel free to criticize my interpretation as well. I viewed it as more of a philosophical treatise, something more in line with A Critique of Pure Reason, and less of a model for physics as I keep seeing it described in the media.
What I took from his CTMU stuff is –
Basic thesis – There are logical inconsistencies in the way that most people think about “the Universe,” because the way that most people think about “the Universe” is isomorphic to the view of it as a “set of all sets” as defined by naive set theory. The inconsistencies of naive set theory manifest via this isomorphism as the challenges and dilemmas faced by modern metaphysics.
1) Many people, without realizing it, have a cognitive model for the Universe that is somewhat similar to the naive set theory “set.” The subtle inconsistencies of this cognitive structure parallel the inconsistencies of naive set theory itself.
For example, at one point Mark said “some things in the Universe can be modeled by sets, and some things can’t.” This was a good point, but I think that what Chris was getting at is – if you’re saying that the Universe has “things” at all, then you are modeling it, mentally, as a set. Specifically you’re modeling it as set of all the things there are.
So Langan claims that this paradigm is equivalent to trying to create a set of all sets in naive set theory, which leads to problems down the road. The rest of his paper shows why this simple view of the Universe causes most of the problems.
The thing about whether the Universe “is a set” or not is a red herring, because when he claims that the “Universe” is a set he’s saying, as per Kant, that we can’t separate the actual Universe from the model that we make for it. So he’s saying that the viewpoint of the Universe as a collection of objects is wrong. At least that’s what I think he’s saying.
2) This way of thinking about the Universe is fundamentally flawed, and furthermore it leads to a number of false dilemmas that underpin modern philosophical thought. In this case he claims that the mind-body problem is one of these false dilemmas, and that dualism is the incorrect resolution of it.
Langan claims that many of these dilemmas can be addressed by realizing that they stem from this invalid schema for the universe, which most people have without realizing it. I’m not yet convinced, but I found the claim intriguing, as it’s a similar claim as that made by Kant.
It is also notable that things like the mind-body problem are actually problems with our model of the Universe, not a problem with the Universe itself – in the Universe, everything fits together nicely with no paradoxes.
3) The CTMU and his “SCSPL” claim to resolve these problems by defining a better structure with which to model the universe. By coming up with such a model for the Universe, one can become instantly enlightened and realize that monism is the way to go.
He claims to resolve the paradox by defining exactly in what sense the Universe contains itself while also being contained by a larger set, and in so doing defines a meta-language outside of the original one. This is where I stopped reading, so maybe it’s bunk, maybe it’s not.
He also claims that one can also realize that thermodynamic entropy is the process of the Universe cognizing itself, which represents reality being self-aware, and so we’re all just little bits of an ultimately self-aware reality. And he also claims that one bit of the Universe is holographically reflective of every other bit of it, and since one of those bits is our brains, which are constantly perceiving order and cognizing things, that order and cognition are everywhere. Or something like that.
____
He seems to be not too adept at expressing himself, and the choice of word “God” for what he’s describing will no doubt put off scientists and Christians alike, but this is what I got from it – and for what it’s worth, I think it’s a fascinating idea, whether you have to decipher his word salad in places or not.
Any thoughts on my interpretation as written above?
I’m hoping you reply to this. From what I’ve read, this seems to be exactly what he’s getting at. I think I may pick up where you leave off. It seems that his new method of defining the Universe is analogous to a continuously resolving set that expands in both “directions” (with directions being the “levels” of the set) i.e. it is dynamic and resolves in the same way, forever. The easiest way to think about this is to make a set of some arbitrary elements, lets call it M. We can then define a power set of M that includes the power set of M. The process of writing the set in the long form is exactly the process that the universe takes in “realizing” itself. Even more interesting is that according to Langan, it “writes” itself at the speed of light. At least this is my interpretation of it. What do you think? Also, Mr. Langan if you’re still around, I’d definitely like to hear your assessment of my interpretation.
I’ve read through every response, God that was long, and it’s obvious no one here is stupid. Don’t know if people are still reading this, but I’d like to give a few thoughts.
1.First and foremost all this hostility and blame of its initiation needs (especially Mark and Chris) to stop. It’s counterproductive.
2.Chris I have to admit I’ve read your paper and have very little idea what you are talking about. Let me tell you my story, that might be relevant to you. When I was a lowly PHD student my first couple journal articles I sent in kept getting R and R (Revise and Resubmit). I couldn’t figure out why. Finally my adviser sat down with me one day (he was kind of a ghost) read through my shit and told me it was incomprehensible. I was pissed. But he gave me little examples, little jumps in logic that I thought were intuitive or obvious to everyone, they weren’t. The accumulation of all these little jumps led to an incomprehensible paper. (Now looking back I think this is why I was so poor at writing essays for history etc. during undergrad). So I sat back down went through both the papers and in painful and what I thought redundant detail went through every little step. After I did that both got published in tier one journals.
So yeah I think there might be an element of this with you. People aren’t as smart as you, you have to spell out every single little transition, often during your paper I would find myself thinking “What does this have to do with the last statement, or how am i here?”
3. Thirdly I think of lot of this is miscommunication. I’ve some of your interviews and I pretty much agree with you about academia. One positive thing about academia though, is that it acts as a coordination mechanism in terms of jargon. Everyone uses the same language and there aren’t 50 different names for a set floating around. When you get that kind of divergence in terms, translation honestly becomes an issue. I mean shit, it’s still an issue in academia, let alone between academia and the “outside.” I believe miscommunication and translation are issues here.
TLDR
Problems
1.Needless hostility
2.Missing logic
3.Lost in translation
Also Chris try to be a little more………diplomatic. It’s a stupid social norm I know, but it goes a long way.
Sorry to double post I do have a question to ask though. I am going to break away from the all the abstract stuff and go to something a little more concrete.
You talk about morality being akin to maximizing “global utility.”
Everyone has different preferences and hence different utility functions.
How do we max global utility when we only know our own utility function and not others? Are laws and religion attempts? Are we just supposed to use our best guess? What if someone really loves raping and he rapes a retarded girl that is too disabled to feel pain etc., and his utility far exceeds her loss of utility. Wouldn’t I be maxing global utility by raping in the choice of (rape vs not rape)?
@Steve C
First, sorry for the bad writing. It’s true we don’t write very carefully. You’re absolutely right. But most of us don’t have much free time. We write fast, or we don’t write. Bad writing may be worse for communication that no writing!
I don’t think your idea of a materialistic World brings anything useful to the question of the Universe as a set.
“In my formulation, the concept of set has an existence in this universe as a pattern of physical events ocurring in each of our brains”.
Sorry about it, but you can not use physics to prove the universe is a set. Not if you apply it to the Universe, and I don’t see you solve any problem if you apply it to the brain only. Physics defines models. Physics is an experimental science. You can find sets and elements in your model, but they are not objetive elements in reality.
Other than that, it would be very difficult to say what an element is in modern physics.
You say the Universe can be seen as the set of particular events in your brain. What is an event in your brain? What is a signal in your brain? Remember, don’t rely on time in your reply: we don’t have a good model for time in quantum physics. Don’t rely on individual particles. Don’t rely on interactions, if you don’t have a good model for renormalization (which you don’t). I believe your are thinking in a very simple way about “signals in the brain”.
As I previously said, you have a model (in your case, independent signals on your brain), and you can identify elements and sets in your model. And that’s OK. But thats not the Universe, even in an objetive, absolute, material Universe.
@Mike B
Wow, you made an impressive work of translation! Good job!
Unfortunately, I don’t believe it changes anything. I still see pseudoscience in your interpretation.
I don’t really believe anybody thinks the Universe is the mathematical set of all sets. So the premise is misguided.
I believe almost everyone agrees “the mind-body problem” is a false dilemma. I mean, I don’t expect anybody to believe the World has a problem with that. The problem is in our interpretation, if there is any problem at all. So the conclusion is trivial.
The rest is empty words glued together without meaning. What the hell does he mean by “thermodynamic entropy is the process of the Universe cognizing itself”? No, seriously. What semantics does he associate with this sentence? What is he trying to say? Where does he get that conclusion? Does he even know what thermodynamic entropy is?
I’m certainly not fascinated by any of these.
A theory that doesn’t theorize ANYTHING AT ALL is no theory and has all the use of the tits on a bull.
Mr “The Smartest Man in the Room” with an ego to make up for the lack of even basic genius is indulging in Post Hoc Reasoning and Question Begging with the smell of liniment in his nostrils and possibly suffering the side effects of steroids.
There is no intuitive leap just a word salad chasm below. No new paradigm but a POMO whining.
He wants a free ride …what with, only one can imagine. The thrashing he gives his dead horse keeps away the flies, but the stink is unmistakable.
Pure hubris.
Challenge accepted. Ask me any single question about the CTMU, (exclusive) or offer any single piece of criticism. I’ll answer these one by one.
@John Fringe – sorry for the late reply, I didn’t see this until now.
“I don’t really believe anybody thinks the Universe is the mathematical set of all sets. So the premise is misguided.”
What exactly do you mean by this?
“The rest is empty words glued together without meaning. What the hell does he mean by “thermodynamic entropy is the process of the Universe cognizing itself”? No, seriously. What semantics does he associate with this sentence? What is he trying to say? Where does he get that conclusion? Does he even know what thermodynamic entropy is?”
I don’t really know what he means, I was honestly hoping he’d show up here and comment on my interpretation. What I took from that concept is something along the lines that when an event happens on the “physical” side of the duality, it is paralled by a “cognition” happening on an assumed “mental” counterpart of the physical corpus that is the universe.
The following is my own reasoning which I had thought of long before reading Langan’s article, so I have again no idea if this is what he intended, or if I am being too generous in my interpretation, or if there’s a flaw in my interpretation I haven’t seen. But to clarify further, the process of cognition, which takes place on the “mind” side of the supposed mind/body duality, is represented on the “body” side as a specific thermodynamic event occuring in the brain. The two things are really one thing, however, it just depends on how the detection of this specific event reaches our senses.
For example, let’s say you have a patient and a doctor, and the patient is in an MRI and asked to imagine scenes from his or her childhood. The imagining of these scenes will cause various neurological events which will show up on the MRI (we will assume that they do for the sake of argument). A dualistic interpretation of this principle would be that in the “physical realm” what is “really happening” is this particular pattern of brain activity, whereas in the “mental realm” what is happening is the actual qualitative cognition that the patient is experiencing.
A different, monistic interpretation might be that these two events (the MRI blip and the actual qualitative experience of cognition) are really one event just experienced through two different modes of sensory perception – literally. In the one case, the neural event leaves the patient’s brain by interacting with the MRI, at which point the signal is digitized and sent to a computer screen, where the light from the screen enters the doctor’s eyes and he now experiences this event visually. Either way, this is the perception of that event from the standpoint of the event beaming information through space, where it is detected by the senses of another human being (probably with the help of tools like an MRI) and cognized over there. On the other hand, this neural event is perceived differently from the patient’s point of view, where it is experienced directly by causing other patterns of neurons to fire in such a way that the qualitative experience of a “cognition” is formed.
The above was an idea I had thrown around for a while, so it seemed like Chris Langan was on the same page with his CTMU. I took him to propose that just like one can either “see” or “be” the neural event that I laid out above, that just as we “see” thermodynamic events occuring in the universe, we also “are” them, and hence there may be another way to experience them directly and qualitatively, just as there is another way to experience patterns of neural activation rather than seeing them as blips on an MRI screen. It seemed he was proposing that from the perspective of interacting with all of these events by “being them,” you’d arrive at something that he unfortunately chose to call “God.” Again, I have no idea if this was actually what he’s saying, which is why I was hoping he’d show up to comment.
@Mike B
> “I don’t really believe anybody thinks the Universe is the mathematical set of all sets. So the premise is misguided.”
> What exactly do you mean by this?
You interpreted Langan says “There are logical inconsistencies in the way that most people think about “the Universe,” because the way that most people think about “the Universe” is isomorphic to the view of it as a “set of all sets” as defined by naive set theory.”
What I meant was this: there is not much people who believe the Universe is something like “the set of all sets as defined by naive set theory”, if any.
Most people don’t know about the set of all sets, and they have a lot of diverse ideas about the Universe, but I doubt any of them to be “isomorphic” the mathematical set of all sets. People think the Universe is the set of all material things, or the set of all existing sets, the set of all consistent sets, whatever, but not the set of all mathematical sets. At least, I have never found a person with this idea.
I may be wrong. We could make a poll. Here it would be biased, but let’s try: Is there anyone here who thinks the Universe is something like the mathematical set of all sets?
With respect to the rest, I can not comment. I have the sensation you’re saying one can define a “mental counterpart of the Universe” as “the result of somehow interpreting the physical events as cognitive events”. So yes, then there would be a “mental counterpart”, by that definition. But this is a change of name. It doesn’t have any “mind” properties just because we called it “mental counterpart”.
“I don’t really know what he means, I was honestly hoping he’d show up here and comment on my interpretation. ”
He’s here now…he’s the anonymous poster right above you.
Sorry to disappoint, but I am in fact not Christopher M. Langan.
This comment is directed mainly at Mike B.
I don’t know where you got the point of view Mr. Langan allegedly espoused regarding entropy. I’ve never seen something like that in his writings as far as I can recall, and I strongly doubt such a view is present in his introduction to the CTMU. Please explain where he says or implies this.
You are on the right track with your views inasmuch as they are monistic. Though your views fit more or less into the framework of the CTMU, I do not think they originate from where in the CTMU you think they originate. Specifically, Mr. Langan’s attack on dualism does *not* originate from anything related to thermodynamics. Instead, his argument against dualism proceeds by syndiffeonesis, a process which he describes in his 2002 paper.
Any further questions?
Oh, sorry about that. I thought you were Mr. Langan because I noticed your other comment on the americanatheist.org blog, where he was also posting. My bad.
Such an unfortunate waste of Mr. Langan’s time, rather than using the opportunity to ask him some deep logico-mathametical questions, instead we can’t get past the first paragraph of an introductory essay meant for a general audience…and here I was hoping to hear his technical explanation (which admittedly I probably wouldn’t completely comprehend) for why self-duality and topos theory are not quite enough as they currently exist to pick up where set theory left off…another wasted learning opportunity, such is the Tragedy of the commons.
I agree with koinotely, seems like mob mentality even reaches the PHD level. Funny enough this whole thread reminds me of the movie Good Will Hunting where the pompous PHD’s are fumbling trying to understand the Genius and he finally explodes. Let’s make no mistake here, Most of you are extremely intelligent I’m sure but Mr. Langan is not just extremely smart, he is an off the charts genius. I believe he deserves more respect than he got here period whether he made himself clear or not. Has anyone heard of asking him nicely to explain his theory on a more comprehensive level instead of insulting the man by calling him a crank ? I think not…
I agree with both koinotely and Justin, but I would like to add that Mr. Langan has explained his work quite clearly over the Internet. If one wishes to learn about it in more detail, one must simply look at the correct websites. I’d be happy to provide an interesting discussion over the comments on this blog.
Cool. We’re back at the argumentation by authority.
So, wherever this guy say, it’s is correct. No matter what. Because, hey, he is intelligent!
Well, he may be intelligent, but some people here seem to be pretty err… the opposite. Maybe he is using his intelligence to sell himself to simple people who don’t think by themselves, accepting any argument by the I.Q. number. He can be very intelligent, but maybe he is lazy or does other motivations or whatever, and it doesn’t take an Einstein to fool someone who is blinded by I.Q.’s.
You can continue to think that heavier bodies fall faster. Aristotle was a very intelligent people. I at least will continue to think and judge on ideas, not authority.
Seriously, I have a big problem trying to understand you. Are you really trying to convince us that he is right using as your only argument that some unknown guy said he was very intelligent?
Unbelievable.
John, I assume you are addressing Justin. All I can say is that Mr. Langan considers his IQ to be ultimately irrelevant next to his intellectual contributions. If you wish to debate those intellectual contributions, namely various parts of the CTMU, with me, feel free to proceed right now. Simply state a specific qualm you have with it and I will gladly debate it with you here.
Well, I was addressing anyone who basically speaks about intelligence as an argument. Nobody specifically, they are scattered over the post.
I’m a bit tired of people talking about intelligence. I still don’t have a clue about what intelligence is. Maybe to be willing to learn, but that is not the way people use the term. And nobody seems to know, yet people try to use the word to settle arguments. You’ll agree this is not very “intelligent”.
All this “intelligence” issue tires me.
My impression about IQ is this: A lot of people trying to get into mensa-like-clubs to feel superior, only to later hide their IQ to not feel inferior once there. Talk about irony!
I am not criticizing Langan here, but people who use this argument.
Regarding your offer to debate the theory, I believe his pages speak by themselves. I would be a hard time finding an specific qualm.
“It follows that reality itself should be a set…in fact, the largest set of all. But every set, even the largest one, has a powerset which contains it, and that which contains it must be larger (a contradiction).”
Of course, this is not an argument. I’m not convincing you.
I am not sure why you included that last quotation so I will not reply to it.
I also feel that many high IQ societies originally founded as places for members to befriend like-minded people have become breeding grounds for insecure egos. It is of course extremely likely that some societies are worse than others in that respect and there are probably still societies truly dedicated to helping the gifted overcome their isolation.
I probably can’t contribute much more to this discussion than that.
The citation (from http://megafoundation.org/CTMU/Articles/IntroCTMU.htm) was just my poor attempt to justify somehow why I don’t believe I can contribute anything more to the discussion, neither. I just meant “this is an example of what I consider bad logic”.
Why do you consider that quotation bad logic?
Because every sentence is a premise, an assertion. An they are assertions widely known to be false.
– reality should be a set. (why? this is not infered, so it’s a free assertion)
– it should be the largest set of all. (why? free assertion)
– every set, even the largest one, has a powerset which contains it. (what is the largest set? if it doesn’t exists, how can we talk about its properties? does it really have a powerset? why? free assertion)
– a powerset if larger. (is this assertion valid for infinite sets? why? free assertion)
Good logic is about inferring things from acceptable premises.
Bad logic is about disguising unaccetable premises (premises not much people would take for granted) as being inferred, despite having no connection with the rest. It’s bad logic because logic is about inferring things using logic rules.
If you don’t use logic, it’s not logic. That’s why. Sorry, I thought it was obvious.
In hopes of rebooting this discussion from scratch: Can someone explain, very simply, a correct interpretation of the CTMU?
You need to look at that quotation in context. It’s the beginning of a proof by contradiction. The assumption is that reality is a set. It follows that it is the largest set of all because all conceivable things necessarily fall into reality. Now that we have (for the sake of contradiction) come to the conclusion (albeit illogically) that reality is the largest set, its powerset is the set of all mappings between its members, as is true for all sets. Assuming that reality is a set as we have, it has a powerset. As for the cardinality of that powerset, Cantor’s diagonal argument establishes that the powerset of a set has a greater cardinality than that of the set itself regardless of whether the set is finite or infinite. Just remember that Mr. Langan does not actually believe reality to be a set and that this is merely the beginning of a proof of its not being such.
Sorry, but no.
> “The assumption is that reality is a set”.
No. The assumption is that reality is a set, that it is the largest set, that the largest set exists, that reality is the largest set, that infinite sets can be compared in size, that… he actually makes a lot of assumptions. But, as they’re in disguise, some people don’t immediately see them.
> “It follows that it is the largest set of all because all conceivable things necessarily fall into reality.”
It follows from where? Eh? Wow, not so fast. That’s pretty much a word play, so vague it would let me prove anything. Want a proof? Let’s try.
Consider this: if anything conceivable fall necessarily into reality, I tell you I can conceive a world where that sentence is false, and where Langan’s theory is false. As I conceived it, it is part of reality. So hey! I just proved you’re wrong!
Why is my proof empty? Because I’m only playing with words. First: what do you understand by conceivable? Imaginable? Then why is it necessary for something conceivable to fall into reality? Maybe there are conceivable things that are not real. Why not? Maybe there are a sets of inconceivable things that are bigger. Why not?
You’re only hiding a lot of assumptions in misleading language there (possibly not consciously). You have inferred nothing, you’ve asserted it.
> “Now that we have come to the conclusion that reality is the largest set, its powerset is the set of all mappings between its members, as is true for all sets…”
As the previous conclusion is erroneous, the conclusions based on that conclusion are erroneous. And so on.
To make things clear, some of his hypothesis are:
– the universe is a set
– there exists a set larger than any other, which we call the largest set.
– the universe is the largest set
– we can build a set larger than the largest set
(You’re adding some additional hypothesis, such as that we’re using a concept of set that admits the diagonal argument. But he could be referring to a more relax concept. It doesn’t matter)
I would not need so much hypothesis to build a contradiction. 2) and 5) would do. The problem is he is not proving anything about the Universe at all. All he is proving (and you’re trying) is that your set of premises is inconsistent. But then you select one of the premises and say it is wrong because inserting it in a set of inconsistent hypothesis it results in a new set of inconsistent hypothesis. That’s pretty bad logic.
> “Just remember that Mr. Langan does not actually believe reality to be a set and that this is merely the beginning of a proof of its not being such.”
If he does not believe that, and nobody really believe that, why is he asserting it?
