I’ve been sent Yet Another Proof of God. This one goes to rather a lot of trouble
to appear to be mathematical. I thought that it would be fun to rip it apart. For a change, this one is from an Islamic moron, rather than the usual Christian moron.
Alas, it’s pretty much as stupid and shallowly wrong as the usual christian one.
Our genius prover starts off with a bunch of definitions. They’re a classical example of what I call “obfuscatory mathematics”; that is, mathematical notations and definitions that are created for the purposes of obstruction, not clarification. Obfuscatory math is one of the best signs that what follows is going to be bullshit.
Before I get to that, allow me to rant for a moment.
As you know, I love math. I wish I were better at it. I like to think that I’m
pretty good at interpreting other peoples work, and writing about it in a style that
makes it approachable. I’m pretty good at understanding it, and seeing the beauty in
it. But I’m not a mathematician: I’m a computer scientist, or a software engineer if
you prefer. I’m nowhere near good enough to be a real mathematician, producing new
mathematical results. My talents are in the applied realm, and no matter how I might
wish to be, I could never be a great mathematician. But I have a profound appreciation
for math: I think it’s beautiful and wonderful and fascinating. A big part of the
beauty of it is the way that you can take complex phenomena, and use mathematics as a
tool to wrap those phenomena up and make them comprehensible – to find a simple handle
on the complex. Notation is an example of that. The point of using mathematical
notation isn’t that it looks cool. The point of it is that it’s clear. Try to
say something like x=(-b +/- (b2-4ac)1/2)/2a without using notation, and you’ll get a good idea of just what it can save – and that’s a simple
example, made a bit obfuscated by the limitations of HTML rendering. Mathematical notation is a clear, compact, unambiguous way of writing complex things. That’s its point.
Obfuscatory math betrays this goal. The point of it isn’t to be a compact, clear,
and unambiguous notation. The point of it to look scary. It’s to obscure things behind notation, so that the fact that you’re spouting bullshit is disguised by the fact
that you’ve hidden beneath layers of symbols.
So, our moron starts with his definitions:
E = Existence (Every thing that really exist)
U = Universe
X = a deity outside the Universe
C(a) = Creator of object a
G = God (an Intelligent Creator)
f(t) = function of time (State), at a specific time t
Y [Fn]→Z, means using Fact n, Y leads to Z
What is the point of defining the symbol “E” to mean existence, without
defining what existence means? “X” as “a deity outside of the Universe”, when
you haven’t defined what it means to be outside the universe? The point is to hide
the weakness of your argument under the obfuscation of symbols. What’s the point of
introducing this new notation “Y[Fn]→Z”, instead of the more standard “Y ∧ Fn ⇒Z”? Same thing. Nonstandard notation is more confusing to a reader. And obfuscatory math is all about confusion.
The definitions as shown above are, pretty clearly, gibberish. You can’t build
any kind of meaningful proof out of rubbish like that. But our buddy isn’t going to let that stop him. So he moves on to a stack of “facts”, by which he means what we’d generally call “premises” – the fundamental, unproven statements that are the basis of logic. Here are his facts:
F1- There is nothing beyond logic, illogical is impossible (Paradoxes do not exist).
F2- Facts never contradict
F3- A fact is true by itself and true with any other fact
F4- Nothing comes from nothing (Cause & effect)
F5- Natural laws are independent from each other.
F6- Σb=N ∩ N<∞ where b∈U Number of elements (or objects) in the universe is finite
F7- U(T) ≠ U(T+t) where t≈0 for all T, t Universe is not static, state of U at any time T, does not equal its state after a small time t.
Already, he’s run off of the rails of his own notation. Above, he defined “U” as the universe, an object; in his facts, he treats U as a function. Even if we accept his notational sloppiness (which we shouldn’t, since he’s abusing for the alleged purpose of rigor), he’s asserting that U, as a function, has an important property, which he hasn’t proven, but which is far from being an obviously clear, atomic axiom.
