A few weeks ago, I received an email about a new book, “The Faith Equation”, by Marvin Bittinger. Bittinger is an author of math textbooks – including, I think, my first calculus text. The book is supposed to be Bittenger’s explanation of how mathematics validates christianity. Needless to say,
I asked for a review copy – this is something right up my alley.
I’ve taken longer to get around to reviewing it than I intended, but life’s been busy
lately. I’m going to review it in several parts: it’s too dense, full of bad arguments of so many different kinds that I can’t possibly do it justice with only one post.
Today, I’ll cover the introdution and first two chapters: “The Beginning of a Mathematician’s Journey”, “Apologetics and Faith Axioms”, “Paradoxes in Mathematics and Christianity”.
The introduction introduces the eponymous central idea of the book, the faith equation itself.
Bittinger is extremely clear that he intends it to be metaphorical, rather than a really literal
mathematical statement – which is fortunate given how silly it is. The faith equation is: “Faith = Mind +
Heart + Will”. According to Bittinger, this means that really being religious has to have all of those elements. That’s fine as an argument, I suppose.. It’s definitely a Christian version of the idea, but since Bittinger is deliberately expressing a Christian viewpoint, that’s fine. On the other hand – when he’s writing an allegedly mathematical book, to deliberately put a non-mathematical idea into an admittedly meaningless pseudo-mathematical equation seems to be worse that silly. It’s inappropriate. It’s a sign of things to come: a huge part of the book is wretchedly pseudo-mathematical, presenting standard Christian arguments in pseudo-mathematical terms, in order to lend them the
credibility of math.
The rest of the introduction is Bittinger’s explanation of why he wrote the book. It’s pretty typical Christian apologetics. For example, he gives his version of the history of science:
The growth of scientific knowledge flourished; but in the process, humans – carried away with
newfound intellectual power – began to conjure the notion that they could figure it all out by themselves
and no longer needed a concept of God. In effect, science became a god unto itself. Instead of pursuing God, man pursued science; science became a false idol, a false infinite so to speak.
Standard stuff – the good old “science became a false idol replacing god” – how many times have we
heard that argument before? The problem with it is that it’s really meaningless. What does it mean
to say that science became a false idol? As far as I can tell, it means, roughly, that scientists are
very bad for trying to understand the world. Wherever people used to attribute things to God,
if scientists are finding explanations that aren’t “God did it”, well then the scientists are
being bad people, replacing God with science. Seems like a remarkably silly argument: if you use your brain to explore the world and understand how things work, then you’re “worshipping a false idol”.
Moving on… Chapter one. Chapter one has two themes: Bittinger’s explanation of the idea of apologetics, and his attempt to draw a parallel between mathematical arguments and apologetics by way of what he calls “Faith Axioms”.
Apologetics, according to Bittinger, are reasoned defenses of Christianity. This book,
according to Bittinger, is a work of apologetics. He goes on to present an apologetic argument, which is
truly dreadful. He uses, as an example, an examination of the question “Could the resurrection of Jesus
have been a hoax?”. Here’s his argument against it:
Assuming you accept the reliability of the New Testament, let’s look at Matthew 28. Matthew was the
first of the four Gospels written and could be presumed to be the most accurate. In it, we’re told that on
the Sunday after Christ’s crucifixion, Mary Magdalene and possibly other women went to the tomb. They
discover the stone displaced and no body remaining. The discoverer(s) of the empty tomb was a
woman or women depending on which Gospel you read. In the society of that day, women
were held in very low regard. If the disciples were attempting a hoax, wouldn’t they have sent men to
discover the empty tomb? The men would have commanded a higher level of believability.
That is his example of good apologetics. That’s also what’s known as “a spectacular display of ignorance masquerading as knowledge”. Jesus was, supposedly Jewish, living in Israel. Touching
a dead body is a bad thing according to traditional Judaism. Dealing with the dead is
unclean, and anyone who does it becomes ritually impure, and must go through a cleansing process. Most tasks that would involve contact with a tomb are things that the supposedly righteous men that surrounded Jesus would not do. As the authors of the Gospels would have known. Having a prostitute
being the one to do it makes perfect sense in the light of the culture of the time: a prostitute is
already pretty much as impure as anyone could get.
That’s all I’ll say about his introduction to apologetics. From there, he moves on to the
allegedly mathematical part: the idea of faith axioms. He spends a lot of time explaining
the idea of axioms in mathematics, and then goes on to say that religious faith can be based
on axioms as well; and that proofs about matters of faith come down to the faith axioms. The
faith axioms strengthen the mind part of his “faith equation”.