There’s no proof that the Universe is not a set. He proved that is the Universe is a set, and it is the largest set, there exists a largest set, and you can build an even larger set, then you’ve got a contradiction. You only need the last two for that, so he said nothing about the Universe being a set or not.
But then, as I said, I’m not saying nothing new. That’s all obvious.
This paragraph is just an example, but you can see he is just asserting things. At least, I believe it’s clear why I call the theory bad logic.
The “He proved that is the Universe” should be “He proved that if the Universe”. I’m always increasing my typo count 🙁
As almost all of your second last post rests on my statement, “It follows that it is the largest set of all because all conceivable things necessarily fall into reality,” being false, I’ll tackle that first.
I admit that what I said is terribly inaccurate. My bad. Let me give a better reason for reality being the largest set of all, assuming it is a set.
I provide here the method by which Mr. Langan goes about this in his paper, which I should have read more carefully before replying to your earlier post. He provides the sentence, “Reality contains all and only that which is real.” This sentence is clearly tautological; specifically, it is autological, which means that reality is clearly a self-defining predicate. Predicates may be described as sets and vice versa, so a self-defining predicate may be described as a self-including set. By the way, I mean predicate in the mathematical and not grammatical sense. Wikipedia, for example, distinguishes between the two, and you need merely find the article “Predicate (mathematical logic)” for more information.
By definition, all that exists is included in reality. As reality is also a self-including set, as shown above, it both contains itself and contains everything real. Thus, if it could be described accurately as a set, it would be “the set of all sets”, or the largest possible set.
Now that we have really established in which sense reality is the “largest set”, I think you’ll see that the rest of Mr. Langan’s proof by contradiction follows neatly.
You also claimed that Mr. Langan may be using a definition of “set” that does not admit the diagonal argument. His references to Russell’s paradox and related problems in other papers make it very clear that he is using “set” in the well-defined mathematical sense.
Your second and fourth hypotheses would not in fact do alone, as the first hypothesis is necessary to establish that we’re dealing with reality in the discussion and the third hypothesis is necessary to establish that being the “largest set” in fact applies to reality.
You seem to be confused about how Mr. Langan’s proof works, so I will lay it out here for your convenience.
1) The real universe necessarily contains all that is real. (This is an autology.)
2) That which is real is *topologically* contained in the real universe, and the real universe is *described* (descriptively contained) by that which is real. (This is a tautology. This is also where Mr. Langan first distinguishes between topological and descriptive containment.)
3) As reality contains itself and also contains all that is real, it may be described as the “largest set”. (This is an assumption establishing the proof by contradiction. The proof justifies his distinguishing between topological and descriptive containment.)
4) Consider the powerset of reality. It is the set of all subsets of reality, and it follows from Cantor’s diagonal argument that it is of a larger cardinality than reality, assuming as in 3) that reality is a set.
5) The solution to this conundrum is to incorporate two senses of containment, topological and descriptive, in terms of which reality can be said to simultaneously contain its powerset (descriptively) and be contained by its powerset (topologically). But with two senses of containment it is more than just a set. Q.E.D.
So you say: reality contains all and only which is real. That’s not a tautology, that’s pretty much a definition for me. In any case, I’m not sure what do you mean by self-defining. I believe it is this:
a) reality as you defined it exists
b) as it exists, it should be an element of itself
If this is not the case, would you please provide an explanation? Excuse my ignorance.
Langan and you are both making a mess confusing elements of the universe you’re studying with elements of the metalanguage you’re using to study it, and interchanging its properties. I wrote a long, detailed and very boring explanation on what is wrong in your deduction, but I believe we’ll all see it more clearly if I show you an example. I think its very illustrative. If you still have doubts when you read it, or if you don’t see the connection, I’ll post the long and boring explanation.
Let suppose we have a box, with at least three objects (which we will call A, B, C) in its interior. You’re basically doing the following. We define the contents of the box as anything in its interior, and only that. By this definition, object A is one of its contents. Right? Objects B is another.
Then, take the set of objects A and B. This set is in the box, so it’s one of its contents. Right? Let call this set {A,B}. The set {{A,B},C} is in the box. So it’s one of its contents.
In fact, the set of its contents are in the box, so this set is one of its contents. Eh! It’s a self-defining predicate again! The contents of the box is a content of the box! So it’s a self-contained set. So it’s the largest set. So… what do you want me to conclude? I can infer anything you want. Just say anything.
I can do this with boxes, reality, thoughts… just name it, I’ll give you your self-containt paradox, and infer anything you want.
Do you see this is trivially wrong? Do you see this is exactly the same you’re doing? And what about you, the rest of people here? Any doubt?
The problem is this: the set of things in the box is not in the box. You can open the box and you’ll never find the set. No. The elements of the set are in the box. Those you’ll find there.
The set of things that are real is not real. Its elements are real.
What Langan (and you) are doing here is mixing language and metalanguage. I’m not saying you’re doing it conciously, but you’re doing. Can you see it?
If you explain why my example is not exactly the same as you’re deduction, I’ll post my long and boring explanation 🙂
Apart from that, my post does not rely only on that. You missed the most interesting part. The most interesting part is this.
I’ll explain more carefully.
Langan starts with these axioms (with more than these, but these are a subset):
1) the Universe is a set
2) there exists a set larger than any other
3) for any set, even the largest one, there exists a larger set
He then says that the axioms are inconsistent, and then he inferres that 1) is false, because of this.
The problem is this is trivially bad logic. You can not decide an axiom is wrong just because if you insert it in an inconsistent set of axioms the result is an inconsistent set of axioms.
If you could do that, you could prove anything:
1) I like peanut butter
2) there exists a set larger than any other
3) for any set, even the largest one, there exists a larger set
The set of axioms is inconsistent, so I don’t like peanut butter. Or
1) Mr. Langan is right
2) there exists a set larger than any other
3) for any set, even the largest one, there exists a larger set
But then again
1) Mr. Langan is wrong
2) there exists a set larger than any other
3) for any set, even the largest one, there exists a larger set
The set is again inconsistent, so Mr. Langan is wrong.
In fact, with 2) and 3) and this bad logic we can infer anything we want.
No, sorry. The problem is that he is inserting the axioms “The Universe is a set” in an inconsistent set of axioms, and later deciding the conflicting axiom is the anyone he chooses. Which is clearly wrong.
If you still don’t see it, I’ll like to post one last example.
You are saying reality is the set of all real things. Then you are extending the properties of the elements to the set: this set is also real, so it’s contained in itself.
The problem is you can not assign the properties of its elements to a set.
If I have two blue marbles, what colour is the set of the two marbles? Blue? No, the set has no colour. Its elements are blue. That’s all.
If you have a box with two marbles weighting 1 unit each, how much does the set of the two marbles weight? Nothing, the set itself has no weight. You can not extend the weight to the set. You can not say: the set of the two weights two units. Each marble is contained in the box, that’s two units. But the set of the two is contained in the box, so that’s another two units. We have for units if weight in the box, and go on.
In the same way, you can not say: I have elements that are real, so they are included in the set of real things. But as its elements are real, the set of real things is real. So it must be contained in the set of real things. You have no justification to say that.
“We have for units if weight in the box, and go on.”
should be
“We have four units of weight in the box, and go on.”
However, reality *is* real, so it is a real thing. That answers your last two posts.
In fact, this also answers your example of a box. Reality is a real thing, and it is at the same time a collection of real things. This is indeed another major difference between reality and a typical set. The property of being real applies to both it and its elements. If you claim that reality is not real, i.e., that it doesn’t exist, you’ll be hard-pressed to back up that claim given that this conversation is occurring. 😀
Also, Mr. Langan’s proof that reality is not a set is not the result of a true axiom being inserted into a system of inconsistent ones. It states that, were reality a set, it would have a powerset. As reality contains all that is real and its powerset is well-defined, its powerset is real so reality contains its powerset. However, its powerset, being its powerset, contains it as well in a well-defined sense: one of the subsets of a set is the set itself (although it is not a proper subset) and the powerset is the set of all subsets, so the powerset does contain the set. As we have an apparent paradox here (reality contains its powerset and is contained by its powerset), Mr. Langan resolves it by pointing out the two different uses of the word “contain”: the descriptive and the topological. Notice that nowhere in this proof was it necessary to call reality the “largest set”. Instead we merely had to see that it contains all that is real.
Speaking of the sentence, “Reality contains all that is real,” this is both a tautology and a definition. You already see why it is a definition, so I will only explain why it is a tautology. Being real is the property of being in reality. Reality is all that is real. These definitions are circular, but that does not make them false. In fact, reality must necessarily be described intrinsically as something would have to exist apart from reality for reality to be defined extrinsically.
> “However, reality *is* real, so it is a real thing. That answers your last two posts.”
> Reality is a real thing, and it is at the same time a collection of real things.
No. You have to choose which definition you want, but not both.
You can take reality as that that is real. Well, OK with that.
Or you can take reality as the set containing that which is real. Under this definition, you don’t know if its real. OK with this one, too.
What you can not do (if you’re not that confised) is to take both conflicting definitions and decide to apply their properties to one same thing. Because then your paradox is because your mixing.
I can do that to anything, too. It’s a very old form of fallacy.
Let’s say we define a rich as anyone having at least the same money than Bill Gates.
Let’s define also a rich as anyone who is able to buy anything you want.
Now suppose Bill Gates lost all his money and properties, so he’s got nothing.
Then, we’ve got the following: every person in the World would be rich, by the first definition. That’s OK. But then, if everybody is rich, by the second definition everybody will be able to buy anything he wants.
You know what? We all would have the same purchasing power as before. We have to choose: the first definition, where you can have someone rich who can buy nothing, or the second.
What you can not do is to take as much conflicting definitions as you want and mix them, believing they define the same thing.
Do you believe this example is totally silly? It is, in fact. But it is also exactly the same logic you’re using here.
You say “reality is something that exists”, and “reality is the set of all that is real”. Sorry, that’s two conflicting definitions. You can take one, and try to prove the other as a consecuence. That’s what you’ve failed two times to do before trying this form of fallacy.
(By the way. I define John as being the physical person I am. Then I define John as the most cool person in the World. But then, I have just proved that I’m the most cool person in the World! I can prove anything this way. Too easy.)
Here, you can see. Your fallacy is classified and described in wikipedia:
http://en.wikipedia.org/wiki/Equivocation
I have no problem affirming that reality does not exists in the Universe, considering one of your definitions of reality: the set of everything that exists. I have no problem affirming you’ll never find an object in the Universe that is this set. Go look for it.
If you switch definitions in the middle of the conversation, affirming now that reality is that which is real, then I can’t say that. But that’s a very low trick of yours 🙂 You’ll have to stick to a definition to play fair.
Or to be taken seriously.
I see now that due to earlier mistake on my part you are partially correct in attacking my position. I contradicted myself by saying that “reality is not a set” and also referring to it as a collection of things. Reality IS in fact a structured set, but it is *more* than just a set. Describing reality as a set leaves out some crucial properties of reality, such as its interplay of descriptive and topological containment with its powerset.
Reality is contained by its powerset because its powerset is its powerset. On the other hand, it is the case that reality = {x : x is real}, and “real” must be defined intrinsically and circularly. Because the powerset is real, it is an x such that x is real, so it is an element of reality. But it also contains reality because it is the powerset of reality.
Please correct me if you see any errors in this reasoning.
Real = existing in the Universe. Ok, no problem with that.
Reality = { x : x is real }. Ok, no problem with that.
Reality is contained by its powerset. Ok, no problem with this neither.
Because the powerset is real… <– alarm, alarm!
Why is the powerset real? Do you expect to find a powerset of the Universe floating in the Universe? In fact, you do know that assuming the powerset to be real leads to a contradiction. So, you actually know it is not real. Why do you say it is, knowing it is not (by contradiction)?
Again I believe the problem is you’re mixing two meanings of real. Real as actually existing, and real as conceivable. I said before that you can not take something as true just because you can conceive it (I can conceive this theory as false. If that makes it false, we should have ended long ago).
You’re mixing this two meanings. What you’re proving is that you can not decide an arbitrary thing (the “superset of reality”, the “set of all real things”) to be real just because you want, because that leads to contradictions.
You’re inferring nothing more.
I don’t expect to find it “floating around”. However, I never claimed that it is “physical”: I merely claimed that it is “real”. That means it can be said to exist. All well-defined mathematical objects are actualized as information, but not necessarily as physical things. For example, one may not be able to hold the Cantor set in the palm of one’s hand, but that doesn’t mean it does not exist in a purely informational sense.
The contradiction exists when considering any “set of all sets”, and it is simply the case that Mr. Langan’s resolution is somewhat different from that of other approaches to set theory. While typical models of set theory tend to introduce axioms preventing a set of all sets or stratify the concept of a set into multiple exclusive levels, Mr. Langan uses two different types of containment.
Where in my last two posts do you think I made the mistake of passing “real” off as “conceivable”? If one conceives of a unicorn, that just means the conception of a unicorn exists, but not that the unicorn itself exists.
In my 1:48 p.m. post, I said that a thing’s being “real” means that, “It can be said to exist.” I meant, “It exists.”
> However, I never claimed that it is “physical”: I merely claimed that it is “real”. That means it can be said to exist.
So real means it can be said to exists? Well, the problem then is in your understanding of real.
I can speak of the falsehood of the Langan’s theory. This falsehood can be said to exists. In fact, I said it exists. So it exists.
Knowing that Langan’s theory’s falsehood exists, what are we arguing about?
I can’t take that meaning seriously, or you’re wrong in any case as you see.
A concept needs not to be real. If you can’t accept that, then we finally find our problem: your concept of “existence” leads to contradictions. It’s that concept what is inconsistent. Nothing more in the reasoning chain is right.
> If one conceives of a unicorn, that just means the conception of a unicorn exists, but not that the unicorn itself exists.
I read this now. Then again, why do you say the powerset if real? The concept of a powerset if real, but why the powerset itself? You have the proof (it leads to contradictions), yet you insists.
My 1:52 p.m. post addresses your 1:55 p.m. post. A concept does exist as a concept, and that addresses your 1:57 p.m. post. To address your 2:00 p.m. post, indeed it is the concept of the powerset that is real. On any account, this diminishes the powerset’s existence as much as the existence of the number 4 is diminished by the same argument – it doesn’t at all. These are both mathematical abstractions, and that is the sense in which they have informational existence. It does not make them less real.
The powerset as a concept exists. But certainly it does not contains the entire Universe as a subset.
In fact, the concept of powerset is a concept, not a set. The concept of powerset does not contain anything. It’s a concept about a set containing things.
So your argument is still trivially wrong, because now we agreed that the concept of the powerset of the Universe exists, but it clearly is not a set, and it clearly does not contain the Universe as a subset. As your argumentation was based on this, it is wrong.
I believe you’re still playing with words, and confusing language wuth metalanguage.
I see we’ve both ignored CausticDuality, and on my part this was a result of simply not noticing the post. In response to him or her, the CTMU is rather difficult to summarize concisely as a result of its many implications. Though I may not do it much justice, I will attempt a summary.
In short, the CTMU is a theory of reality based entirely on tautologies and which may be used simultaneously to analyze the subjective and objective sides of reality. It is a theory of reality-as-mind and its wide scope allows it to be used to decisively answer questions relating to topics as diverse as the expansion of the universe, the nature of consciousness, and the existence of a creator.
If you, CausticDuality, have any more specific questions about the CTMU I will be glad to answer them, and I will probably do a better job of it than I did of this little summary. 😉
Do you agree that the number 4 exists? Then does the set {4} exist? Of course it does as an abstraction. Reality is also an abstraction. So is the powerset of reality, and it is well-defined as the set of all subsets of reality. You cannot go out and physically hold reality. If you object that the universe is treated in cosmology as a physical object, this does not do the universe justice. It must be treated intrinsically, not with respect to some wider encompassing medium, as no such medium exists. Just as reality may be defined in terms of the predicate “real”, so may its powerset be predicated on reality. If one exists, both do.
I don’t agree that the powerset of the set of all existing things exists. I can’t agree with that, because it leads to a contradiction. You have seen it.
It existence is not obvious. You don’t infer it from anywhere. You’re just taking its reality as an axiom. And you’ve got a contradiction, but you take another axiom as the culprit.
I agree that the concept of powerset (and that of the concrete powerset of the set of the entities that exist) exists.
But that is not the thing, and the concept doesn’t share the properties of the things.
If there’s any doubt, I invite you observe how the World works: despite I having the concept of a sheep in my garden, my grass continues growing. It seems that I need an actual sheep, and not only the concept.
In this very way, the concept of the powerset of the entities that exist is not a set containing the entities that exist as a subset.
The concept is not the thing. If it’s still not crystal clear, invite you to cut a paper with the concept of a pair of scissors.
That’s all we have until now.
I repeat myself because I do not found any new information or argumentation in your last post.
Sorry. It’s being a pleasure to argue with you 🙂
Like Carl Sagan said, we are a way for the cosmos to know itself. We are made of the universe, and the universe is in us. The atoms of our body simply came from the centers of high-mass stars. Why do we need to define such things as “consciousness” in metaphysical terms when we already know what it is? Sentience is just the result of various processes working together. Every aspect of our mind is traceable to the brain. It’s all material.
How can one possibly posit an “objective reality” when all we have is perception? The only “objective” thing we can determine about our reality is that a subjective reality exists — in other words, there is existence.
And the fact that Langan is invoking a Creator/God is a huge red flag. It doesn’t get you any closer to solving anything. It all sounds like crackpottery.
The paradox associated with a set of all sets will arise regardless of whether or not the powerset is so much as mentioned as a result of Russell’s paradox. Even if Mr. Langan or I had not brought the issue of the powerset up, there would still be a paradox. As I see it, the powerset is as well-defined as any powerset of an infinite set, and this makes it as real as any powerset of an infinite set.
The phrase “abstract concept” is redundant. All concepts are abstract and all abstractions are concepts. E.g., the concept of a linear mapping is a linear mapping. The difference between concepts and things in themselves becomes a problem when one moves from the abstract to the concrete. E.g., there it is true that the concept of a pair of scissors is not the same thing as a physical pair of scissors. As both the powerset and reality are abstract concepts, like a linear mapping they exist if we may so much as conceive of them.
It is a pleasure to argue with you, as well.
Do you (or that different person who is Mr Langan) have the slightest idea of the meaning of ‘topological’, my friend Anonymous?
I will reply to Errr…. first as a somewhat shorter reply will suffice to answer his or her query.
In most cases “topological” means “of or relating to topology”. However, Mr. Langan uses it in the phrase “topological containment” (which I assume you are asking about) to refer to the type of containment used in set theory, i.e., the way in which sets contain or are contained. This may be contrasted with “descriptive containment” which is the way something in a language contains its referents.
The rest of this comment is in response to CausticDuality’s 3:36 p.m. comment.
No large-scale consensus exists on the nature of consciousness. For example, many philosophers (e.g., Berkeley, Chalmers) would likely object to your statement, “Sentience is just the result of various processes working together.” It is not intuitively impossible for there to exist intangible subjective phenomena that determine the mind’s processes. Assertions are not absolute proof, which is why the nature of consciousness is of great metaphysical importance.
Absolute knowledge exists in the form of logical tautologies. That is the objective side to reality in which you seem to lack faith.
> there it is true that the concept of a pair of scissors is not the same thing as a physical pair of scissors
So… you’re accepting that the concept of a pair of scissors is not a physical scissor. But you don’t accept a concept can not contain a physical scissors.
I mean, you agree that concepts are different from physical things, but you believe they can contain physical things. You believe the concept “powerset of the reality” contains an existing physical scissors. As much as every one of them.
Despite it being the origin of contradictions.
I find this very curious, and I can not see why I should (or can) go beyond that. You assert things that lead to contradictions. That things are not deductions, but your axioms. And they lead to contradictions. But they lead to contradictions way before considering the Universe the largest set. So that’s not the conflicting axiom. So, by the time you are speaking of that idea, you’re in an inconsistent system. So you’re reasonings about the largest set, based on that inconsistent suppositions, are wrong.
I really have nothing to add. I have being repeating the same. The information is here. I’ll let people judge by themselves.
No, I still have one doubt.
> “As both the powerset and reality are abstract concepts, like a linear mapping they exist if we may so much as conceive of them.”
This is clearly an axiom for you. A concept exists if we can conceive it. Then, why so much theory to prove god exists?
I mean. You have the concept of god, and an axiom saying concepts exists. Why so much wasted words?
(Of course, this proof of the existence of god means nothing. As I say before, this god may not share any properties with other definitions of god, and you can not mix definitions to prove properties. Anyway, we saw that axiom leads to inconsistencies, and the proof is indirectly based on that. But depending on the same axioms, my proof is a lot shorter than Langans and has the same validity [none]. Which is good).
You continue to amaze me, Mr. Fringe, in your lack of understanding for why an unfashionable powerset cannot be dismissed. The term “concept” is clearly being used very vague so I will drop it entirely. The fact remains that if reality is a set as you claim it has a powerset. All sets have powersets. Why? Because the powerset of a given set is simply the set of all subsets of that set, and all sets have subsets. Yes, even reality has subsets, and you cannot dismiss those subsets because they lead to a paradox. Paradoxes are not irresolvable as you seem to believe, and where they arise from proper mathematical reasoning (like this one does) they are beneficial as they show fundamental problems with given systems (e.g., naive set theory).