But let’s be methodical. F1 is false. Logic isn’t a single thing; and for any given logic, per Gödel, there are things beyond its reach. You can argue about the interpretation of Gödel, but whatever your interpretation, there are statements that cannot be proven true or false. (The classic interpretation is that there are true statements that cannot be proven true within the system; many people are uncomfortable with that version, because “truth” is a property of the logic. But in any case, you can formulate a statement for which you cannot construct a valid proof of its truth or its falsehood.) So with F1, he’s already lost his argument.
F2 and F3 I won’t quibble with.
F4 is another big problem. “Nothing comes from nothing” is not a mathematical statement. And worse, it contradicts the statement that he wants to prove. He wants to prove that God exists and created everything. But if nothing comes from nothing, then where did God come from? The usual answer
to this is some variation of “God isn’t part of the Universe”, or “God is outside of the parameters of the proof”. But if that’s the case, the proof can’t reason about God. So he’s going to be stuck: if God could come into existence without a creator,
then the universe could come into existence without a creator. Either way, you need an exception to this fact.
F5 is another totally bogus statement. What’s a “natural law”? What does it mean for natural laws to be “independent”? He’s not defining those mathematically, while alleging that he can use them in a mathematical proof. Sorry, not allowed.
F6 is, ostensibly, the statement that the universe is finite. Sorry, no.
If your proof is going to rely on the finiteness of the universe, you’re going
to need to prove it. And the statement itself is a classic of obfuscation. Near
as I can tell, it’s ill-formed. Given that he invents his own notations, maybe
he’s got something in mind by this, but I can’t make head nor tails out if it. It’s nonsensical.
F7 is, basically a statement that there is no recurrence of states of the universe after a short period of time. Again, it’s something that needs to be proven. There are, demonstrably, ways of showing state recurrences given a sufficiently long
period of time. But there’s no reason, a priori, to assume that you can’t have a short-period recurrence. This is not an acceptable premise.
So, we’re off to a roaringly bad start, and we haven’t gotten past the premises. Let’s get to his proof. He divides it into parts: part one is “Proving the creator”,
two is “defining the creator”.
For part one, he states the goal of his proof as “E=U+X (X≥φ)”, or “Existence = Universe + Possible X”. What does this mean? Nothing, near as I can tell. Once again, he’s using undefined notations that look good, and waving his hands to claim that it makes sense: “see, it must be math, it’s got greek symbols!”
Step one of this proof is “If we have two options, if one of them is impossible, the other is proved”. Well, that’s a pretty sloppy way of saying it. In math, we’d say something more like “For any statement S, S∨¬S” is true. Except that that doesn’t appear to be what he means. It’s something more like “(A∨B) ∧¬B ⇒A” – that if we know that the disjuction of two statements is true, and we know one of them is false, then the other must be true. The catch, of course, is if B is difference from ¬A, then we need to prove (A∨B) is true.
Naturally, he doesn’t do that. He just throws out one of his ill-formed statements: “If U(t)=0 [F1,F4] → X>0∩X=C(U)”. He translates this as “If at any point in time, U did not exist, then a deity existed and created U.” I’m really not at all sure where the hell this came from. It’s nonsensical gibberish and non-sequitur. Looking at the notation, my translation is still confused, but it’s something like “If the state of the universe at time t is 0, then given facts F1 (Nothing is beyond logic) and F4 (nothing comes from nothing), then God is greater than 0 and God created the universe.” You could replace 0 with “the empty set”, which makes a bit more sense… But it’s still nonsensical rubbish. F4 says nothing comes from nothing. So where’d X come from? In a logical proof, symbols don’t appear from nowhere.