As for Mr. Langan’s proof of the existence of God, it turns out that this God has properties associated with omnipotence, omnipresence, and omniscience. Whether or not that qualifies as a true God for you, that’s the case.
“It is not intuitively impossible for there to exist intangible subjective phenomena that determine the mind’s processes. Assertions are not absolute proof, which is why the nature of consciousness is of great metaphysical importance.
Absolute knowledge exists in the form of logical tautologies. That is the objective side to reality in which you seem to lack faith.”
Just because something is not impossible doesn’t mean we have any good reason to believe it. It’s not intuitively impossible for there to exist intangible Leprechauns, either. It’s not intuitively impossible for it to be true that we can’t explain 100% of the variance in the data of heating up a cup of water without invoking pixie intervention.
There IS a widespread agreement in the scientific community as to the nature of the conscious mind. To imply otherwise is akin to implying that there is still “controversy” over something like evolution. Modern neuroscience/neurobiology shows that everything is linked to the brain. We can knock out (temporarily, with electric shocks) various parts of the brain and see all sorts of corresponding functions wipe out. We more or less know how stimuli is processed, how feelings/senses are interpreted, how memory works, etc. Even if we don’t have all the nitty-gritty details, we know sufficiently enough to explain the basics. We have all we need to explain how sentience actually operates. Of course guys like Chalmers would object (they aren’t scientists!). They frequently misuse quantum mechanical jargon and misunderstand how quantum theory works. It’s too easy to invoke argument from ignorance when it comes to philosophy.
And in terms of logical tautologies, that is not a matter of knowledge. Logic itself does not constitute knowledge. Logic is a framework in which we discuss relationships of other concepts. Logic is based on axioms which we take as self-evident because our universe is wholly conducive to these axioms.
The CTMU holds little scientific value. It’s just philosophy.
I’m not the one saying the Universe is a set. You’re defining (sometimes) the Universe as a set. You’re forgetting your own definitions?
I’m not saying (nor I believe it) that paradoxes are irresolvable.
You said the there exists a largest set, and there exists sets larger than the largest set. I don’t agree with at least one of those. No contradiction for me. The paradox is yours: you’re the one who stubbornly defend contradicting axioms, despite know they’re inconsistent, and despite not being able to explain nothing, beyond blindly asserting them: reality is a set, is real, a set as a concept has the same existence as a tree, and all that.
I know paradoxes are solvable. And as almost everybody else, I know how to solve them: discarding some of the axioms. Nothing new here.
Why are you blaming me for your definitions and your contradictions? I’m responsible of none.
You needn’t be so quick to judge, CausticDuality. First of all, I was unaware that you were referring to the *scientific* community, in which there is indeed a bent towards physicalism and materialism. You should know that Mr. Langan agrees with your view that consciousness is not the result of unobservables and for the same reason, which is ultimately Ockham’s razor.
Moreover, I am sure Mr. Langan can identify with your criticism of traditional philosophy. Of all modern disciplines, philosophy is one of the worst off, and that is in fact why Mr. Langan chose to pursue it over other disciplines, such as physics or biology, that have many individuals actively improving them on a daily basis.
As for your claim that logical tautologies are not a matter of knowledge, I must draw an objection. Tautologies are axioms of 2-valued logic and the complementary truth values True and False correspond to systemic inclusion and exclusion, respectively, so violating tautologies corrupts the informational boundaries between the cognitive and perceptual predicates applied or recognized in reality as well as between each predicate and its negation. The fact of our unbroken perception thus proves that tautologies constitute absolute truth within reality.
As for the CTMU “just” being philosophy, you need only notice that major changes in physics are preceded by major changes in metaphysics (which is somewhat ironic because “metaphysics” is essentially Greek for “after physics”). For example, the theory of relativity was largely the result of a changed viewpoint towards space, time, and matter. A profound shift of paradigm such as the CTMU could provoke would likely change the sciences forever. Moreover, the CTMU has scientific value in its own right as it deals with the nature of artificial intelligence, resolves several largely mathematical paradoxes, and has much to say about cosmic expansion.
Paradoxes are rarely so — they’re usually just conflated interpretations of axioms and/or misunderstood applications of mathematical/logical principles.
I am not forgetting my definitions, Mr. Fringe. That is you. You unflinchingly accepted that reality is a set, and looking through your comments above proves it. On any account, I am sure that reality is a set, and you can quote me on that. Discarding axioms is not a good way to solve paradoxes. For example, consider Russell’s paradox. One of the only axioms of naive set theory was that any collection is a set. Consider R = {x : x is not an element of x}. Then R is an element of R R is not an element of R. The solution to this paradox is not to eliminate the axiom, “Any collection is a set.” Instead it is to *add* axioms, like ZF set theory does, or to add types of containment, such as the CTMU does.
I rest my case always on mathematics. Reality is a set. Reality has a powerset because all sets have powersets because all sets have subsets because all sets are sets. This powerset contains reality because reality is a subset (though not a proper one) of reality and powersets contain all the subsets of the sets of which they are powersets by their definition. However, this powerset is a real thing because all sets have powersets and reality is a set as mentioned earlier, so because reality = {x : x is real} it contains its powerset. The ONLY assumption here is that reality is a set, and even this can be justified because reality is a collection of distinct objects, considered as an object in its own right. I am not even going to go into the issue of “concepts” as that is entirely beside the point when discussing the CTMU. Oh, and reality exists as I’m sure even you’ve noticed so it is indeed real and it is a member of itself.
CausalDuality, you’re exactly right. All paradoxes are *seemingly* valid or their consequences are *seemingly* absurd, but this just points to problems in whatever system they are defined.
*CausticDuality
*this just points to problems in the systems in which they are defined.
I’m just correcting some minute errors I made.
Anonymous: Yeah but relativity came about because we had evidence that suggested we needed it to explain something. It wasn’t brought about just because of some shifting viewpoint about space and time in opposition to guys like Newton and Mach. The viewpoint evolved along with the new theory. The CTMU is not suggesting anything of practical application or value with respect to new problems/evidence/physical phenomena in the same way Einstein did with relativity.
As for your paragraph on logical tautologies, what I mean is that we can take a logical tautology such as “if A implies B then not B implues not A,” the law of contraposition — and say it doesn’t represent “knowledge” in itself. I define knowledge via the epistemological concept of “justified true belief” when it comes to the ways laws and matter interact in our universe. We have knowledge because we are sentient and capable of perceiving within our reality. But the logic itself is an “objective concept” but I wouldn’t define it as “knowledge.” I see logic as more of a “fundamental framework” for existence itself. If logical tautologies are unsatisfiable, they become contradictions and they would make no sense when it comes to defining reality. In other words, I consider logic/mathematics to be self-evident, necessary concepts for existence itself, and this I consider to be “objective.” I just don’t like to call it “knowledge” in the same way that we might call our understanding of the sun and moon “knowledge” (what’s true for me is true for you and true for everyone).
The CTMU is suggesting many new things though. For example, it pushes the theory of computation forward as protocomputation is shown to be behind typical consciousness. It also resolves Newcomb’s paradox and extends the scope of symmetrization of probability distributions. It opens the way for a new theory of computational grammar that leads to better grammatical parsing systems. It has much to say about the manner in which the universe expands (or rather “conspands” in CTMU terminology) and this will enter new models of physics incorporating the CTMU. Philosophical revolutions leak into mathematics and physics, which leak into the other sciences, which leak into the “softer” sciences such as psychology and sociology, and eventually this leaking causes engineers to come up with new technologies to which the public is exposed through popular culture. All large philosophical contributions eventually help create new technologies in this manner.
As for your paragraph on logical tautologies, I understand what you mean and I have no objections to raise to it.
So reading my comments, I accept that reality is a set. And I understand that is contains itself. And you say that based on mathematics.
Now, what’s that? A proof by negation of reality?
I’m leaving here. The situation is getting ridiculous. The information is here, for anyone wanting to read it.
The problem is you have a theory so trivially wrong you have to just negate reality and say we believe it’s true.
Your theory requires any concept one say to exists. Then the falsehood of your theory exists and is real. And you even don’t bother negating it, because you really need that any concept to be real and true for your theory to work. Well, for you to believe it works.
Then you write a thousand pages to prove an omnipotent god exists, having one axiom that is that, being able to talk about concept of an omnipotent god, then it exists.
It’s all ridiculous. As you can’t go that way (reasoning), you turn around and you’re again just asserting things: that I agree with what you want.
This is just getting too random. Good bye with your “mathematics”. Be happy.
I’ll try one last time to explain.
It is not Mr. Langan’s belief that thinking about a thing makes it real, and the discussion that led us that way is irrelevant to the CTMU. You’ve successfully ignored the 7:37 p.m. post addressing you, but I’ll just restate its contents for future observers to read. This is the entire, pure chain of reasoning that leads to the conclusion that reality contains its powerset while being contained by its powerset.
1) Reality is a set. Specifically, it is the set {x : x is real} = {x : x exists}. (This follows because it contains objects and is considered an object in its own right.)
2) Reality has a powerset. (This follows because all sets have subsets. You can’t say that reality doesn’t have subsets because the fact leads to a paradox!)
3) This powerset contains reality. (This follows because one of the subsets of reality is necessarily reality itself. This is true for all sets by the way. For any set S, S is a subset of S, but not a proper subset of S.)
4) The powerset of reality is real. (This is the step Mr. Fringe really has trouble with. He seems to believe that we should be able to find a *physical* copy of this powerset, which is of course not true. (E.g., one can’t find a derivative floating in outer space!) However, if reality is real its powerset is well-defined and so exists. If reality = {x : x is real}, P(reality) would resemble {subset1({x : x is real}), subset2({x : x is real}), …, {x : x is real}, …}. Reality, which Mr. Fringe agreed is a set, would literally be found within the curly brackets of P(reality)!)
5) Reality contains its powerset. (This follows from it being real, as described in 4).)
There you have it Mr. Fringe & Co. There are several reasons I didn’t mention the “axiom” that anything conceivable exists: a) it is entirely irrelevant to the CTMU and especially this section of Mr. Langan’s “Introduction to the CTMU”, and b) it is largely the result of my not being careful enough in wording and your taking advantage of that, which is alright because that’s your job as a debater.
Have a nice life, Mr. Fringe!
Anoynmous: The CTMU, as far as I can tell, isn’t suggesting anything new in terms of scientific application or insight. It’s just philosophical pandering mixed in with a misunderstanding of quantum mechanics, information theory, and laced with a heaping of extreme verbosity due to a lack of clarity. If you aren’t framing a new discovery through the scientific method, it’s not science, and it shouldn’t be passed off as such.
You also don’t need anything crazy to resolve Newcomb’s Paradox. As I suggested earlier, paradoxes typically aren’t really paradoxes. Newcomb’s Paradox is already a problem with a screwed-up definition to begin with. I can choose either the clear box with $1000 or take both the clear and opaque box, but if I take both, the opaque box is predicted to be empty. If I take just the opaque box, it’ll have $1,000,000. The paradox calls into question the nature of things like free will.
In practice, people like the Oracles don’t exist. We’re better off taking both boxes because whatever’s in the boxes are in the boxes, and we’re better off taking as much as we possibly can. The only way the Oracle could really predict my actions is if he had access to every variable involved in my brain and the environment it interacted with from the time of determination up until the box-selection process. The Oracle would be able to know exactly which boxes I would choose based on the way the processes of my brain would compute the situation, and from there he could load the boxes ahead of time accordingly. If he knew that by giving me the problem, I would take both boxes, he would know ahead of time that he should only load the clear box with $1000 and nothing more. In other words, the paradox is resolved by taking away the concept of free will and framing choice as a deterministic concept.
Newcomb’s Paradox is only a paradox if you frame it as “Well, the Oracle can’t change the contents of the boxes and yet I have free will. If I have free will, I should be able to make my own choice and have the outcomes scale to my choice, but how can the outcomes scale if the outcome is static from the beginning?” It’s only a paradox in that logical sense, but like I said, paradoxes are only paradoxes because they’re usually either misinterpretations or misframings. You do nothing by invoking the concept that “We have free will.” The paradox is trying to say “You have free will that can’t be pre-determined by outside sources, and yet here’s an Oracle that can do just that.”
I could say “This sentence is false” but that doesn’t really *mean* anything. Just because we can label something a certain way doesn’t mean it’s actually logically/physically sensible. It’s like trying to find a number higher than 6 and yet lower than 4. It’s nonsense, and things that are nonsense don’t have any place in our universe or its definition.
Philosophers are largely obsolete. Yeah, we can look at guys like Francis Bacon who had a lot to say about the nature of reality and science, but Galileo was *already* using *actual* science to make discoveries. In other words, philosophy doesn’t really “leak into science” — it just likes to think that it does. Science leaks into science. That’s the nature of the scientific method. Quantum physics, for instance, completely revolutized the way we look at the world, and it didn’t come about from philosophy. If you look at philosophy over the years you’ll see all sorts of theories that are, nowadays, largely discarded as demonstrably false. Only in hindsight can we pick out the ones that by sheer chance alone happened to have grains of truth to them. For instance, Democritus posed the rough idea of atoms a long time before we ever actually discovered one, but he was only right by sheer chance alone, as atomic-scale technology didn’t exist at the time. We don’t pay attention to the wide array of other philosophical theories that were proven to be wrong because they were false! The theories that stick around longer are the ones that aren’t easily falsifiable — such as theories invoking Creators and God.
The CMTU, in my opinion, is just a verbose backdoor to Creationism, which is an “ism” of ignorance.
I have never agreed that reality is a set. You can continue to say what you want. But that’s an invention of yours. I agreed to reason under your postulates, and one of then was the definition of reality as a set. So I played your game. I don’t agree that reality is a set. I don’t believe reality to be a set. I have never believed reality to be a set. I would not model reality as a set. Maybe I’m not expressing myself clearly enough. If you ask me, I would never say reality to be a set. I’m not of the opinion that reality is a set. I consider false for reality to be a set.
But if you define reality to be a set, and as I know how to reason, I can understand that, and infer accepting your definition.
But I do not believe reality to be a set. Repeat with me: I don’t believe reality to be a set. Reality is not a set according to John Fringe. John Fringe does not think that reality is a set.
> “if reality is real its powerset is well-defined and so exists”
The problem is, you never proved reality, defined as your set, is real.
The set { x : x is real } is not real because you called it reality. As you have never proved that the set {x:x is real} is real, you’ve never proved that the powerset is real.
By the way, I don’t believe reality to be a set.
The problem is you have no clue how about reasoning. You believe the set {x : x is real} is real just because you’re calling it reality.
When pressed, you simply admit that any concept is real. But then again, I can prove the falsehood of your theory.
Seriously, stop and think a minute. It’s not so difficult. I still have hope.
I almost forget one thing. My fault:
I don’t believe reality to be a set.
That’s all.
There seems to be a little confusion here. The poster “Anonymous” is not me, and has not been authorized to speak for me. He is proceeding on his own initiative, using his own understanding of the theory, in which he has not been coached or personally instructed by me. (Of course, he is free to do what he has chosen to do. But thus far, he has not handled this discussion quite as I would have handled it.)
This forum belongs to Mark Chu-Carroll, and because Mark is forthrightly using his real name attached to his real credentials, his name and reputation are on the line (which is exactly as it should be). Almost without exception, the rest of you are trying to argue without answerability, and unsurprisingly, your argumentation is shoddy. In fact, most of it is so bad that it would be a complete waste of time for me to address it at all. I’m simply too busy for that.
If you insist on having me address any particular point you have made in even a cursory fashion, you need to have Mark clean it up for you and present it as a formal objection along with his personal endorsement. (None of this is negotiable; this way, Mark will pay the price for upholding whatever nonsense I’m forced to spend my valuable time dismantling.)
Alternatively, if you actually claim any qualifications in this field, you can provide such information as will allow you and your home institution to be unequivocally identified and thoroughly checked out by all concerned. That way, you and your institution can pick up the tab instead of Mark. (If you have no reputation or credentials and affiliations in this particular field, then please don’t bother providing any information about yourself – if I put my own reputation at risk by arguing with you, then you must have one to put at risk as well, or no go. In situations like this one, such reciprocity is only fair.)
Thanks for your attention, and have a nice day.
I have to agree with John on that note. There are serious problems when we accept certain axioms and base definitions as true or self-evident, especially if those notions are silly or meaningless to begin with.
Let’s look at Langan’s own writing at http://www.ctmu.org/Articles/IntroCTMU.htm when he talks about sets.
Let’s give some hard definitions, here.
A powerset just means if we have a set S = {x, y, z} when we can define its powerset as a set of all subsets. In other words:
P(S) = {{},{x},{y}.{z},{x,y},{x,z},{y,z},{x,y,z}}
He then goes on to say “If reality is the largest set of all, then reality has a powerset that contains it.” Here he refers to the example of, say, {x,y,z} being a part of both P(S) and S, where S is defined as {x,y,z} to begin with.
But then he screws up: “Every set, even the largest one, has a powerset which contains it, and that which contains it must be larger,” etc. In other words, he is saying “S is a pretty big set. But the powerset P(S) contains S. Because P(S) is a bigger set than S, there is a contradiction. Therefore, there is a problem when we view reality as the largest set.”
This, to me, is complete nonsense. He’s saying “If we define S as the biggest possible set of everything that is real, it can’t be the biggest set because a powerset is larger and contains S.” In other words, it’s akin to saying “If God is all-powerful, can he make a stone so heavy even he can’t lift it?”
His solution: “Define an extension of set theory incorporating two senses of “containment” which work together in such a way that the largest set can be defined as “containing” its powerset in one sense while being contained by its powerset in the other”
In other words, something where S is the biggest set that contains P(S) and yet such that P(S) also contains S. The only way two sets can “contain” each other fully is if they’re equal, and the only way a set and powerset can be equal is if you’re talking about the null/empty set. Screwing around with this means you screw with logic and are therefore talking about something nonsensical with respect to our universe.
Chris: We don’t have to give out our real names/institutions in order for our arguments to be sound. We don’t have to put “our reputations on the line” because the onus is not on us to do so — you’re the one making the claims with your CTMU, and you wish to have it associated with your name. That is your own choice.
You can choose to discard objections if you want, but that doesn’t make your theory true because you simply refuse to acknowledge the criticisms by saying “The arguments are shoddy and it’s a waste of time to address it by people hiding behind anonymity,” especially when a lot of the criticisms have valid points.
You of all people should agree with the notion that “credentials shouldn’t matter.” If that were true, no scientist should bother wasting time with the CTMU.
Hello Mr. Langan,
Indeed I am not affiliated with you and I apologize for any misunderstandings of the CTMU I have caused. I am a Canadian high school student and I don’t have any real credentials as such. I would prefer to remain anonymous for personal reasons, and I have nothing to lose from this to my knowledge due to my lack of credentials. I am an autodidact with respect to your model, so please forgive any errors I have made.
Sincerely,
Anonymous
At any rate, I actually do have plenty of credentials (top-tier school, top-tier employment, lots of research, etc) — but I shouldn’t have to flaunt them here to get across the point that credentials don’t make you any more right or wrong with respect to the actual ideas you put forth.
Anonymous: “Indeed I am not affiliated with you and I apologize for any misunderstandings of the CTMU I have caused.”
I appreciate your frankness. Best wishes, and I sincerely advise you not to allow the kind of argumentation used against you here to dampen your apparent enthusiasm for the CTMU.
CausticDuality: “We don’t have to give out our real names/institutions in order for our arguments to be sound.”
Perhaps not. But as I say, my conditions are non-negotiable.
I used to respond to anonymous posters until I realized that because they have nothing of value to lose, they tend to become totally unrestrained in their style and methods of argumentation. They typically start with subtle provocations harnessed to vague absurdities; when that doesn’t work, they move on to snide remarks and threats of intellectual annihilation; when those have no effect, they escalate to full-blown insults and rhetorical fallacies including ad hominem argumentation, arguments from authority, strawman arguments, red herrings, and sheer propaganda. Finally, one realizes that one is being harangued by a gang of uninhibited imbeciles who will literally stop at nothing to push their “points”, ridiculous though they usually are. Under no circumstances will they offer any meaningful concession as they do so; mudslinging and recalcitrance are simply too easy for them.
I didn’t design the Internet, so I don’t bear any responsibility for the way it works. That it works as I have described is indisputable, at least where I have been concerned. If one thinks about it a little, one is forced to conclude that while the freedom of the Internet is definitely something to be admired and preserved at all costs, personal opinions are another matter entirely. Those must be legitimately defended on a level playing field, or they are worth nothing. This is one piece of cake that you don’t get to keep and eat at the same time.
In this kind of situation, there is no physical threat associated with surrendering your anonymity and revealing your credentials and affiliations. On the other hand, if you lack the courage of your intellectual convictions and refuse to uphold them under your real identity, at risk of your intellectual reputation and that of your primary sponsor, then they do not deserve a response from anyone who has put his own reputation on the line and can thus be held to reasonable standards of argumentation.
That’s just the way it is. I hope everyone understands.
We understand, don’t worry.
In any case, we’re not judging you, but your theory. I hope we all can differentiate the two.
About the shoppiness of the arguments against your theory, I agree. But the reason is the arguments presented here in favor of your theory are pretty illogic and shoddy, too. The way to improve the quality is to provide better arguments that require better counterarguments.
I don’t say you provide those arguments. You’re free not to do it, and if you find more elevated places where your theory is being judged, you better spend your time there. But then, don’t expect masterful arguments to explain why the properties of the elements of a set are not applicable to the set itself. That’s a silly supposition, so we give silly counterarguments (that work).
You might think that everything needs to be out in the open in order to contain the insanities that can sometimes accompany anonymity, and on some level I agree with that — but I simply do not share personal information online for privacy and protection purposes. Nothing to do with defending intellectual reputation. The fact that I can lay claim to top-tier education and employment opportunities should be sufficient. I can’t prove any of that, of course, but it shouldn’t matter: Obviously crazy responses and insulting remarks can be ignored. My point is that there have been many good criticisms against the CTMU so far and I feel like they aren’t being addressed fairly.
There are problems I have with the CTMU all-around, but let’s stick with that set question. Correct me if I am wrong: You are saying that if we describe reality as the biggest possible set, then a powerset of reality is a contradiction since a container of a “biggest-possible set” must be bigger than “the biggest possible.”
Mr. Langan, best wishes to you too. I certainly won’t let such debates dampen my enthusiasm.
John, you’re denying that {x : x is real} is real. This denial amounts to the denial that there is a collection of things that exist. This means you’re asserting that nothing exists. I think you’ll have a hard time proving this. As Wikipedia puts it, “A set is a collection of distinct objects, considered as an object in its own right.” By denying that reality is a set, you are denying that reality is a collection of distinct objects. This means that you are denying that anything exists, for if anything exists that thing is an object contained by reality. Again, I think you’ll have a hard time proving this.
CausticDuality, what specific criticisms can offer of the CTMU? I suggest you focus on explaining how the CTMU misunderstands quantum mechanics and information theory as you allege it does.
Actually, you’re wrong about what the term “science” entails when I use it (and judging from context when Mr. Langan uses it). In referring to the scientific method, you are making a more or less obvious appeal to empiricism, but empiricism is not of what all science is made; mathematics, for example, is entirely rational, and this is the way the CTMU proceeds for the most part.
On a related note, the CTMU is best termed “philosophy” because it deals largely with metamathematics. This is no reason to dismiss it, however: pure logic deals with exactly the same thing. As for your claim that quantum mechanics did not arise from philosophy, I beg to differ. Quantum mechanics’ major premise, the Heisenberg Uncertainty Principle, sets absolute limits on the accuracy to which quanta can be measured, thus defining a relation between measurer and measured that cannot be expressed in a language focused only on what is measured, such as the language of classical physics. Though we may consider it a physical theory now, there was a time when quantum mechanics was indeed regarded as metaphysical.
As for Newcomb’s paradox, it’s not that simple. First of all, you need a logical model justifying why free will does not exist as you claim. Moreover, you shouldn’t ignore the maximization of subjective expected utility in your decision. Also, you need to prove that Newcomb’s Demon can’t exist.
Actually, the CTMU extension of set theory is perfectly logical. Topological containment is the sort by which sets are said to “contain each other”. Descriptive containment corresponds to inclusion by predication, which is a perfectly common mathematical operation in, for example, computational linguistics.
> ohn, you’re denying that {x : x is real} is real. This denial amounts to the denial that there is a collection of things that exist. This means you’re asserting that nothing exists.
So now I’m asserting that nothing exists. Oh, my god. I though the logic could not get any worse. You seemed reasonable.
And Mr. Langan was surprised that the arguments are dumb. It’s very difficult to argue when your opponent happily invents your dialog.
Anonymous: I feel like a LOT of terms are misused in the CTMU. There’s a lot of jargon in there that mean very specific things but they’re used in nonsensical ways. Either Langan is misusing the jargon or he’s not explaining himself clearly enough. But I personally feel like there are a lot of confused ideas in the CTMU that just don’t make sense, even to people who are well-versed in mathematics, physics, logic, etc.
Yeah, we can define a set as an object in its own right in the same way that I can call an “apple” a set of “apple atoms” with all sorts of various properties to them. We can even define the universe as a vast set of information. That is, after all, how we even know about the universe to begin with. It exists and has properties we are able to measure and interpret. But my point is that sets are defined axiomatically, where the axioms have to make sense. Mathematics has to put all sorts of exception cases and rules in place in order for them to work.
The reason why MarkCC brought up naive set theory earlier is because it says “any definable collection is a set,” so therefore I could say S = set of all sets that aren’t members of themselves. If S is a set that isn’t a member of itself, then S isn’t part of S. But if S isn’t part of S, then it should therefore be included in S. That’s where the paradox stems from. But like I said earlier, paradoxes only exist when we confuse the logic.
All Russell’s Paradox is doing is setting up a scenario that logically cannot make any sense. Just because we can define something with language doesn’t mean it has any mathematical sense. It’s not possible to have S = set of all sets that aren’t members of themselves in the same way that it’s not possible to have a number higher than 6 and lower than 4 no matter how much I write 4>x>6. Just because I can calculate the value of something by writing x/y doesn’t mean it’ll make sense if I am talking about a number of apples divided by 0.
The ultimate point here is that we can’t just slap certain mathematical principles onto things, extrapolate a paradox, and then use that to justify invoking things like God. The model has to make sense. It’s like when people try to apply the Stefan-Boltzmann Law to our earth/sun and conclude that the earth temperatures are higher than they should be because the blackbody temps are below 0. The whole thing goes out the window when you take into account that the earth isn’t a blackbody — we can model the earth as one, but it’s failing to take into account other influential factors like rotation, greenhouse effect, dimension, etc.
On a fundamental level, we use mathematics to describe our reality. That’s a very different distinction from saying reality IS the mathematics. In doing so, it’s too easy to run into “mathematical paradoxes” that lead you down a path of describing reality in a way that is nonsensical.
Anonymous:
“As for your claim that quantum mechanics did not arise from philosophy, I beg to differ. Quantum mechanics’ major premise, the Heisenberg Uncertainty Principle, sets absolute limits on the accuracy to which quanta can be measured, thus defining a relation between measurer and measured that cannot be expressed in a language focused only on what is measured, such as the language of classical physics. Though we may consider it a physical theory now, there was a time when quantum mechanics was indeed regarded as metaphysical.”
This is just false. Quantum Mechanics came to light because of physics. The cathode ray, photoelectric effect, ultraviolet catastrophe, black body radiation, quanta, etc, all of which are scientific, physical concepts that aren’t settled in philosophy. The Heisenberg Uncertainty Principle is also not a matter of philsophy or observer effect or the accuracy of the measuring instrument. It comes about because of the fundamental way momentum and position are defined. The more you know about one, the less you know about the other, and this is intrinsic due to the nature of waves.
Regarding Newcomb’s Paradox: It actually is that simple. The “logical model explaining why free will doesn’t exist” is just physics. We know that wavefunctions are essentially deterministic, and so we can say that even though we do make our own choices, they aren’t independent. Choices are made as a result of the physical determinism of the universe — our brains determine what thoughts and feelings we have, and brains can be broken down into complex neuron systems that abide by physical laws just like anything else. This is not only obvious, but evident through neuroscience: You manipulate the neural level, you can manipulate the outputs. We’re not independent systems that operate autonomously with respect to the universe.
I don’t need to appeal to concepts of expected utility to show why Newcomb’s Paradox isn’t really a paradox. I explained in sufficient and simple detail why in my earlier post.
(Quantum mechanics is science. It has always been contrasted to experiments. It can be.)
This way is not working, but I’ll try one more time. I’ll arm myself with patience. You continue mixing definitions and properties, of reality, of existence, of being real. Let me try other way.
You’re mixing two meanings of “to exists” just because the colloquial word is used with that two meanings. And you’re mixing the properties of the two.
Consider A as “the chair in front of you”.
If I ask you, does A exists?
If you go look in front of you and check if there is something physical, then you’re using one of the meanings. Suppose the answer is negative. (I hope you can conceive giving that answer). I’ll call that meaning exists_1.
Then you can consider “the chair in front of you” as a concept. That that concept exists? You’ll answer: yes, it exists. It can be evaluated to exists_1, we can talk about it. The concept exists. I’ll call this meaning exists_2.
(Technically, they are not properties of the same universe of discourse. But I bet you don’t understand these technicallities.)
You see they are different predicates applied to different entities: in the first case you can answer no. In the second one, you’ll never answer no. But you’re mixing them in your argumentation.
You say “reality” (which may not be reality. Remember, I don’t believe the universe to be a set) is the set {x : x is real}.
Imagine you’re referring to exists_1. “Reality” (the name you give to the set) is {x : exists_1(x)}. The set of things that exists according to the first predicate. But you have to understand that “reality” (just a name, remember, don’t me bring a nitpicker’s corner) exists_2, but not exists_1. So no problem here: “reality” (remember about the name) is not self-contained.
Imagine now that you’re referring to exists_2. “Reality” is {x : exists_2(x)}. The set of things according to the second. Then I believe you’ll accept you’re not speaking of the intuituve meaning of reality. That “reality” would not contain material physical things, for example. You’re not speaking of reality with that “reality”. That set is self-contained. But it just a concept, and we know there is inconsistent concepts. No problem with that, because that “reality” has no relation to reality.
As ever, what is confusing you is that you can not use all the meanings of an informal word formally. Some words have more than one meaning. You mix them all which is wrong reasoning.
Can understand what I’m trying to tell you? If not, please, don’t invent yourself what I’m saying.
“there are a lot of confused ideas in the CTMU that just don’t make sense, even to people who are well-versed in mathematics, physics, logic, etc.”
Particularly in those people.
I should add why the expected utility and dominance principles are silly regarding Newcomb’s Paradox:
If we have a clear and black box, with $1000 and potential $1,000,000, respectively, I can do two things:
Dominance principle: This is ensuring a highest possible minimum utility, such as in Prisoner’s Dilemma when I always choose to defect because I can’t possibly get stuck in jail for ten years unless I choose to cooperate in the face of defection from the accomplice. So, in this case, dominance principle tells me to pick both boxes because ensuring $1000 is better than taking a risk and getting nothing. ($1,001,000 or $1000) [we take both] than ($1,000,000 or $0) [we take black].
Expected Utility:
If we assume the oracle is the real deal:
Choosing both boxes = 1000
Choosing clear box = 1000
Choosing black box = 1,000,000
If the oracle is full of it and has no prediction ability:
Choosing both boxes = 1000 + .5*1,000,000 = 501,000
Choosing clear box = 1000
Choosing black box = .5*1,000,000 = 500,000
Expected Utility (fusing both scenarios together, assuming the probability of BS is 50%):
Choosing both boxes = .5*1000 + .5*501,000 = 251,000
Choosing clear box = .5*1000 + .5*1000 = 1000
Choosing black box = .5*1,000,000 + .5*500,000 = 750,000
Here, expected utility hypothesis tells us that we are better off choosing the black box, whereas dominance tells us to pick both. This isn’t really a paradox here because this comes down to utility either way. Dominance principle is applicable if you’ve got a high risk-aversion profile, and expected utility hypothesis is applicable if you’re more of a risk-neutral kind of guy.
For instance, in Prisoner’s Dilemma, let’s say that instead of the following:
Mutual cooperation = 1 month punishment, defecting in the face of cooperation = no punishment, cooperating in the face of defection = 1 year punishment, and mutual defecting = 3 months punishment
We have this instead:
Mutual cooperation = 1 month punishment, defecting in the face of cooperation = no punishment, cooperating in the face of defection = 4 months punishment, and mutual defecting = 3 months punishment
Dominance strategy still tells us that defecting is optimal since (no punishment, 3 months) is better than (1 month, 4 months), but we may not use it. The downside to cooperating and being met with defection isn’t that much worse than the dominant strategy of mutual defection, so I am more willing to risk cooperating and locking in a lower 1 month punishment, and my accomplice would know the same. We’re more likely to cooperate because the downsides aren’t so extreme and we both get to reap the rewards of cooperation.
So, in other words, dominance strategy and expected utility hypothesis are still utility theories. Newcomb’s Paradox just tries to pit the two against each other because $1,000,000 is extreme compared to $1000, and $1000 is extreme compared to $0. It doesn’t matter if expected utility tells me what I can expect if I absolutely do not want to risk a particular downside.
But again, none of this has anything to do with whether or not the premises of the paradox are valid, themselves, which is why I didn’t bring any of it up before. It’s not necessary to invoke in order to explain why the paradox isn’t a paradox.
I mean, let’s say the clear box had a penny and the black box had either $0 or $1000 in it. We obviously wouldn’t bother taking both boxes because we don’t really care about missing out on a penny and if the oracle’s right then we miss out on $1000, and we do this even if dominance strategy tells us that ($1000.01, $0.01) is better than ($1000, $0).
If you want more depth about my previous informal explanation, you’re basically using the predicate exists_2 as
exists_2(x) = true, for all x
It’s not spectacular that you find inconsistencies defining set with it. You’re basically defining the set
{x : exists_2(x) } = {x : x }
So you’re defining the set containing all elements. That inconsistencies are well known. The axioms using that kind of sets are inconsistent.
So when you mix that predicate with our exists_1(x) predicate, you arrive at contradictions. The contradictions say nothing about the predicate exists_1, because they are already present using only exists_2.
But then again, if you understood my previous post, only exists_1 says something about reality.
You have all the information to judge again the theory under new light.
To answer Mr. Fringe’s qualm, I have used the verb “to exist” consistently. To demonstrate this, let’s take a look at your example of a chair. Suppose there is no chair in front of me. Then “the chair in front of me” does not exist. However, “the concept of the chair in front of me” does. These are two different things. Insinuating that the concept of a chair is the same as a chair is like insinuating that {{}} = {}: it is simply not the case. I am using the predicate exists(x) as true for all x in which x is a valid mathematical formula or well-defined mathematical object (as well as certain other x of course). For example, the Cantor set exists under my definition. However, a unicorn doesn’t (assuming that one can’t find a unicorn in reality), though pictures of unicorns and descriptions of unicorns do.
CausticDuality, yes, certain strategies apply to certain players, but that is not a complete resolution. A rational player would arguably see ND’s long streak of correct guesses as evidence that the Demon is a master of human nature, but it is indeed possible that one would not think this way. Also, coordinate systems have traditionally been linked with mind-body dualism since the time of Descartes. In placing absolute limits on the accuracy with which we can perform measurements on such coordinate systems, the HUP is a philosophical development as much as it is a mathematical or physical one.
A description *is* a model, and our rationality, our very perception, rests on models. If mathematics serves as a model for reality, reality is being embedded in a larger space of theorization, and it is this space that, existing and having reality embedded in it, becomes reality. Mathematical paradoxes are expressions of mistaken mathematics, not valid mathematics. The set concept itself is not restricted by the axioms of (e.g.) ZF set theory. Instead the uses to which it can be put are restricted.
My point is that the actual paradox itself is framed strangely to begin with. If we’re saying that ND is the real deal, then I don’t really have choice/free will by definition, if I can be predicted. Those two concepts are at complete odds with each other. Assuming the predictor is always right, then BOTH dominance and maximal expected utility theory tell me to pick the black box because $1,000,000 is more than $1,000. It wouldn’t even be possible to reap $1,001,000 because we can’t choose both boxes and have the black box contain money.
And yet, at the same time, the problem tries to tell me that since the money’s already been put into the boxes, I have free will and therefore if ND has placed money in the black box, he can’t take it back. Therefore the dominance strategy tells me I have a chance of reaping $1,000,100, thus generating an apparent contradiction with what I stated in the previous paragraph.
I say “apparent” because at the core, all you’re saying is “ND is infallible, and yet there’s a chance that he’s not,” which is also nonsense. If he’s infallible, then it doesn’t matter if he puts money in the black box or not because he already knows what I am going to do. And if he’s not infallible, then this contradicts a premise of the problem.
Therefore, even looking into expected utility theory is a waste of time because it doesn’t make sense to calculate probabilities for something if we’re being told that certain outcomes can’t happen. It doesn’t make sense to factor in, say, the possibility of gaining $1,001,000 if we’re being told up front that choosing both boxes will always yield us $1000 under an infallible predictor.
In other words, we’re being told that we’re being bound by some form of causality (whether forward or reverse) that is deterministic due to an infallible predictor, and yet at the same time we have free will that is somehow independent of an infallible predictor. You can’t have it both ways.
So it doesn’t do much good to say “Well, you have to show that free will can’t exist or prove that ND can’t exist.” ND *can* exist if we assume he has access to a sufficient amount of information about your decision-making processes ahead of time such that he can use that information to decide how to load the box — but then you cannot have free will by definition.
Besides, the evidence to date suggests that we don’t really have free will. We have the illusion of free will insofar as we are unaware of all the variables that are involved in our decision-making processes, and so we typically model a lack of such data as randomness. The more I know about your decision-making algorithms, the more variance I can explain. There’s no evidence suggesting that our decision making processes are anything BUT the result of the physical processes of the brain, and we know that physical processes can be predicted given sufficient depth of accuracy of information.
So, really, the paradox is resolved by saying if ND has sufficient deterministic information, he will predict what you choose and nothing you do will be able to stop it. Decision strategies go out the window since you are basically faced with $1000 versus $1,000,000, any any rational utility maximizer will choose the black box. But not to worry — even if you’re not rational, ND will know this, too.
Oh, almost forgot:
“In placing absolute limits on the accuracy with which we can perform measurements on such coordinate systems, the HUP is a philosophical development as much as it is a mathematical or physical one.”
Just because you call it a philosophical development doesn’t make it one. There’s nothing philosophical about HUP — it’s a physical concept that you can define mathematically:
(deltaX)*(deltaP) >= h-bar/2 from (deltaA)(deltaB) >= (1/2)*|| (the commutator) where A and B are canonically conjugate variables.
Wave packets follow this perfectly — it’s the result of not only empirical verification, but a derivation from the Schrodinger equation. It’s not “philosophical.”
For some reason the post ate my equation, lol (probably thought it was HTML or something)
Supposed to say (deltaA)(deltaB) >= (1/2)*|@[A,B]%|
Where % @ refer to > and <
The problem is that you’re taking “the existence of the concept ‘set of real objects'” as “the existence of the set of real objects”, and you don’t want to think deeper about it. Anything I say will not make you change your opinion. So the arguing is silly.
I’ll rest my case on time. In science when argumentation does not work, one has to rest on observation or experimentation.
Thirty years from now, I’ll take a look at this theory, if it still exists. During this period, I invite you to spend as much time developing it as you can. If you can spend all your time developing its important applications, the rest of us will be happy 🙂
> “I am using the predicate exists(x) as true for all x in which x is a valid mathematical formula or well-defined mathematical object”
The funny and ironic issue is he is actually signaling what’s wrong with his arguments.
The problem here is that the set {x : exists(x)} is not a well-defined mathematical object. You can not even define its universe of discourse (at least, not recursively). And a lot of people here has point this sloppy use of language. For example, CausticDuality, and of course, MarkCC.
Just because you say something is well defined it is not. I’d advise you to go learn something about sets.
By the way, the fact that {x : exists(x)} is not a well-defined is a very well known fact. It’s not something new.
You just use the expression “well-defined mathematical object” too happily, too informally. As everything you use.
I desisted because, for any explanation, you came with an answer with ten sloppy language uses and ten made up facts. Too much. If I point your problems, you return with a hundred. Exponential bad logic. Sincerously, it’s impossible. Sloppy language, made up facts and a layer of apparent logic is indiscutible.
So I take the Langan approach: your arguments are silly, easily refutable, I could refute them with my eyes closed, but I’m not going to. If it’s right for him, it’s right for me.
The only judge will be people and time.
Anyways, my general point is that if Chris wishes to be understood better, he absolutely needs to be clearer in his writing and he needs to use jargon correctly.
While some aspects of the CTMU make sense, a majority of it does come across as word salad, to mirror MarkCC’s comment. It’s like tossing a bunch of disjoint ideas together in a blender and hoping that something will make sense out of it to someone. And if it doesn’t make sense to you, or if it comes across as nonsense, “you’re just not competent enough to understand it.”
Chris, if you’re still reading, this is what it feels like to read the CTMU:
“When we consider the Hamiltonian invariant operator of X(Qo, c, S) mapped onto a continuous manifold of invertible metacognition functions we can show that the mind-body duality inherent in the utility definitions are rendered invalidated as a result of a contradiction in the self-inclusive computation of binary syntax. Given behavior function F with Hermitian operators/attributes, let its iterative states be analogous to the path-vector of conspansive recursion, but only in accordance with the regressive nature of one-to-one transmutation with respect to the Lagrangian multipliers for each element of the universal set. Cellular automata in the cognition states therefore become time-dilated but with a skew-normal distribution of relativistic identities.”
I mean, it just doesn’t make any sense. The way you use certain mathematical arguments/scientific jargon is not going to sit well with people who have spent years in their fields and are well-acquainted with what the jargon means versus what it doesn’t mean, and when certain models apply versus when they’re ill-fitted.
Personally, I don’t think we get anywhere by trying to stuff the universe into a “set.” Even if you have a set that defines all the real-valued operators/measurables in the universe, it doesn’t mean it’s self-inclusive.