Really, he’s working from two hidden premises: One is a totally new thing in this proof: “for all entities E, if there exists a time when E didn’t exist, then E must have a creator”. The other is a bit of a variation of one of his “facts”. That is, his facts state that God is outside of the Universe – but what he means is “God is the only thing outside of the Universe”. So if the Universe has a creator, and the only thing outside the Universe is God, then God must be the creator. If you add those in, then this statement sort of makes sense: if everything needs a creator, and there’s only one possible creator, then you’ve identified who the creator might be. Of course, once you flesh it out like that, it’s not nearly so impressive as a proof. The premises include the idea that God exists outside of the universe. Which is exactly what we’re allegedly proving. So it’s a good old variation on “If we assume that God exists, then God exists”; A ⇒ A.
But he’s not quite done yet. Because according to his proof, that’s only true if there was a time when the Universe didn’t exist. The alternative is his statement two: “If X=0 → E=U [F1,F5] → E=U(t) for every T ∩ U(t1) ∉ U(t2)”. He claims that this translates as “If a creator does not exist, the Universe is Eternal, and it is all existence at any time. It’s states are random.” I’m
not sure what that translation is supposed to mean, but whatever, it doesn’t seem
to fit the notation at all. The notation looks to say something like “If God is the empty set, then existence equals the Universe, and combined with F1 (nothing beyond logic) and F5 (natural laws are independent) that means that existence = U(t) at every time T (huh?) and the state of the universe at time T1 isn’t a subset of the state of the universe at time T2”. He claims that this also implies that “Invidual events based on natural laws are not random, but independent events are random if there is no god”. This, obviously, doesn’t follow from anything else that he said. et another that that he pulls out of nowhere.
Looking at that mess, some things are obvious. Once again, he’s switching between universe as object and universe as function, which makes the logic pretty much ridiculous; you can’t switch things like that. One thing that we know going back to the days of Cantor and his contemporaries is that you need to be very careful about distinguishing first order objects from second-order objects, or your logic collapses
into contradiction and paradox.
But even ignoring that, this is a wretched muddle. The statement about U(t1)∉U(t2) is also another crazy thing that he just pulls out of his ass for no reason whatsoever. It has no relation to anything that he’s said before, and in no way has any logical relation to anything. His statement makes
no sense, doesn’t say what he thinks it says (even giving him lots of latitude for the definition of his non-standard statement syntax); and his conclusions don’t follow logically at all.
But he doesn’t stop there. He claims further, from that t1/t2 rubbish that combined with F6 (the universe is finite) and F7 (states in the universe don’t repeat)
that the universe is cyclic. Why? Well, if you assume that the universe contains a finite set of objects, and that it is eternally unchanging in size, then
the state of the universe must eventually repeat. So we’ve got another
problematic unstated premise: the size of the universe is fixed. Without that,
you can’t conclude that the states are cyclic. But even his proof of cyclicity is
wrong! Because one of the fundamental assumptions of it (as you’ll se in a moment) is that events are necessarily random – and random events don’t follow, deterministically one from the other – because determinism is non-random. So if events are random, then a single state that repeats is not necessarily followed by the same subsequent state.
But what comes next is the silliest of all of this; overall one of the silliest piles of pseudo-mathematical rubbish that I’ve seen so far. He says
if the universe is cyclic, then it can’t be random, and since it’s random if there
is no God, then it can’t by cyclic, because cyclic is non-random. And since
no God means randomness, and cyclic means non-random, then the entire idea of
a universe without God is contradictory, and so you can therefore assume that the universe must have been created, and requires a God. He states this conclusion as “X=φ ∩ X=C(U)”, which at least enlightens me as to what “φ” means – to him, “X=φ” means X is random.
Euch. Part two, where he allegedly proves a bunch of properties of God, including
the ultimate correctness of Islam as contrasted against other religions, is even
worse. I can’t take any more of it, so I’ll just stop here. You can go look
yourself if you want to see the rest of his train-wreck. Just goes to show you: the
morons aren’t limited to Christianity and Judaism: Islam has morons just like the
other religions. Now, anyone know of a nice Hindu mathematical proof of the existence
of supernatural beings I can dismantle?