> “When we consider the Hamiltonian invariant operator of X(Qo, c, S) mapped […]”
😮 You really need some kind of talent to write that. It feels true so authentic (crankery)!
I agree that that paragraph is quite cranky.
I wish to have somewhat more time off during my summer break, so I am going to stop replying to the debate soon, probably after this comment.
CausticDuality, if there is one thing you should get from the beginning of that essay, it is that Mr. Langan doesn’t believe describing the universe as a set does it justice either. As for its allegedly not being self-inclusive, I beg to differ. The sentence, “The real universe contains all and only that which is real,” is indeed tautological as “real universe” is predicated on “real” and “real” is defined on inclusion in “the real universe”. (I hope this answers Mr. Fringe’s earlier objection!) Being tautological, it reflects a truth that led Mr. Langan to note that the real universe topologically contains that which descriptively contains the real universe.
To the extent that coordinate systems are mathematical representations of mind-body dualism, it has always been entwined with philosophy regardless of its being traditionally mathematically described. As for Newcomb’s paradox, the formulation you offer here is pretty much an outline of a proper resolution to the paradox. One just has to prove from here that ND can determine our actions and that this is likely.
Well, it’s been fun. Have nice lives.
Hi Chris,
I am one of your supporters. I do think you should become more familiar with Godel’s Incompleteness Theorem as it is very relevant to your area of research. perhaps you are already familiar with it but I don’t see any mention of it in your writings and commentary.
Well, we all know what tautologies say — nothing new.
As for mind-body dualism, it’s already a pretty flimsy concept to begin with when we already understand that the mind IS the brain, and the brain is physically bound just like everything else.
> The sentence, “The real universe contains all and only that which is real,” is indeed tautological as “real universe” is predicated on “real” and “real” is defined on inclusion in “the real universe”. (I hope this answers Mr. Fringe’s earlier objection!)
Yes, it answers my objection as much as “the real blue chair in front of you if blue and real”, which predicates that chair to be real and blue, proves it exists. I’ve just proved that there is a blue chair in front of you, because I call it real and blue!
Just because you defined something with the name “the real universe” does not make it real. You have a string belief in your words, but sorry: the fact that you say something does not make it so. Sorry again.
Didn’t we already discussed this? Deja vu? Proof by insistence? Exponential bad logic with circular argumentation? Noooooooo……!
You can define “the blue chair” as “what there is in front of you”.
Or you can define “blue” as the perception you have when certain radiation of certain frequency hits your eye.
What you can not do is to define “blue chair” to be what you’ve got in front of you, and “blue” as the perception above, and them expecting the thing in front of you to be blue according to the second meaning just because you “defined” it in the previous sentence.
You can define what a “blue chair” is, but not if you have a previous definition of “blue”. If you have one, then your definition of “blue chair” should be compatible.
That’s what the situation. Your “real universe” is not real in other sense just because you’ve put a word “real” before it. If you’ve got a previous definition of “real”, you have to prove your concept of “universe” to be real before calling it “real universe”. If you do not, you can call it “real universe”, but it’s not real in the other meaning.
The discussion followed an tortuous path, and we arrived at this: your definition of real for concept is “well defined mathematical object”.
But then you can not call the set {x : real(x)} real, because it is not a well defined mathematical object. What’s its universe of discourse? You can not define it.
Well, you can, because with relaxed language you can say “it’s the set of mathematical concepts, well and wrong defined”.
But of course that’s not a formal definition. You need to have a well-defined universe of discourse to well-define a set with a predicate. This is probably not something you don’t know, (you don’t seem to know very much about reasoning or logic), but I’m sure you’ll be able to find information about it. To learn is always good, no shame in that.
So we’re again in the same situation: you don’t have any meaning for “real(x)”. You are just mixing a lot of informal incompatible meanings, in the hope nobody notices.
(The shame is in repeating the same refuted arguments).
I read this stuff slightly after Langan’s last reply, and really don’t know which side to take. I spent a couple of years developing a similar theory, and I’m not sure whether Langan knows everything that I know. I’d like to contact Langan, but don’t know how.
Wikipedia quotes Chris Langan as saying: “Biblical accounts of the genesis of our world and species are true but metaphorical.” I guess the same could be said of CTMU, at least in a metaphorical sense. If I’m able to contact Langan, I’ll give him our article containing a formalization of the idea behind Diamond Sutra and Carnap’s Überwindung. It was subjected to peer review but rejected as obvious, which it certainly wasn’t for me. In any case, Langan doesn’t address the issue in The CTMU: A new kind of reality theory. The issue is often ignored in metaphysical texts, but in this kind of a work it should not be.
In any case, telic recursion is the kind of a concept some people would need. If the concept were usable, epistemologists trying to solve the problem of induction would use it to create a feasible concept of relevance. For more information, see Jüri Eintalu, The Problem of Induction: the Presuppositions Revisited (2001). It is not in any way silly that Langan attempts to create such a concept. To me, it is much sillier that people, who are aware of the things we pointed out in our rejected paper, even ask for such a concept.
The issue I previously mentioned is about ontology being bound to language. According to CTMU, reality is SCSPL, that is, Self-Configuring Self-Processing Language.
In ontology, it is quite valid to make theories that emphasize: “All reality is X”. Here X is, for example, “matter”. But it is much less valid to make theories that emphasize: “All reality is X, and all other ontology is wrong.” Except if you are not an ontologist, and instead, for example, a physicist. In that case nobody cares what you say about ontology, unless it is weird. You might even get an award for writing a book containing inferior ontological insight, if the non-ontological content were good. This was the case with Kari Enqvist, who was awarded the Tieto-Finlandia for his book Olemisen porteilla, which emphasized: “All reality is matter, and all other ontology is wrong”. Simply put, the book had a part of physics that was good, and a part of ontology that was bad, and nobody cared about the ontological part. Maybe ontology ranks low. In any case, this is highly confusing, as it gives the impression that an invalid way of making ontology is valid.
Our rejected article was long, full of formulae, and in Finnish, so I’ll just try to summarize. We pointed out that it is commonplace in philosophy to talk of “reality”, “the truth” or “all that exists” as if that concept would be universal in the sense that if you take materialism as axiomatic, and in this system talk of “all that exists”, and then you switch to idealism, and keep talking of “all that exists”, you are talking of the same thing. Many people write things that seem to imply this is ok, but it’s not. The theory shapes the concepts, and treating concepts as if their exact meaning would be the same in any theory is similar to, or maybe even equivalent with, having a contradiction in the metatheory that spans both theories.
Chris Langan is trying to overcome this limitation, that is, the state of affairs that ontology is bound to language. I tried to do the same thing, because I did not for a moment consider that it could be impossible. I changed my mind only when a friend advised me to read the Diamond Sutra. After that the very existence of ontology seemed frivolous to me, and I still don’t understand why anyone would consider it interesting, but some do. I see Langan failing the same way as I did, except that he’s not aware of doing that. Of course it would be great if I’m wrong, but Langan needs to address this concern if he’d like to win my support.
But it’s quite simple that reality is not SCSPL for someone who does not think that way. That actually sums up everything I wanted to say about CTMU in particular. If you want to go beyond language, stop writing. Scrap philosophy. Live your life. In any case, that’s what I began to do.
I’d still like to emphasize that I don’t consider CTMU any more ridiculous than the rest of ontology, and in fact it could be a bit less ridiculous than ontology on average.
He claims to be closer to absolute truth than any man before him.
I think that the attacks on Chris Langan are off the mark. I admit that I haven’t studied CTMU in much detail but the gist of his paper seems to me to be similar to the ideas behind Godel’s Incompleteness theorems (self describing language). I don’t think Mr. Langan references Godel and I suspect he has rediscovered Godel’s Incompleteness Theorem, albeit in a less rigorous form. The genius of Mr. Langan is to realize that these ideas are not mere mathematical formalism but rather describe reality initimately. In other words, Godel’s Incompleteness Theorem is not just some interesting result concerning Set Theory but rather are the foundation of reality itself because reality is just a mathematical set . He advances the notion that physicality and abstract mathematics are fundamentally equivalent. Indeed, physicality is an emergent phenomenon from abstract set theory rather then abstract Set Theory simply describing reality.
I don’t think Langan could be uncivilized enough to not know of Gödel’s work, because it is of such great importance. The Metaphysics of Quality by Robert Pirsig is a similar, and in my opinion, currently somewhat more usable version of CTMU. The MOQ, too, features a mechanism that could be considered an informal generalization of Gödel’s incompleteness theorem, and it is of essential importance.
Unlike the CTMU, the MOQ is occasionally taken seriously in the academy. But the latter has been around for decades, and the first book describing it was an artistic masterpiece and a best seller. The same can’t be said of CTMU, but the amount of theoretical detail is indeed intriguing, and could facilitate the development of a theory that outperforms the MOQ in some ways.
I’m a bit suspicious of your last sentence, though. Seems too dualistic to fit what is my first impression of the spirit of the CTMU.
Due to Godelian Incompleteness a formal system that can describe the integers is able to generate truths that are not provable within that system. This is what I mean when I say that physicality is an emergent phenomenon from a more abstract substrate of reality. I think that the physical universe owes its existence to Godel’s Incompleteness theorems and I suspect that’s what the CTMU is really all about.
OK, I get it. And if I don’t, surely someone will point that out and call me a poopyhead(PH).
Legal disclaimer: I’m not the smartest person in the room or the most credentialed.
My paraphrase of others’ descriptions of Lagan’s argument (I admit, I found his verbiage pretty impenetrable (see disclaimer)):
1) Reality is a set, the set containing everything that is real.
2) Reality as a set has a powerset (the set of all subsets of reality and reality itself.)
3) Reality’s powerset is a real thing and therefore contained by reality.
Contradiction ensues as a) reality is bigger than (contains) its (real) powerset and b) the powerset is bigger because it contains reality. Recursion makes a bigger powerset (including reality and its real powerset) then bigger (reality, its powerset and the powerset of both) ad-forevermore. Lagan offers some resolution to this contradiction involving many big words at which point my eyes glazed. I think he proved that black is white and should look out at the next zebra crossing he encounters.
This recursion requires that each powerset be real (to be contained by reality.) But in what sense can a powerset be considered to be real?
If it is in the sense of a Platonic Ideal, I don’t think we’ve found them anywhere and CTMU becomes another footnote to Aristotle.
If it is real in the sense of being encoded in the stuff of the Universe, matter and its configurations; e.g. text on a page, configurations of ions in my son’s brain or written in thirty-foot-high letters of fire on top of the Quentulus Quazgar Mountains, then eventually you run out of Universe to encode it and the largest possible powerset is NOT larger than reality. The largest possible powerset is simply the largest powerset which can be encoded in the stuff of a finite Universe. Cantor’s diagonal fails and the recursion stops.
There is no paradox in a finite Universe and the rest of Lagan’s extrapolations are not required. However, two plus two DOES equal five and I AM the Queen of England.
The universal set (the set which contains all objects including itself) does not lead to contradiction in New Foundations set theory. I’m not an expert in neither the CTMU nor NF, but both mention stratification, which is apparently related to NF having a universal set.
Long live the Queen! 🙂
Thank you John Fringe. Please consider yourself knighted.
I’m not a philosopher, and much of the previous comments go way past me, but I get the impression that we’re confusing two different concepts of real here. My apologies if this has been discussed before, this thread is getting rather weighty.
#1. The apple on my desk is real, it exists, I can point at it, I can grab it, and once I eat it it will cease to exist.
#2. The set of apples (or any other mathematical construct) is real, it exists, however it does not exist in the same sense as the apple described above. It is an abstract notion that exists inside our heads, which we use to reason about the universe around us. When we say it exists, we mean it is well defined, it does not lead to logical contradictions. In that same sense, for example, the largest prime number does not exist. I’m using reality and existence interchangeably here.
When we talk about the universe as the set of all real objects, I think we’re using the first concept of real. When we talk about subsets of this set, or its powerset, these objects are real by the second definition.
In any discussion of reality as a set, you’ll have to define what you mean by real, and what you mean by set (as in, what set theory do you use if its not the standard one.) I’ve seen some discussion here on the set theories, but none on the definition of real thats used.
“When we talk about the universe as the set of all real objects, I think we’re using the first concept of real. When we talk about subsets of this set, or its powerset, these objects are real by the second definition.”
Why?
“Why?”
I can point to my apple (well, not anymore actually, since I ate it…), I cannot point to the set of apples, or the number three, or any other abstract concept.
Its the basic difference between something which is observable and an abstract concept which only exists in our minds.
Now I suspect you’re going to make the point that anything we observe only exists as an abstraction within our visual cortex or something like that. I wouldn’t know how to respond to that except to say that it will still be just as important to define what you mean by “real”.
That’s just the point. According to Langan, and i agree with him, physicality is not more real than abstraction. The opposite is true. Physicality emerges from an abstract substrate of reality. Physical objects seem to us to be the only “real” things simply becasue we are ourselves physical beings and therefore place the infrastucture of our existence at the pinnacle of what is “real”. We are biased.
@Robert
I almost completely agree with you, only disagreing in one little detail. You said
“When we say it exists, we mean it is well defined, it does not lead to logical contradictions.”
No, Langan does not requires a concept to be well defined and contradiction free to call it “real” in this second meaning. He only requires you can speak vaguely enunciate it.
For example, he says the set containing all the sets is real, when we all know it’s not well-defined and it leads to contradictions.
His second meaning for “real” is more relaxed than you’re supposing.
The set containing all sets including itself is not well-defined in ZFC set theory, but is well defined in NF set theroy. See Wikipedia. I don’t think CTMU is based on ZFC.
Great, because Langan uses the fact that it leads to a contradiction. So we have two options here:
– He speaks under the assumption of a set theory where the set of all sets leads to a contradiction. Then he uses “real” as I described, and the theory is meaningless.
– He speaks under the assumption of a set theory where the set of all sets does not lead to a contradiction, as you propose. Congratulations, you’ve proved the wrongness of his theory again, because he uses that fact in his proofs.
I consider that funny.
By that reasoning, the largest prime number also exists or is real, since we can enunciate the concept.
Exactly, I agree with you again. The largest prime exists, the set of all sets exists, and everything exists under his axioms or initial assumptions.
But that’s nothing surprising: if you start with an inconsistent set of axioms, you can infer anything you want. That’s a well known fact.
Wrong. There is a proof that the largest prime number does not exist.
You probably missed the “by that reasoning” part.
The spirit of the CTMU could be that the largest prime number is the largest one that is actually being used. While it is possible to find even larger prime numbers, they have not yet been found. Prime numbers being important in cryptography, it is actually reasonable to talk of the largest prime number, that is, the largest that has yet been found. Also, even in a mathematical point of view, the “largest prime number” does exist as an object whose extension is empty.
Universal set with a contradiction could be something one comes up with, if he tries to somehow ignore or bypass the fact that ontology is bound to language. I’m not sure whether Langan is trying to do something like this, but the theory supposedly being an informal generalization of the incompleteness theorems would support this idea. The theory may attempt to conceptually contain things formal logic cannot contain.
In any case, if Langan himself acknowledges that the universal set leads to contradiction, pointing that fact out again and again amounts to nothing more that mutual back-patting among those who disagree with him. If you want to actually challenge Langan, you have to do something else. You have to figure out what his goal is, and make the argument that the goal cannot be reached.
So, if I want to challenge Langan, I should make an argument showing that his goal can not be reached? Are you serious?
Langan says he has proved the existence of god mathematically.
> “Can a denial of God be refuted by rational or empirical means? The short answer is yes; the refutation follows the reasoning outlined above.”
If I say his proof is nonsense, you say what I should do is to make an argument against the possibility of proving the existence of god. Why? I could even not think so! I mean, I could actually believe you can prove god’s existence and still say Langan’s proof is nonsense. I’m not saying I believe you can prove that, nor am I saying you can not. I’m simply saying you’re asking us to talk about something else. Why should we? What we’re saying is clear: Langan’s theory is nonsense. Point. His goals I don’t know.
It’s even worse. What if his goal is to get famous and make a living without work too much by convincing people he’s the next Einstein and creating a lucrative society? Be carefull, I’m not saying he’s actually doing this, but sorry, it’s a possibility. If his goal were this, should I make the argumentation that his goal cannot be reached? Despite me believing it’s perfectly possible to reach it?
Are you serious? Should we argue another independent subject?
Chris Langan has created a “theory” that has about as much usefulness as the ramblings on a Dr Bronner’s soap bottle…
I heard about CTMU through the Atheist Experience podcast so I was curious about what the argument is. As a layperson, 99% of the discussion here went over my head. I tried to follow it as best I could.
Is CTMU basically arguing the following?
We exist in the universe and the universe is us but not wholly us. The universe includes everything that is real. Concepts are real. Because we conceive of the concept of a god, god is part of the universe and real?
I am sure I have that totally wrong.
What do you guys think about what he says about souls and reincarnation? From the Q&A on his website:
http://megafoundation.org/CTMU/Q&A/Archive.html
Q: Does the CTMU allow for the existence of souls and reincarnation?
A: From the CTMU, there emerge multiple levels of consciousness. Human temporal consciousness is the level with which we’re familiar; global (parallel) consciousness is that of the universe as a whole. The soul is the connection between the two…the embedment of the former in the latter.
In the CTMU, reality is viewed as a profoundly self-contained, self-referential kind of “language”, and languages have syntaxes. Because self-reference is an abstract generalization of consciousness – consciousness is the attribute by virtue of which we possess self-awareness – conscious agents are “sublanguages” possessing their own cognitive syntaxes. Now, global consciousness is based on a complete cognitive syntax in which our own incomplete syntax can be embedded, and this makes human consciousness transparent to it; in contrast, our ability to access the global level is restricted due to our syntactic limitations.
Thus, while we are transparent to the global syntax of the global conscious agency “God”, we cannot see everything that God can see. Whereas God perceives one total act of creation in a parallel distributed fashion, with everything in perfect superposition, we are localized in spacetime and perceive reality only in a succession of locally creative moments. This parallelism has powerful implications. When a human being dies, his entire history remains embedded in the timeless level of consciousness…the Deic level. In that sense, he or she is preserved by virtue of his or her “soul”. And since the universe is a self-refining entity, that which is teleologically valid in the informational construct called “you” may be locally re-injected or redistributed in spacetime. In principle, this could be a recombinative process, with the essences of many people combining in a set of local injections or “reincarnations” (this could lead to strange effects…e.g., a single person remembering simultaneous “past lifetimes”).
In addition, an individual human sublanguage might be vectored into an alternate domain dynamically connected to its existence in spacetime. In this scenario, the entity would emerge into an alternate reality based on the interaction between her local level of consciousness and the global level embedding it…i.e., based on the state of her “soul” as just defined. This may be the origin of beliefs regarding heaven, hell, purgatory, limbo and other spiritual realms. – Chris Langan
—————————————–
He also seems to believe that we can lose our “souls” for doing evil.
Q: Given my own self-awareness and inability to separate from reality, *I* have no doubt that this reality *does* exist (the proof is in the pudding). So while I do not need “proof” that there is a reality, that I am part of that reality, and that my awareness is reality’s awareness of itself – I do not know WHY all of this stuff exists (myself included).
If there *is* a reason that reality MUST exist, then that would also be the reason that *I* exist. Which is probably what I am really wondering. Is the answer that giving myself a reason to exist is the reason for my existence? – Bill
A: The first part of your “why” question is answered at the end of the above response to Celia. Since the meaning of life is a topic that has often been claimed by religion, we’ll attempt to answer the second part with a bit of CTMU-style “logical theology”.
Within each SCSPL system, subsystems sharing critical aspects of global structure will also manifest the self-configuration imperative of their inclusive SCSPL; that is, they exist for the purpose of self-actualization or self-configuration, and in self-configuring, contribute to the Self-configuration of the SCSPL as a whole. Human beings are such subsystems. The “purpose” of their lives, and the “meaning” of their existences, is therefore to self-actualize in a way consistent with global Self-actualization or teleology…i.e., in a way that maximizes global utility, including the utility of their fellow subsystems. Their existential justification is to help the universe, AKA God, express its nature in a positive and Self-beneficial way.
If they do so, then their “souls”, or relationships to the overall System (“God”), attain a state of grace and partake of Systemic timelessness (“life eternal”). If, on the other hand, they do not – if they give themselves over to habitual selfishness at the expense of others and the future of their species – then they are teleologically devalued and must repair their connections with the System in order to remain a viable part of it. And if they do even worse, intentionally scarring the teleological ledger with a massive net loss of global utility, then unless they pursue redemption with such sincerety that their intense desire for forgiveness literally purges their souls, they face spiritual interdiction for the sake of teleological integrity.
Such is the economy of human existence. Much of what we have been taught by organized religions is based on the illogical literalization of metaphorical aspects of their respective doctrines. But this much of it is true: we can attain a state of grace; we can draw near to God and partake of His eternal nature; we can fall from God’s grace; we can lose our souls for doing evil. In all cases, we are unequivocally answerable to the System that grants and sustains our existence, and doing right by that System and its contents, including other subsystems like ourselves, is why we exist. Sometimes, “doing right” simply means making the best of a bad situation without needlessly propagating one’s own misfortune to others; the necessary sufferance and nonpropagation of personal misfortune is also a source of grace. Further deontological insight requires an analysis of teleology and the extraction of its ethical implications.
Now for a couple of qualifiers. Because we are free, the teleologically consistent meaning of our lives is to some extent ours to choose, and is thus partially invested in the search for meaning itself. So the answer to the last part of your question is “yes, determining the details of your specific teleologically-consistent reason to exist is part of the reason for your existence”. Secondly, because God is the cosmos and the human mind is a microcosm, we are to some extent our own judges. But this doesn’t mean that we can summarily pardon ourselves for all of our sins; it simply means that we help to determine the system according to whose intrinsic criteria our value is ultimately determined. It is important for each of us to accept both of these ethical responsibilities. – Chris Langan
That’s the whole point.
As we’re seing, even the most elemental deductions of his theory have lots of problems. They’re simply illogical. Yet he expects to convince people he made incredibly complex deductions and proved souls exists mathematically. This time without errors.
That’s too much.
I find it curious how a lot of people is carried away by complicated words and hard-to-follow arguments, and maybe the promise of a superior intelligence. That’s the first trick in the little crank’s manual.
Anyone who is actually educated enough to understand the jargon and are well-versed in mathematics, physics, and philosophy typically see right through the crackpottery.
I wonder how well Langan *actually* understands, say, evolution or the cosmological timeline/the Big Bang. Does he understand concepts like abiogenesis? Quantum physics? Something tells me “I severely doubt it.”
I’m going to be severely disappointed if he turns out to be a crank.
He is not a crank. His theory is not useful to the point where one can make physical or mathematical predictions from it but the ideas it is very profound.
“His theory is not useful to the point where one can make physical or mathematical predictions from it but the ideas it is very profound.”
Profundity is subjective…
Supposedly, if I am to believe Chris’s press releases, he is smarter than Einstein and Newton.
Yet Einstein and Newton’s contributions to the world were understandable and recognizable as significant advancements by their peers. Chris’s “theory” is neither of those things…
Einstein came up with his theories in a patent office, while Newton holed himself up in his castle for a few years and *POOF* calculus. (Newton also tried his entire life to turn lead into gold… which just goes to show that being REALLY smart is not a panacea for being REALLY stupid.)
Seriously, if I had a nickle for every time I came up with a “profound” idea after a few bong rips, sitting on my porch then I would have about $77.45… you couldn’t make any physical or mathematical predictions from those either.
Seriously, Chris’s vast hubris is his Achilles Heel – he should go to school and SUBMIT to being TAUGHT.
Suppose Newton realized that what makes an apple fall to the ground is the same thing that keeps the moon in orbit but then did not take that idea any further. No Calculus, no mathematical formalism to make predictions etc.. Would you not then conclude that he had come up with a profound idea but could not make any testable predictions?
That’s what I mean by profundity without testability.
It surprises me how people concede that much importance to saying things with conviction but without evidence, and so little importance to the hard work of proving and developing things.
To propose hypotheses without evidence is not profound.
The fact is this: If Newton had made what you say, his work would be of no importance. You would not have heard of Newton, so you would not be able to propose this example.
In fact, many people invented (and invent even today) their own “theories” about gravitation.
This is called imagination, and it’s not profound. They are not correct, not wrong. They’re just imagination.
And to defend such an hypothesis without supporting evidence is cranky behavior.
If you have such a theory, the first step to defend it is to look for evidence. To convince you first, or to prove it wrong. When you’re convinced by evidence, you can take step two: to convince people.
The problem is this requires work. Hard work. Not many people are willing to. Not many people value it (you’ve got the proof here).
So I repeat: to propose hypotheses without evidence is not profound. It happens every day, millions of times.
(Well, in this situation at least Newton would not have said anything contradictory in itself.)
Just one question: do you consider Aristle’s idea of heavier bodies falling faster a profound idea?
I mean, we now know it’s false, but when Aristle proposed it he offered no supporting evidence, just as you say.
Is it a profound idea?
Arrgh, I hate keyboards. I meant “Aristotle”.
Hi John
I do not consider Aristotle’s ideas to be profound because he simply voiced what was the common person’s belief at the time. There was nothing counter intuitive or unusual about his ideas. To believe that heavier objects fall faster than lighter objects is the default intuition of most of humanity. Aristotle did not produce a leap of intuition. On the other hand, Newton’s intuitive leap was very counter intuitive.
You said that to be considered a profound thinker in science one must not only have a great idea but must also work out the technical fruit that arises from that idea. What about Copernicus? He had a great counter intuitive leap but did not produce anything testable. Yet, he is honoured to this day as one of the founders of the scientific enlightment.
What about String Theory that makes no testable predictions?
Copernicus work was based on observations. The Heliocentric model worked. He actually checked his theory. You chose a bad example.
I don’t believe string theory ideas to be profound. No, they’re interesting. So interesting a lot of people is spending time developing it.
But these people know very well the state of the theory. They know it’s only an speculation. In fact, most interest seems to be mathematical, rather than a purely physical.
Nobody will be that much surprised if no connection with reality is found. And nobody will remember the theory in a few decades.
You too can spend time developing Langan’s “theory”, if you find it promising or interesting. You can look to develop some profound results. But to do so you must know what its current status is.
John, at the time that Copernicus lived the Heliocentric model of the universe produced no better fit to observation than did Ptolemy’s Epicycles theory. To prefer the Heliocentric model over the Epicycles model was due to philosophical considerations (Occam’s Razor) rather than any empirical or mathematical considerations. Copernicus had a profound intuitive leap that he could not confirm by observations or mathematical formalism. My example stands.
Being of equal fit, Copernicus model was accepted because it was practical, not for philosophical reasons.
I don’t see how your example stands. You said:
“What about Copernicus? He had a great counter intuitive leap but did not produce anything testable. Yet, he is honoured to this day as one of the founders of the scientific enlightment.”
You say he produced nothing testable, yet you admit he proposed an hypothesis and it produced results that fit the observational data. Not only his theory was testable, it was tested and it fit the data.
Am I missing something?
I mean, it was your example of a non-testable idea you called profound.
But it was testable. Yes, the previous model was also testable and it also fit the data. But that does not mean Copernicus’s model wasn’t testable. It was.
Copernicus profound idea was: we are not the center of the Universe, we’re not so special. But it worked!
If it hadn’t worked, if it hadn’t been checked and verified, you will not know who Copernicus was.
So I still believe it’s not a valid example of someone producing non-testable hypothesis being considered a great thinker. Which was the motivation of your example. Because it was testable.
John, all I’m saying is that the role of intuition plays a very important role in the advancement of science, particularly Theoretical Physics. I agree with you that any profound idea must be tested to be considered of relevance but the testing need not be done by the originator of the idea and the testing and verification might be completed many years later. Hypothetically, had Newton just proposed his intuitive leap but left it for someone else to eventually leverage it into a falsifiable theory he would still be remembered to this day, albeit in a lesser light.
Newton, Einstein and many other scientific luminaries began their scientific journeys with leaps of intuition that were born of something other than mathematical formalism or the conventions of logic. What do you mean by saying that the Heliocentric model appealed to Copernicus due to practicality? Are you implying that Copernicus favoured the Heliocentric model because it was a simpler model? If so then we are basically saying the same thing at a supeficial level but differ widely at a philosophical level. I think that the role of beauty and elegance plays a central role in the impetus towards ground breaking scientific theories, particularly Theoretical Physics.
Correct me if I’m wrong but I think that you consider the scientific enterprise to be a purely pragmatic one where great theories are constructed solely by the tools offered within said enterprise. I diverge from this way of thinking by proposing that truly ground breaking theories require something from outside their universe of discourse. This externality takes the form of intuitive leaps that are powered by a yearning for beauty and elegance. Please don’t understimate this factor in shaping Theoretical Physics.
How does all this relate to our initial disagreement? I propose that those in the scientific community who originate intuitive leaps born from a sense of beauty and elegance also have a role in the scientific enterprise. This is true even if they are not the ones who eventually leverage these leaps of intuition into falsifiable theories.
By the way, I completely agree with you that String Theory is an abomination.
> “I completely agree with you that String Theory is an abomination.”
Oh, a misunderstanding here, sorry. You can’t agree with me that String Theory is an abomination, because I don’t think so.
Well, we disagree in two points. The first one is the importance we assign to promising ideas. The second is the responsibility of the original thinker.
> “I think that you consider the scientific enterprise to be a purely pragmatic one where great theories are constructed solely by the tools offered within said enterprise.”
No, not at all. I’m not so far from reality. I understand the process by which an idea becomes a theory. I mean, someone somewhere has an intuition, which leads to an idea, which leads to an hypothesis, which blah blah. I know, I agree. I know we people do not think in equations. I don’t understimate the intuition. It’s very important. That’s not what I’m talking about.
But you should not fool yourself. When you have an idea you believe it’s promising, all you have is a promising idea. Nothing more, nothing else. A possible _profound_ idea. But you can not know if it’s a profound idea until… well, until someone check it.
Can a false idea be profound? I don’t believe so. Was the man as the center of the Universe profound? Was aether profound? The existence of an absolute space?
Do you believe false ideas can be profound?
Maybe what you call profound I call interesting or promising. But if an idea is interesting or not is a subjetive matter. A promising idea is, again, potentially valuable, but maybe it has no value at the end. I have no problem with you saying “I find Langan’s ideas interesting”. I may not know what you find interesting, but that doesn’t matter. That’s subjetive.
To sum up: one thing is to find interesting unproved theories, and other thing is to take unproven theories aa truth just because you like them. That’s not science. You can guess they’re true, but you really should be aware you do not know. That’s the place of intuition in science. Yes, very important, but not what you’re saying.
With respect to the second point, I expect the proponent of a theory to try to check the theory. By several reasons (why does he divulgue the theory, why does he believe it to be true if he doesn’t try to refute it, as a way to respect others time,…), but one is specially relevant: if you have a theory, an idea, you really consider interesting, you will be the first _interested_ in knowing if it’s true.
Of course, the proponent may not manage to prove the theory. But then he should be aware of the situation: he’s theory is unproven, and potentially false. At least he may contribute to the final proof, and people will recognize that.
What you can not do is to try to convince people you have a proven theory when you have none.
This is what Langan is doing. Of course, he may not see he’s proof is incorrect. That’s why people discuss this.
Finally, Copernicus.
> Are you implying that Copernicus favoured the Heliocentric model because it was a simpler model?
Right, I’m implying exactly that. Yes, he favored the Heliocentric model because it was simpler. But that’s not the whole story.
Copernicus made two contributions. One was a method to compute celestial movement. The interest of this model lies in its simplicity and practicality. This doesn’t make the previous model invalid. You can still compute celestial movement by previous models. Why do we use heliocentrism? Because it’s practical. This theory was provable, and fit the data.
The second contribution was more important. By proposing an alternative model he proved you could compute celestial motion without taking anything related to humanity into account. Previously, to compute Jupiter’s movement you have to refer the computations to the Earth, man’s home. Now you can do it without man. So humanity has no special role in the Universe, at least in its motion. This does not favour the Sun with respect to the Earth. It’s the existence of alternative models without a special role for man what makes it relevant. Any alternative model.
And this is also testable. You can actually check if you can predict (or postdict) Jupiter’s movement without taking anything man-related into account.
So all of Copernicus’ ideas where testable, they were checked right, and heliocentrism is preferred because its practicality.
John, I don’t appreciate your mocking tone. Is this how you choose to participate in a debate? I said no such thing. I simply said that all great theories must start with an intuitive leap, not that an intuitibe leap is all there need be to a theory.
I no longer wish to engage in any debate with you.
My comment above was placed under the wrong thread. Please disregard.
On a slight side note…
According to some biographers, the apple story never happened and was invented after the fact. Furthermore, Hooke came up with the inverse square law independently of Newton but was unable to do the necessary calculations. We remember Newton, and not Hooke, precisely because of this.
Personally, I think Newton’s genius lies not in the ‘intuitive leap’ of the inverse square law. That idea had been floating around for a while, but in the fact that he developed the tools (calculus) to prove that an inverse square law yields elliptic orbits.
In fact, Newton was famous for his “hypotheses non fingo” (I feign no hypotheses), so the whole history of Newton being famous for saying that without checking it before is a bit manipulative.
John, you could equally say that anyone who arrives at incorrect scientific conclusions solely based on logic and equations will also be absent from the annals of scientific history. This is not just a verdict against the role of intuition in science.
My position is that the faculty for intuitive leaps in making correct scientific conclusions is an ability cultivated in some people that diverges from statistical randomness. It is an actual ability whose source I will not speculate on. I will even go as far as to claim that these intuitive leaps are an absolute must otherwise Physics and Astronomy/Cosmology can only produce a collection of ad hoc equations that simply fit the known data without any internal motivation or understanding. Kepler’s equations are a great example of this. Only Newton’s intuitive leap (the apple story) could pave a road towards understanding why Kepler’s equations describe the motion of the heavenly bodies.
Yes, because if you say something by intuition it has the same validity and the same probability to be true that if you say something you have actually checked.
And the probability to be wrong by strict formal deduction is the same as by intuition.
OMG.
Well, nothing more to add.
I don’t appreciate your mocking tone. This is not how to participate in a debate. I said no such thing. I simply said that all great theories must start with an intuitive leap, not that an intuitive leap is all there need be to a theory.
Good bye sir.
Wow, that’s sensitive!
1) “I simply said that all great theories must start with an intuitive leap”
Oh, no. You know that’s not true. That’s the part we all agree with. You said more. It’s written.
a) Langan’s ideas are profound
b) We can know when unproven ideas are profound (as Langan’s)
c) There are scientists, like Copernicus, which are recognized for untested theories.
d) “The faculty for intuitive leaps in making correct scientific conclusions is an ability cultivated in some people”.
e) If one says a person divulging an untested theory as truth will not be recognized, “you could equally say that anyone who arrives at incorrect scientific conclusions solely based on logic and equations will also be absent from the annals of scientific history”.
Point a) evidently means you find them interesting, which is subjective. It is not related to 1)
Not many people will agree with b).
c) is not true, as we saw.
d) is specially… absurd. You can not make unchecked correct scientific conclusions. If you think so, you don’t understand what “scientific” means. I see hard for you to argue about this. A part of the scientific method is to check the results. Until you do that, your conclusions are tentative, not scientifically correct. It’s a contradiction.
e) is specially absurd, again, not to say ridiculous.
In fact, if someone arrives at an incorrect conclusion based solely on logic, I guarantee you he will NOT be absent from the annals of scientific history. In fact, he’d be on the cover!
(Of course, no physical theory is based solely on logic. It’s also based on a set of suppositions. That’s why they require testing. But you do not seem to understand this.)
In any case, I believe anything I say related to d) or c) will seem to you like mockery. It’s only normal, it can’t be helped.
But don’t take it as a personal attack, just as an advise to rethink what you’ve just said.
And please, don’t change your discourse in the middle of the argumentation. You didn’t simply said a theory begins with an intuition.
With some good faith on my part, I can interpret point d) as you saying intuition can be the first step in the making of scientifically correct conclusions. But, in this case, I don’t know why you’re saying that, given the fact that I already agree with that. I don’t know neither how is all this discourse about intuition related to Langan’s ideas being profound, or with how can we accept as profound untested ideas, or who doubted intuition plays a role in science.
I say with some good faith on my part because previously you said Langan’s ideas are profound, you seem to me to say only true ideas can be profound, and when asked how can you say Langan’s ideas are profound if they have not been tested, you start speaking about intuition. But intuition does not make Langan’s ideas true. You can have the intuition than Langan’s ideas are profound, but that does not make them so. And, well, nobody’s questioned the role of intuition in building theories.
The rest of points remains the same. With e) being specially absurd.
How do you define “profound”?
It’s a “theory” can’t be tested, makes no predictions, and answers no meaningful questions. By an actual scientific definition of theory, it isn’t even a theory.
Seriously… CTMU is nothing but an elaborate word-game. Just look at Chris’s bullshit about sets and set theory. He bobs and weaves, but completely avoids defining what he means by the word set. It’s *not* sets from Cantor’s naive set theory. It’s *not* sets as defined in NBG. It’s not sets as defined in ZF. In fact, he gets annoyed when you talk about set theory because, he insists, he’s talking about *sets*, not *set theory*.
That’s an amazingly ridiculous thing to say from someone who claims to be discussing a scientific theory.
Set theory is nothing but a very precise way of defining what we *mean* by the word set. Chris rejects any attempt to provide a precise definition of “set”. Why would he do that? Because his theory is transparent nonsense. But by refusing to define one of the fundamental base terms that he uses, he can weasel out of any actual criticism of the shoddy logic in his theory.
Consider the recent discussions here of this. Is the universe a set? Does the superset of the universe really exist? Is the superset of the universe part of the universe? Those questions *can’t* be answered without actually defining set in a precise way. (For example, in NBG theory, the collection of subsets of an infinite set isn’t a set, so the “superset” doesn’t exist.)
“In fact, he gets annoyed when you talk about set theory because, he insists, he’s talking about *sets*, not *set theory*.”
Langan’s approach indeed seems extremely offensive towards established science. It is not socially acceptable in the scientific or philosophic community to just redefine concepts because “they are that way”. Instead, some anthropological or philosophical evidence should be provided to explain why Langan’s view on the concept of set should be approved and what it’s based on. It’s hard for him to convince people that way. He would need an interpreter, but even the interpreter requires something to begin with. The Metaphysics of Quality does a better job on explaining why its unfalsifiable statements could be useful. Making unfalsifiable claims per se is not unacceptable in philosophy — after all, that’s what the Greek philosophers did.
Gathering anthropological evidence could involve anthropological studies of the scientific community and attempts to make generalizations on what they are trying to accomplish with the concept of “set”. Then Langan could maybe make the point that while his concept of “set” is not well-defined in any particular set theory, it is a generalization of the intentions of the people who practice set theory. This kind of anthropological evidence is, in my opinion, best acquired from philosophical works.
Anyway, since NF is a set theory and has the universal set without contradictions, Langan should probably explain why this doesn’t undermine his theory. After all, that set would also be expected to fall under what Langan considers a set, and according to John Fringe, Langan uses the fact that the universal set leads to a contradiction.
Since Langan seems to question the separation between empirical and formal science, his theory should have more empirical (ie. probably anthropological) content to be convincing.
In any case, there’s no point in treating Langan in a very offensive manner. After all, if he’s wrong, what could he do? Think about his point of view. A philosophical theory this far off the mainstream isn’t an easy thing to advocate. The journal in which it was published didn’t seem prestigious. I guess Langan’s struggle with philosophy is a punishment in itself. For what, I don’t know — maybe for being different. There is little need to add to that punishment, although it’s not necessary to agree with Langan either.
Aren’t mathematical theories um… supposed to have… errr…
Math…?
That’s a lot of talk about almost nothing. You all seem to focus on the “set” part of Langan’s word game about the universe being a set and so what is then its powerset. Let’s try to move past that for a minute, and talk about the more fundamental question, namely this:
Even if the word game wasn’t based on a misunderstanding of set theory, who actually believes that you can “prove” anything about the universe, let alone what is “outside” the universe, using sophisms and syllogisms? It should be pretty obvious that logic, even if used correctly, is in some sense a product of our minds and can never be expected to be used in this way, nothing at all implies that logic, maths or even physics as we know them applies outside, or on a higher level thank, the known universe, whatever that even means.
Regardless, if Langan really takes his theory seriously, he should stop dissecting Marks messages into fragments and commenting every single sentence, and instead try to address the bigger question repeated here by almost every participant, namely what the theory actually means, if it makes any predictions at all or if it is just an exercise in semantics, like “The universe is a dream in the mind of the Great Dinosaur, and we are merely products of his indigestion”. That kind of theory is easy to produce, and impossible to disprove, but not very interesting.
I agree with you, despite being one of those who focus on the “set” problem.
(You probably know why: because it’s one of the few parts with actual semantics. But you’re right).
What a surprise – another rare appearance by the one and only Mark Chu-Carroll. Unfortunately, it almost seems to have been instigated by someone who misleadingly assured Mark that he could win a serious argument with me on the topic of my own work when in fact, that’s quite out of the question.
Having already caught Mark in several glaring instances of mathematical incomprehension (see above), I suspect that the more technical my explanations, the deeper and more petulant his incomprehension will become, and the more impudent and unintelligible his retorts will be. So I’ll try to keep my responses as simple as possible, albeit with the sad expectation that Mark won’t understand a word of them anyway.
This is a long reply. There are two reasons for that. First, Mark is being characteristically dense and thus forcing me to be repetitive. Secondly, as I remarked above, he generates errors faster than he writes – it seems like a paradox, but Mark is one of a kind – and he usually racks up more of them than Kellogg’s has corn flakes. (We’re talking about silly failures of linguistic and/or mathematical comprehension that most intelligent high school students would have the sense to avoid.) In fact, if this drags on, I’ll have no choice but to save time by concentrating less on being informative, and more on the specific personality issues which would seem to account for the fact that Mark is so very, very hard to inform.
Or maybe just ignore him.
Mark: “How do you define ‘profound’?”
I can’t speak for anyone else, but “profound” usually means something like “leading to important or at least meaningful and far-reaching consequences or insights”. Thus, the recognition of profundity is strongly dependent on the capacity of any given reader to recognize meaning and importance when he sees them. Where this capacity is low, profundity is wasted. It increasingly appears that Mark is a person on whom profundity may be wasted. (But here we go again.)
Mark: “It’s a ‘theory’ [that] can’t be tested, makes no predictions, and answers no meaningful questions. By an actual scientific definition of theory, it isn’t even a theory.”
Error 1: There are many kinds of theory. Only some of them are “scientific” in the sense that they take the scientific method as an implicit meta-axiom (a higher-level axiom proscribing the recognition of empirical axioms, or axioms with empirical force). This is a severe theoretical liability; scientific theories are confined by definition to scientific methodology, which, as currently understood, prohibits them not only from being verified in the logical sense, but from exploring the nature and strength of their own connections to their universes, which precludes any form of what we might call “self-verification”. If and when Mark familiarizes himself a bit more with the logical side of model theory and its proper application to the content and methodology of science, perhaps he’ll be able to comment on the subject a bit more fruitfully.
Error 2: Just as there are different kinds of theory, there are different kinds and levels of verification. Making and testing predictions is arguably the only way to empirically confirm a scientific theory … but not all theories are empirical, and scientific theories are not the only theories with empirical content. Theories can be formal or informal, mathematical (axiomatic) or scientific (in which case they are still at least partially mathematical), and if scientific, then descriptive, explanatory, or predictive in character. An explanatory theory can give a superficial explanation of its empirical content, or it can penetrate deeply enough into its subject matter to resolve associated paradoxes on the syntactic or semantic level (a powerful source of veracity in itself). It can even extend the interpretative framework to self-verificative effect, as does the CTMU (unfortunately, this is probably well over the head of most readers of this forum – exceptions are allowed, but improbable).
Error 3: The CTMU is not a mere “scientific” theory. Philosophically, that’s a good thing, because no scientific theory that does more than catalogue data can be validated by any means whatsoever, including empirical testing. At best, empirical testing yields only an imperfect “degree of confirmation”, and is subject to several kinds of inductive and interpretative ambiguity.
Although the appropriate testing procedure is not the same for a theory like the CTMU as it is for an ordinary scientific theory, the CTMU can in fact be tested. First, it can be tested for logical and semantic consistency by examining it for errors or internal contradictions. Unfortunately, one would need to understand it in order to do that, and the vast majority of its critics (including Mark) do not. Or one could try to test the theory by debating it, as Mark seems bent on doing. But thus far, he has not been debating the theory I wrote. He has instead been debating against another theory entirely, a straw-man theory which he *claims* that I wrote, but which I find completely unrecognizable … as unrecognizable as he apparently finds the theory I actually wrote.
Of course, the fact that the CTMU is not strictly scientific, i.e. dependent on the scientific method for confirmation, does not in principle stop it from yielding predictions or explanations of empirical phenomena. But using it for such purposes is a bit tricky, not least because many of its predictions and explanations may be unrecognizable as such to a philosophically naïve, quasi-religious neo-Darwinian apologist like Mark sometimes appears to be.
Error 4: As errors 1-3 amply confirm, Mark is again indulging in what has now been revealed as a most unbecoming habit: mistaking his personal incomprehension for an actual property of someone else’s theory. This is obviously something that he should try harder to control. Much harder.
Mark: “Seriously… CTMU is nothing but an elaborate word-game.”
Probable error: If Mark is using “word game” to mean “a verbal contest regarding matters of fact,” then he is correct. But if he’s using the term to mean “words chosen merely to create the illusion of victory in some basically meaningless, content-free debate or other communicative process,” which is probably what he’s doing, then he is mistaken. (I’m just trying to do the right thing, and stop Mark from hysterically misleading others regarding my ideas out of sheer ignorance and resentment.)
Mark: “Just look at Chris’s bullshit about sets and set theory. He bobs and weaves, but completely avoids defining what he means by the word set.”
Error: In fact, I explicitly agreed with Wikipedia’s definition of “set”. Mark evidently disagrees with that definition. The burden is now on Mark to explain why it is wrong, why the universe fails to instantiate it, or failing that, why it automatically implies reliance on some specific brand of set theory that Mark loves to hate.
Mark: “It’s *not* sets from Cantor’s naive set theory. It’s *not* sets as defined in NBG. It’s not sets as defined in ZF.”
Error: Ruling out these versions of set theory is pointless, because my usage of “set” is indifferent to any standard version of set theory. When Mark insists on shackling this definition to his least-favorite version, he renders the concept foundationally irrelevant, necessitating its replacement by a more basic and flexible kind of mathematical object and language.
Mark: “In fact, he gets annoyed when you talk about set theory because, he insists, he’s talking about *sets*, not *set theory*.”
Mirabile dictu, a point of agreement! (Of course, we differ on its significance.)
Mark: ”That’s an amazingly ridiculous thing to say from someone who claims to be discussing a scientific theory.”
Error: I do not claim to be discussing a “scientific theory”. If I were to make such a claim regarding the CTMU, it would imply an extended definition of science achieved by eliminating the dualistic brick wall that sits between theory and observation in the standard formulation of the scientific method (something which people who sound like Mark typically have no idea how to do, and which they often assume to be impossible). Again, this in no way implies that the CTMU is devoid of empirical content. Its empirical content necessarily includes the entire perceptual universe, as does that of logic.
Mark: “Set theory is nothing but a very precise way of defining what we *mean* by the word set.”
Another point of agreement. Mark, in specifying “naive set theory” as the core ingredient of his personal erroneous interpretation of my essay, has been very clear that this is what *he* means that he thinks *I* mean when I use the word “set”. But that’s yesterday’s news.
Error: Unfortunately, Mark’s personal interpretation of my interpretation of concepts like “set”, “set theory”, and “the relationship between set theory and the general definition of a set” is out to lunch … a six- or seven-martini lunch, to push the idiom. As explained above, I’m using the term “set” in a very general way … the way that, e.g., Wikipedia uses it. If Mark doesn’t like this definition, then he needs to explain why it is inadequate for my purposes even when I’m not relying on it in my essay, and why I need to settle for one standard version of set theory or another even while explicitly rejecting set theory as an exclusive basis for the CTMU.
One almost gets the impression that in declaring the “set” concept meaningless except in conjunction with some standard version of set theory, Mark would also declare the “quantum gravity” concept meaningless except in conjunction with some existing and probably mistaken theory of quantum gravity. If Mark were to have his way, scientists would be unable to meaningfully address such unexplained phenomena without first adopting whatever half-baked theory might already exist regarding them (which itself can only have been formed in violation of that rule). It’s a catch-22, a conflation of definition and theorization that would stop science dead in its tracks.
Like so many of Mark’s ill-conceived and ill-informed opinions, it makes absolutely no sense (except in certain highly restricted formal contexts, none of which are presently operative).
Mark: “Chris rejects any attempt to provide a precise definition of ‘set’.”
Error: Wrong again. I explicitly deferred to Wikipedia’s definition of “set”, which, though general, is admirably precise in its generality. Again, if Mark doesn’t like this definition, then he needs to explain why it’s so awful, and why I should be concerned that he doesn’t understand that I’m not relying on it (except to observe, as I did in my essay, that to the extent that the universe is a set, it is seemingly vulnerable to certain paradoxes associated with sets, and therefore in need of a foundational theory capable of resolving those paradoxes on a level deeper than conventional set theory allows).
Mark: “Why would he do that? Because his theory is transparent nonsense.”
Error: Mark has already been repeatedly called on the carpet for inserting his own hare-brained speculations in place of the actual meaning of certain material which he absurdly pretends to have read. That carpet has just gone from threadbare to ratty. If it gets any thinner, it too will be “transparent”.
Mark: “But by refusing to define one of the fundamental base terms that he uses, he can weasel out of any actual criticism of the shoddy logic in his theory.”
Error: But I did define “set”. (See how Mark is obstinately forcing me to repeat myself?) I defined it just the way it is defined by Wikipedia and its reputed mathematical experts, i.e., the mathematically trained subset of Wikipedia editors allegedly involved in editing and re-editing its mathematical articles. Perhaps Mark should explain his beef with them.
If Mark doesn’t like Wikipedia anymore, then here’s how “set” was defined by Georg Cantor: “A set is a gathering together into a whole of definite, distinct objects of our perception and of our thought – which are called elements of the set.” (This is in Wikipedia too.) Note that Cantor, once having rendered this general theory-independent definition based on perception and cognition, was no longer in a position to insist that his own “naive” version of set theory be shoehorned into it. This theoretic independence is what protected the general definition from being completely discarded when certain aspects of his personal theory about it came under attack.
Need sets always be “well-defined”, and does this always imply embedment in some formalization of set theory? Obviously, a set should be well-defined in precisely the sense given by Cantor, as this is enough to render it perceptible or intelligible. Once this criterion has been met, however, any particular version of set theory is beside the point; the notion that one must be attached is merely an arbitrary formal criterion that has nothing immediate to do with the percept or concept in question. The point of proving a set to be “well-defined” is to establish the possibility of its existence; when something is perceived as a set, or mathematically conceived as an image or generalization of a perceived set, its existence is clearly given by perception and need not be formally established. That’s a very good thing, because there are several versions of set theory available, some of them self-consistent, and any given one of them may or may not be suitable for particular scientific or philosophical purposes. My purposes, for example.
As it happens (and not by accident), consistent versions of set theory can be interpreted in SCSPL. The problem is, SCSPL can’t be mapped into any standard version of set theory without omitting essential ingredients, and that’s unacceptable. This is why the CTMU cannot endorse any standard set theory as a foundational language. But does this stop the universe from being a set? Not if it is either perceptible or intelligible in the sense of Cantor’s definition. One thing’s for sure: if it is neither, then it is theoretically unidentifiable. And in that case, Mark is wasting not only his own time, but everybody’s time, by going around and around about it like a tape loop of a broken record in an echo chamber.
Mark: “Consider the recent discussions here of this. Is the universe a set?”
Yes. As I’ve already stated, the universe fulfills the general definition of “set” in numerous ways, and this indeed makes it a set (among other things with additional structure). Otherwise, its objects could not be discerned, or distinguished from other objects, or counted, or ordered, or acquired and acted on by any function of any kind, including the functions that give them properties through which they can be identified, discussed, and scientifically investigated. If something is “not a set”, then it can’t even be represented by a theoretical variable or constant (which is itself a set), in which case Mark has no business theorizing about it or even waving his arms and mindlessly perseverating about it.
Does this mean that a set is all that the universe is? Of course not, although one would never know it from Mark’s interminable fussing and fuming.
Mark: “Does the superset of the universe really exist?”
Yes, provided that Mark means “power set”. It exists in SCSPL syntax, which itself exists by logical necessity. One can’t even conceive of logic without applying a distributed “power-set template” to its symbols and expressions, and such templates clearly perform a syntactic function. However, because Mark evidently has a definition for “syntax” which differs from my own (and perhaps from most other peoples’ as well), but which must nevertheless be interpreted in a way appropriate to the specific theory under consideration, namely my theory and not Mark’s, and because Mark probably defines “existence” in a shallow and materialistic way that he hasn’t really thought out very well, he doesn’t understand what this means.
Mark: “Is the superset of the universe part of the universe?“
Provided that the “superset” in question is the power set, the short answer is yes. More accurately, the power set is a distributed *aspect* of the universe by virtue of which objects and sets of objects are relationally connected to each other in the assignment and discrimination of attributes (the intensions of sets). Without it, the universe would not be identifiable, even to itself; its own functions could not acquire and distinguish their arguments. In fact, considered as an attributive component of identification taking a set as input and yielding a higher-order relational potential as output, it is reflexive and “inductively idempotent”; the power set is itself a set, and applied to itself, yields another (higher-order) power set, which is again a set, and so on up the ladder.
Of course, even the perceptual stratum of the universe is not totally perceptible from any local vantage. The universe, its subsets, and the perceptible connections among those subsets can be perceived only out to the cosmic horizon, and even then, our observations fail to resolve most of its smaller subsets (parts, aggregates, power-set constituents). But a distributed logical structure including the power set can still be inferred as an abstract but necessary extension of the perceptual universe which is essential to identification operations including that of perception itself.
The scientific import is obvious. Where the universe is defined, for scientific purposes, to contain the entire set of past and future observational and experimental data, plus all that may be inferred as requirements of perception, its power set is integral to it as a condition of its perception and scientific analysis, not to mention its intrinsic self-differentiation and coherence. Without its power set, its parts or subsets would be intrinsically indiscernible and indistinguishable, which would of course amount to an oxymoron; “parts” are distinguishable by definition, and therefore constitute a set with the discrete topology construed by relevance (any reference to which naturally invokes the power set) and the indiscrete topology construed by veracity (inclusion-exclusion). Without the power set function and its stratified relational potential, one not only can’t say what the parts and their mutual relationships are, one can’t even say what they’re *not* … and as any parts not relevant to the others are not “parts” as advertised, even referring to them generates contradictions and must therefore be avoided.
Mark: “Those questions *can’t* be answered without actually defining set in a precise way. (For example, in NBG theory, the collection of subsets of an infinite set isn’t a set, so the ‘superset’ doesn’t exist.)”
Error: What utter nonsense. Aside from the fact that NBG avoids supersets by the largely (but not entirely) semantical device of redefining certain sets as “classes”, one can simply move the entire discussion onto a new foundation, i.e., into a new foundational language, and explain how the set concept should be interpreted within it. The foundation I’m talking about is not NBG, or ZF, or naive set theory, but the CTMU and SCSPL. For the hundredth time, sets can be interpreted therein as collections of discernable, distinguishable objects and events (just as Cantor defines them), or if one prefers, as functions and functional arguments whose more involved properties are developed not in set theory, but in (you guessed it) SCSPL. That way, set-theoretic paradoxes, e.g. the power set paradox, can be precluded or resolved with (you guessed it again) SCSPL mechanisms instead of the mechanisms of any standard, foundationally inadequate version of set theory.
Until Mark comes to grips with this fact and desists in his asinine attempts to tell the author of the CTMU (me) what the CTMU says, his understanding of it will remain stunted. As everyone is by now aware, the more blighted and pathetic Mark’s (mis-)understanding of something, the stronger and more irresistible his compulsion to “spread the wealth” by adopting a deceptive tone of authority and brazenly misleading others to the effect that it somehow equates to his own confusion regarding it, when in fact, he has merely attempted to tie his personal confusion around its neck like a squawking, flapping, hyper-opinionated albatross. It is obvious to all but the most deluded of his partisans that this is a brand of folly in which he should not be encouraged, and that those who do so anyway are beneath contempt.
Now for a little sermon containing some useful advice for Mark and others who think the way he does. Mark is seemingly a reasonably intelligent person who appears to be interested in learning some math, but he has what amounts to a personality-driven learning disability: instead of taking the time to properly absorb some new bit of math he has found, he rushes to post it on his blog, complete with technical errors and errors of comprehension. Then he moves on to the next tantalizing bit of math and the next blog post. The unfortunate result is that he never properly absorbs and integrates what he thinks he is “learning”. Thus, when he encounters a paper (like my essay) which seems to involve some of the math he has supposedly “learned”, but which he doesn’t really understand at all, he blindly leaps to the conclusion that his confusion cannot possibly be due to any fault of his own. After all, having briefly lit upon that kind of math and then fluttered away like a fickle, flighty mathematical butterfly to visit another, he fancies himself an expert on it (as opposed to, say, a dabbler or a dilettante). So naturally, it’s not Mark who’s in a fog; it must be the other guy! And that makes the other guy irresistible cannon fodder for yet another entertaining salvo from the big guns of the most fearsome rubber-band-powered anti-crank destroyer in the blogosphere, the USS Good Math, Bad Math!
By thinking and behaving in this silly way, Mark encourages some of his commentators to assume that they are able to see technical problems with my work that I can’t see. This is almost always a mistake. I do in fact see the full range of what might be construed as technical problems with my work, but differ from my critics in that I usually see their solutions as well. Because the solutions are obvious to me, the problems begin to unravel before they can take up lodging in my theory, sparing me the trouble of noting their putative existence and agonizing over them and engaging in the kind of masochistic publish-or-perish tail-chasing that they inspire in academics (and others) who don’t really understand them. After all, academics write about problems not only to offer definitive solutions for them, but to explore gaps in their own comprehension. Unfortunately, the precious, carefully cultivated orchids of academia often forget in the course of their well-referenced but ultimately omphaloskeptical self-explorations that they very much belong to an intellectual closed shop, and that their own cognitive gaps preclude definitive judgments on the cognitive adequacy of the weeds that grow wild and free beyond the sheltering walls of their ivory tower hothouses.
When Mark or one of his commentators summarily accuses me of ignorance or carelessness for appearing to ignore such “problems” in some piece of writing he has bumped into, thus prompting him to blow his top like Krakatau and do his trademark hotdog dance for the tourists, he does not merely seem to be trying to pass himself off as my intellectual equal. That alone wouldn’t bother me; I usually have no problem with assumptions of intellectual parity as long as people remain polite. Rather, Mark appears to be trying to pass himself off as my intellectual superior … and believe it or not, I don’t have to let him get away with that if I’d rather make an issue of it.
In other words, if you are one of those who has been encouraging Mark in his folly, you are doing him a disservice. If you’re really his friend, then why not allow him to come to his senses, drop the pretense, hypocrisy, and incorrigible buffoonery, and spare himself the humiliation of being made to look less knowledgeable or intelligent than he obviously thinks he is? After all, if Mark learns to show a little respect, then others are more likely to return it. On the other hand, if he continues to pop off because a few diehard sycophants appear willing to cover for him and get his back even when the springs and cogs and gear oil spray out of his ears, then there’s always a risk that sooner or later, at a time to be determined by fate (and/or me), he’ll learn the unpleasant taste of crow. Raw crow, with the feathers and the mites.
To the few of you who seem to understand what’s actually going on, thanks for hanging in there. But again, you should probably try not to assume that you see technical issues with my theory that I don’t see, e.g. the problem of induction and the relevance of Gödel’s theorems. The CTMU contains ample allowance for both.
I recall putting a few pieces online in which the problem of induction and Godel’s theorem are mentioned. For example, regarding the latter, one piece was called “The Theory of Theories” and written in an easy, breezy style; the other was called “Self-Reference and Computational Complexity” (2001) and contained more mathematical detail. Unfortunately, it doesn’t seem to be available any more. As I recall, it began with an explanation of self-reference and diagonalization in the Liar Paradox, introduced the theory of metalanguages, applied these concepts to Gödel’s proof of the undecidability theorem, moved on to computation theory and Turing’s work on incomputability re the Halting Problem, sketched a comparison between the diagonalization techniques involved in undecidability and incomputability, introduced computational tractability with attention to oracles and relativization, and finished off by discussing the analogue of linguistic self-reference in Boolean circuits with respect to their prospective application to P?NP. The CTMU wasn’t mentioned, but bear in mind that the CTMU is a self-referential system to which the basic principles of self-reference apply.
That paper was online for years. It’s probably languishing on a storage drive somewhere; if I find it, maybe I’ll slap it back up. Meanwhile, please rest assured that I’m aware of most if not all of the major technical issues bearing on my work.
The reason that I’ve focused on the set/set theory thing is simple.
If the basis of an argument is based on undefined, inconsistent, and/or invalid terms, the entire argument is undefined, inconsistent and/or invalid.
In the case of sets, sets are a simple basic concept that can, very easily, become inconsistent. That’s the whole point of set theory. Set theory is a system that produces a definition of sets that doesn’t devolve into inconsistency.
The definition of set that you focus on, from wikipedia is, ultimately, the definition of sets from naive set theory. You can bitch and moan, bob and weave, whine and complain all you want – but if you use the naive set theory definition of sets, then your argument is built on naive set theory.
And naive set theory is inconsistent, and thus invalid.
Your “theory” starts with an argument about whether or not the universe is a set, and derive supposedly deep and profound conclusions from that argument. But you’re argument is clearly based on a definition of “set” that isn’t valid. You cannot derive a valid argument from an invalid foundation. And all of your pointless verbiage doesn’t change that. If you want to use sets in your argument, you need to use a definition of sets that isn’t invalid. If you’re not willing to do that, then your theory is nothing but an exercise in intellectual masturbation.
Attn: Chris.
I hope you will – please – read this and look me up (at my “home institution”: https://groups.google.com/forum/m/#!forum/lilasquad).
All,
I am a metaphysian. And, so that my boldness is revealed up front, I will let you know that, in your regard, I hope to inject some fundamental REASON in to the debate. But, truth be told, I am not particularly interested in rolling around in the mathematical mud; I am trying to get Chris’ attention because I think his metaphysics is wanting, and I think that a proper righting of his implicit fundament might lead him to the fullness of success his framework – the cognitive theoretic model of ? – will, I suspect, eventually provide – someone.
Let it be known, I haven’t yet quite even finished Chris’ paper! I have read a good deal of the above discussion, but I have skipped a lot too. I am – quite confident that I am – aware of (the constraints of) THE Metaphysics (of Everything: M.E.), so I can – I think – see where Chris has violated THE I’dea. The physicist’s Theory of Everything (T.o.E.) should, I suspect, fall out of THE metaphysics – like a ripe fruit; and I think that Chris’ framework is very close!
I have, as I recall, seen Chris use the (derogatory) term “hard materialism”. It seems to me that the comments I have read implicitly assume such a “hard materialism”. The thing is that this is a really immature metaphysics – far sillier than, for instance, a “flying spaghetti monster”. For what it’s worth, though Chris fully recognizes the need to avoid the problem of the “dualistic brick wall”, my understanding is that he lets it in the back door (his “UNBOUND Telesis”).
Before I get into some details, let me ask: why do you (anyone) think “set” is even a meaningful concept? … Do you have an answer? Can you test whether you are right or not? (If you could show that there was a situation in which “set” was the only tool for the job…)
Chris, why do you think “universe” is a meaningful concept?
R.P. Feynman, in his “lectures on Physics”, and in his chapter on algebra (yes, he did have a chapter on “algebra” for his cal tech students!), affirms that one must start in the middle – even just to count! The task of a metaphysician is to find THE proper middle with which to start. I point you to the SUCCESSFUL metaphysician George Holmes Howison, his book “the limits of evolution, and other essays, illustrating the metaphysical theory of personal idealism”:
http://books.google.com/books?id=vAIQAAAAYAAJ&printsec=frontcover&dq=The+limits+of+Evolution+howison&source=bl&ots=w5XKmPBykt&sig=xJtfVO-AP8LfYu2C2FCeTQCWcuA&hl=en&ei=eBSmTZGCDoiCsQPV7PX5DA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBQQ6AEwAA#v=onepage&q&f=false
Briefly, Chris, you underestimate the force behind Kant’s noumenon. Materialism can only be bested by I’dealism. That is, reality is at bottom idea! There is no matter as such! “matter” is, rather, information representing real I’dea. I say I’dea, singular, because … give me a moment please.
I know that there has been some talk about mind-matter duality above. Philosophically, the point I make is that no conception of “universe” is going to be acceptable unless it accounts for the thinker. I state this only dogmatically here; but Howison proves that there are certain limits to evolution, specifically that MIND must be a priori rather than the result of evolution. Materialism must be bested; and, as I have said, it is idealism which bests it. Furthermore, minimal complexity is the key to producing THE real I’dea. Chris, the problem you make is that you have not quite pushed yourself to that one real I’dea! And, rather, you make a very novice mistake (which might be easy to remedy – like a sign error in a long math problem) of conforming yourself to a creation ex nihilo. Or, as you say, on your summary page:
“Unbound Telesis (UBT) – a primordial realm of infocognitive potential free of informational constraint. In CTMU cosmogony, “nothingness” is informationally defined as zero constraint or pure freedom (unbound telesis or UBT), and the apparent construction of the universe is explained as a self-restriction of this potential. In a realm of unbound ontological potential, defining a constraint is not as simple as merely writing it down; because constraints act restrictively on content, constraint and content must be defined simultaneously in a unified syntax-state relationship.”
Let me go into some detail. The first sentence and the first clause of the second sentence represent … a problem. Why do you think it makes sense to postulate a “realm … free of informational constraint”? This does not comport with a meaningful idea! But, you close your second sentence with “the apparent construction of the … is explained as a self-restriction of this potential”. You will notice that I omitted only the –offending – word “universe”. Now, this is all (more or less) in line with both the fundamental axiom of all philosophy: “nothing” is meaningless, strictly speaking; impossible: and Feynman’s assurance that we need a “starting in the middle”. What if I replace “universe” with “idea”? Granted, my “more or less” was needed because “this potential” is not a truly possible potential, but we see, through “self-restriction”, the ever present hint that the real I’dea is “I am”! Thus Howison’s “personal idealism”. “I am” is the proper, now bounded, metaphysical fundament (telesis?)! But, again, I give this dogmatically now; you have not yet seen the I’dea in it’s full and minimal complexity – or at least I haven’t presented it 😉 But, “I am” does conform to your proscription that “constraint and concept must be defined simultaneously in a unified…”
The picture, then, is that reality is fundamentally idea. There is but one (type) of I’dea: I am. In order that this I’dea should be a real and meaningful I’dea it must be a certain “working complex” – if I may. Interestingly, if there is any such capacity to destroy souls in the universe (as you have suggested elsewhere, I think), it would have to be some additional, non-fundamental advance pursuant to some increased capacity, potential, or complexity. I see no need for recourse to any such development, and my best guess is that it is actually impossible; either way, you won’t hear me talk about it again. It seems that everything can be accounted for by the “starting in the middle” with “I am”, when once we’ve recognized what this I’dea really means. To close the big picture, reality is, in our time, a plural society of I am.
Every “I am”, from human, to dog, to cat, to, presumably, insect and plant, etc., and to God too!, is precisely equivalent noumenally. Chris, this is the force behind Kant’s noumenon that you miss. While the I’dea “I am” is a working complex, composed of the noumenal aspect, the spiritual aspect, and the phenomenal aspect, that is, “complex”, it is the noumenal aspect which is most characteristically idea – if I may. The noumenal aspect is eternal (philosophically speaking). Descriptively, it is the “mind of God”; and every “I am” is endowed with it equivalently! But, this aspect in itself does not amount to a real and meaningful idea; it is but an aspect of the minimally complex I’dea. How does one “bound” an infinite and eternal “idea” so as to make it definite and real? How is one idea separated from another, even conventionally speaking?! To be sure, this is where the beauty of complexity (as opposed to a sea of distinct ideas / axioms) comes to the fore. One I’dea is kept separate and distinct from it’s neighbor I’deas (/ kin) by what Howison has chosen to call the “spiritual” aspect; I will refrain from burdening you with any faulty picture I might use… But, similarly with the noumenal aspect, every “I am” is endowed with the same spiritual potentials, preeminently free will. As the spiritual aspect is working to bound the noumenal, the spiritual aspect is decidedly temporal. But this is not quite enough. The phenomenal aspect completes the picture, literally. The information about the real and living I’deas is derivatively represented, fairly, and logically, meanigfully. One can impose his will on the plural society of “I am” and then ask questions about the effect. The answer one gets is a function of the question one asks (and one cannot refrain from asking questions – the eternal aspect must be bounded by the temporal aspects). Not only is the information one receives from such questions predominantly about oneself, one’s question is an essential ingredient: one holds himself together this way! Each “I am” truly is inviolate (and his noumenal aspect is, further, incorruptible). Thankfully though, we (humans eminently) are phenomenally developed enough that the information we gather about ourselves is sufficient to let us start to understand other “I am” as well 😉
Above I had said:
“There is no matter as such! “matter” is, rather, information representing real I’dea. I say I’dea, singular, because … give me a moment please.”
Have I fulfilled my burden? At least dogmatically (Howison offers a more thorough handling)?
So, Chris, I again ask: why do you think “universe” is a meaningful concept? For my part I am quite convinced that you have got your socks on inside out! That you have let materialism through your back door, and that you are giving over the reality which is YOU to some illusory conception of US, or a pantheistic god. And, to be sure, having rejected pluralism you call it “universe”. What’s REAL issues from the superphenomenal – and plural – society of “I am”. The derivative picture of it is – though integral – only a picture, and only derivative. It appears “solid” (is “abiding” better?) because the I’deas are real. We can “use” it because the I’deas are real.
Can you show us the physics that falls out of this metaphysics, Chris?!
Either way, my confidence in this “starting in the middle” is exceedingly strong. “Confirmed” even. It gets you out of all sorts of trouble you get yourself into, Chris. God is a person now. Not a “pan” immanent in … There is now a place for free will. The real is now a “self-restriction of [the possible]” rather than some weird (impossible) collection a la your words, Chris:
“Where the universe is defined, for scientific purposes, to contain the entire set of past and future observational and experimental data, plus…”
Rather, the I’deas are living; and reality is evolutional. To be sure, where you are thinking “universe”, you should now be thinking “my body”. That everybody’s “my body” appears “similarly” should be no surprise!: we are all individual, proprietary quanta of the single type of real I’dea, distinguished only by “spirit”. I don’t think I need to go into an example of how the information (body) is personal and proprietary, even though the distant star we are looking at is the “same” star, or the football we are fighting for possession over is the “same” football. In the everyday we are developed enough that these variations pose no hurdle. In the wet dreams of scientists and tyrants, I will stake my life on the fact that it is precisely impossible for you to violate me. Of course, you (general) could, no doubt, “violate” “me” so much that I’d wish our universe / phenomenal bodies didn’t coexist so.
Thanks,
Sincerely,
Tim
Mark: “The reason that I’ve focused on the set/set theory thing is simple. If the basis of an argument is based on undefined, inconsistent, and/or invalid terms, the entire argument is undefined, inconsistent and/or invalid.”
Not if the reason they’re “undefined” is that you, Mark Chu-Carroll, refuse to accept their definitions as given, and then refuse to explain why you’re refusing to accept their definitions as given.
Mark: “In the case of sets, sets are a simple basic concept that can, very easily, become inconsistent. That’s the whole point of set theory. Set theory is a system that produces a definition of sets that doesn’t devolve into inconsistency.”
So then let’s have a look at some of these inconsistencies. Carefully write an essay on them – the specific ones, not just the ones at which you’ve been frantically waving your arms – and post it on your site. If it’s good enough, maybe I’ll respond.
As I’ve remarked above, the formal well-definition of sets is unnecessary regarding sets that are directly perceived. Otherwise, the last time you perceived a set, you should have refused to follow through with the perception until the set announced that it had duly embedded itself in some consistent version of set theory.
Did you insist on that? (Why, sure you did!)
Mark: “The definition of set that you focus on, from wikipedia is, ultimately, the definition of sets from naive set theory. You can bitch and moan, bob and weave, whine and complain all you want – but if you use the naive set theory definition of sets, then your argument is built on naive set theory.”
You really don’t have a clue, do you, Mark? Cantor’s definition of “set” is not explicitly parameterized by Cantor’s “naive” version of set theory. The theory is not a definiens of the definition; the definition has explicit definientia, namely, the well-established and patently consistent operations of discerning its elements and gathering them together. You’re simply asserting otherwise without adequately explaining yourself.
Mark: “And naive set theory is inconsistent, and thus invalid.”
That’s why I don’t use it. As explained, over and over again.
Mark: “Your ‘theory’ starts with an argument about whether or not the universe is a set, and derive supposedly deep and profound conclusions from that argument. But you’re argument is clearly based on a definition of ‘set’ that isn’t valid.”
No, it isn’t. Stop trying to tell the authors of the theories you criticize what they meant when they wrote their theories. It’s ridiculous.
Mark: ”You cannot derive a valid argument from an invalid foundation. And all of your pointless verbiage doesn’t change that. If you want to use sets in your argument, you need to use a definition of sets that isn’t invalid. If you’re not willing to do that, then your theory is nothing but an exercise in intellectual masturbation.”
So is this dialogue, as long as you refuse to pluck the scales from your eyes and open your mind a little.
You can’t BS your way out of the pickle you’ve gotten yourself into here. You may as well lie down and play dead.
Stay down, Mark. Don’t even try to get up.
Hi Chris
I don’t see any point in arguing with the people on this board. Many here have no appreciation for the role of intuitive leaps in launching scientific revolutions. Can you fathom the unsatisfactory state of Physics (classical) if history had only offered Keplers and no Newtons? We need more Newtons and Einsteins today to shine a clarifying light instead of offering ad hoc hypothesis such as dark matter/energy/flow without any internal motivations and explanatory power.
I am one of your supporters and I plan on studying your CTMU paper in detail. I currently have an inkling of the gist of your ideas but would like to be in a better position to offer agreement and/or or a constructive critique of the CTMU.
Newton se jactó de not forging hypotheses he could not test by data. Einstein was refining all his theories until they were in great agreement with data (see the perihelion of Mercury, for example), and he was always willing to modify his theories depending on the results of experiments. They both conviced people by the agreement of their theories with observations. They both always checked their theories, correcting them accordingly. They defended their theories with data, not with words nor insults.
They have nothing to do with Langan, as you can see.
We certainly need more Newtons and Einsteins today. Calling Langan a “Newton” or an “Einstein” will not make his theory correct.
I have particularly a great respect for intuition in physics in the generation of scientific ideas. But… I understand the role of intuition. Intuition can be right or wrong. Being so, you can not use intuition to prove a theory correct.
Mnnn, my software switched into spanish (?) for some reason. I believe it’s getting out of its mind (with me).
By “Newton se jactó de not forging hypotheses” I meant “Newton was proud of not forging hypotheses”.
Hi Chris
I would like to add that your theory, if correct, is a great starting point but it needs to be refined to the point where it can make some kind of falsifiable prediction about physical reality. For example, it would be a ground breaking achievement if the CTMU could predict Dark Matter as a consequence of some abstract concept outlined in the CTMU. Einstein, for example, derived Lorentz’s contraction equation as a consequence of his intuition that the speed of light cannot be exceeded in any reference frame. Newton derived Kepler’s orbital equations as a consequence of his intuitive realization that an orbit is simply a falling object.
Yes, you don’t need to continue. We get the point. We already know it. People do things based on other things other people did before. Nobody doubts that.
That’s not a defense for Langan’s theory. Maybe we can derive formulas describing the Pioneer’s anomaly from the negation of Langan’s theories. My intuition says me that.
What nonsense.
You are very annoying. Go away!
Chris, I think your theory could benefit if you cooperated with the Metaphysics of Quality community. Not that your theory necessarily has any flaw — there are other reasons which involve your theory gaining more acceptance. Do not take me or Tim as representatives of that community.
You are actually doing a pretty good job at arguing with these people — but you might end up with something more useful if you popped up at Lila Squad.
If you send me an e-mail address you actually use via this form, I’ll do the rest for you to get this thing going.
If you have the time, I’ll have some questions for you, too, but there’s no hurry, and I should read your entire paper first before presenting all of them. But this is not the right place for it.
You can infer anything you want from inconsistent axioms. Cantor’s definition of set leads to inconsistencies (it’s well known), as the definition assumes inconsistent axioms. Everything you infer from there is inconsistent, and you could infer anything you want.
It’s not so difficult, it’s very common knowledge, and it can be trivially shown.
At this point, Mr. Langan, where I can not take you seriously anymore (you’re just insulting people), I, as always, will let time judge.
Drop a note when you succeed, Mr. Langan, with such a great contribution to humanity.
[
I hope to discover the step 2:
Step 1) Talking nonsense and insulting people as if everyone else accepts your “theory”
Step 2) ?
Step 3) Profit!
]
“the formal well-definition of sets is unnecessary regarding sets that are directly perceived”
But we’re not talking about these sets, are we? Unless you claim that you have directly perceived the entire universe…
Mr Langan,
Could you please give us a short outline about what your theory is really about. If it is the case that we are indeed too stupid to grasp its brilliance, there is no theory that is so complex that you can’t explain what it is about. If we disregard the proofs for as while, could you help us understand
a. What exactly it concerns (the existence of something, the quality of something, the number of dimension etc?)
b. In broad outline, what are the conclusions (for example, the universe is infite in size, or there are 15 underlying dimensions or time is circular)?
c. Can CTMU make any sort of predictions that are empirically testable? Not necessarily hitherto unknown phenomena, I would be quite happy, for now, if you could help me understand how it relates to the physical reality at all, from what I’ve read I haven’t been able find any examples of this
d. If possible, can you briefly describe the methods you use for proving what you do prove? So far, we have been focusing on a part of the theory that seems to be using semantic proofs, is that the case for the entire theory or do you rely on empricial observations and/or mathematics too?
Chris:
Okay, so correct me if this is wrong. You say the universe is the biggest entity there is, and can be represented as a set of objects. But a power set P(S) is necessarily larger than (S) and therefore we’re talking about a set that is bigger than the entity we already said was the biggest entity there is.
Is this correct?
The formal definition of sets IS very much necessary. If you’re simply defining a set as a “collection of objects” then that says nothing about the logical attributes you apply to the objects themselves, which is why we run into inconsistencies in naive set theory. Any collection of objects we can perceive typically fits within set theory just fine because that’s what it models.
From your own CTMU page: “It follows that reality itself should be a set…in fact, the largest set of all. But every set, even the largest one, has a powerset which contains it, and that which contains it must be larger (a contradiction). The obvious solution: define an extension of set theory incorporating two senses of “containment” which work together in such a way that the largest set can be defined as “containing” its powerset in one sense while being contained by its powerset in the other. Thus, it topologically includes itself in the act of descriptively including itself in the act of topologically including itself…, and so on, in the course of which it obviously becomes more than just a set.”
How does this not scream “naive set theory” to you? How is the naive set from Russell’s Paradox “The set of all sets that don’t contain themselves” any less naive than “The biggest possible set and its even-larger powerset”?
You can’t make claims like these and then insist that it’s not naive set theory and then insult people for not agreeing with you. Yes, reality may contain “sets” of objects, but that doesn’t mean you now have free-reign to apply invalid axioms to those objects. If you’re defining something outside of science, then no amount of science can possibly attack it. But, then again, if what you’re talking about is outside of science, then it doesn’t have much worth here in reality. The burden is not on Mark to “disprove” you (even though he already has), but since you’re the one making the positive assertions in your theory, the burden is on you to defend it.
Of course, you have to actually defend it in a way that makes sense. If you’re using neologisms, you have to define them. If you’re using well-understood words differently, you have to redefine what you mean. My point here is that you’re committing errors/fallacies that are already well, well-understood by people who’ve studied mathematics and physics. If you mean something different, then you have to elaborate in a clear and concise way. Simply popping open a can of word soup doesn’t prove that you’re right.
If you keep going down this path of “It’s a set, but not set theory. It’s Cantor’s definition, but not naive. The universe is a set, but the powerset contradicts. The theory is scientific, and yet it’s not” — then people are going to write you off as a crackpot and move on.
Just a couple of friendly observations.
First, I don’t fully trust bare external links posted on this site. I will probably neither click on them, nor paste them directly into a browser. To put it bluntly, I’ve had too many problems with the kind of person who tends to frequent this (skeptical / materialist-physicalist / “anti-pseudoscience” / “debunking” / atheistic or anti-religious) kind of forum, especially for the purpose of criticizing me or my work in the way that we’ve seen here. Too many such people, confused but nonetheless committed to their beliefs, turn out to be more trouble than direct communication with them could ever be worth.
More generally, although I try to make reasonable exceptions, I have a hard time regarding those who share what appears to be Mark’s basic mindset as trustworthy by those who share anything resembling my own perspective. In fact, I regard them as lacking any firm basis for ethical understanding or behavior, something for which I have a sad abundance of experiential confirmation. (Of course, this is a statistical judgment which says nothing personal about Mark or anyone else.)
Secondly, it’s a small world … for some of us, at least. I’m familiar with Robert Pirsig’s work because, at one time, we shared certain acquaintances. It’s something that I’ve heard enough about and even find interesting – Robert is clearly a very bright man – but which I find a bit too nebulous to be very useful to me. On the other hand, some of his ideas make a great deal of sense as far as they go, so please don’t rush to the conclusion that I dismiss his philosophy. It’s just that comparing it to the CTMU would be like comparing a Ford Model T to the Starship Enterprise. Any associated knowledge-transfer would be pretty much one-way, from me outward. Such a transfer will probably occur one of these days, but on my own terms and in my own good time.
To the extent that anyone’s interest in my work is sincere, I very much appreciate it. But please try to remember that when you read something I’ve written about it, you’re probably reading a highly simplified version from which much of the detail has been regretfully omitted. Why has it been omitted? Because most people, even those who claim to know some mathematics, would merely be distracted by it, are possibly incapable of understanding it (as we’ve seen), and/or would take it as something to be misleadingly attacked out of context.
With all due respect, those who assume that such detail does not exist, or believe that something I’ve said about the CTMU is invalidated by something they think they know, have another think coming. Praemonitus, praemunitus.
Good day.
Mark, thanks for the forum.
Tuukka, thanks for turning me on to the CTM(?), and Chris, and for the (attempted) assist.
Chris, let me “forearm” you with Howison’s second version of his book, from 1905, which is preferable for its set of 5 appendices – and its second preface too:
http://books.google.com/books?id=dg3wkAkfKQ4C&pg=PA420&dq=the+limits+of+evolution&source=gbs_toc_r&cad=4#v=onepage&q&f=false
You can, of course, find any of the resources I’ve linked you to on your own, through google, which web site might be trustworthy enough for you 😉
Regarding ethics, then: if justice is to be possible, people (I am) must be free to refrain from injustice: this has been my tautological axiom.
Lastly, I think: you, Chris, turned me on to this interview by Wheeler (footnote 10 of your paper), in which he said:
“Wheeler: One of the conditions, I think, for advance in this field, as in any field, is believing that advance is possible. What I hope I’m creating is a sense of faith that it can be done. Faith is the number one element. It isn’t something that spreads itself uniformly. Faith is concentrated in a few people at particular times and places. If you can involve young people in an atmosphere of hope and faith, then I think they’ll figure out how to get the answer. Faith and hope are absolutely central to everything one does.”
So I think you should trust the link:
http://www.bigear.org/vol1no4/wheeler.htm
I take it there’s nothing else then, Chris?
Good night,
Tim