I’m sort-of sympathetic to the basic concept of “faith axioms”. The concept is basically
one that appeals to a mathematical type. If you bore down through your beliefs, whatever they may be,
if they hold together logically, you should come to some fundamental set of basics that define them,
and those are the “axioms” of your worldview. That idea isn’t specific to the religious: any
intelligent atheist, any intelligent agnostic, anyone who’s really thought about things, and
developed a consistent concept of how they think the world works, has some fundamental set of axioms
at the core of that concept. Since he’s writing from a Christian perspective, it’s fine to call them
“faith axioms”, although I’d probably be more inclined towards “philosophical axioms”, or
Unfortunately, it turns out that that’s not what he means. He wastes a whole lot
of verbiage talking about the idea of axioms in math, and their parallels in axioms
of faith. But then, at the very end of the chapter, he includes a “final comment”:
A final comment on the word “proof” or “prove” is in order, especially for mathematicians,
before we continue. The apologetic arguments in this book are not deductions of theorems
from a finite set of axioms as is normally expected in mathematics. Instead, all kinds of
arguments – inductive, statistical, and even metaphorical – will be used to point you towards
a position of faith from a position of non-faith. The theorems we come to will all be
called faith axioms.
In other words: “Please forget the last 24 pages of gibberish. That stuff is all there
just to make it look like I’m being all mathematical, but really, I’m just talking
out my arse, using mathematical terminology to make it look all impressive-like.
Damn, but that paragraph pisses me off. It’s the point where the book moves from
an honest, if annoying, work of christian apologetics, to a dishonest book
that tries to exploit the terminology of mathematics to give its arguments more credibility
than they deserve.
Let’s move on – one more chapter to cover today. Chapter 2, “Paradoxes in Mathematics and Christianity”. This one doesn’t take nearly so long to discuss, because it’s a pile of transparent rubbish.
He wants to use the idea of paradox to build his faith axioms; the idea is that struggling with a paradox can lead you to some kind of enlightenment. Except that he cheats.
He redefines the word paradox – sometimes. He uses it to mean what philosophers
mean by “dialectic”, and he also uses it to mean mathematical contradiction, and he also
uses it to mean arbitrary pairs of things that he’d like to set against one another for no particular reason at all. And he
shifts it back and forth. It’s the same old game: misuse the terminology of math
to try to make lousy arguments look less lousy. To give you an idea of how sloppy this
chapter is, here’s a list of “paradoxes” that he gives in the introduction to the chapter:
- Natural vs. Supernatural
- Deism vs. Theism.
- Believing vs. Questioning.
- Passing a treadmill test vs. five weeks later having a heart attack.
Anyone out there think that any of those are paradoxes?
He moves on to another set of examples: a bunch of people who he asked “What’s the best and worst part of your job?”. He took the best parts and the worst parts from their answers, and said that each
of those was a personal paradox.
Then there’s a bunch of lists of his supposed paradoxes – a discussion of paradoxes in mathematics, based on proof by contradiction, and then a bunch of his cheap apologetic arguments which are
structured to look like the mathematical proof by contradiction, but are really nothing more than
the same old nonsensical hand-waving.
This chapter is painful. It’s sad – Bittinger is (or at least was) a smart guy, who wrote
some good textbooks. That he could write this, and think that he was doing something
worthwhile, that this kind of sloppiness and dishonesty was justified and could accomplish
anything – it’s just pathetic.
Fortunately, later sections of the book get funnier. Not better – just funnier. Wait
till we get to his take on Dimensions and String theory!
Another example of ignorance in that apologetics example: it’s pretty well established by biblical scholars that Mark was the first gospel to be written. Matthew and Luke came later, each cribbing material from Mark and a second source called Q.
Plus, there’s that big assumption that earlier equals more accurate. None of the gospels are eyewitness accounts, and they don’t exactly have a bibliography that says what references their authors used. Accuracy would largely depend on what those sources were. Word of mouth? Written accounts that have since been lost? The author’s own interpretation or imagination?
I’m not at all sure that you’re right about the ritual and anthropological argument with regard to Jewish Burial. Though coming into contact with a dead body was a source of impurity in terms of Torah law, in practice burial ritual was, I think, a male province. Most religious obligations were, except for those related to the home (and female purity). I don’t know enough about the state of things at the time of Jesus to know whether the Torah-mandated purification rituals were carried out (including the ashes of the infamous red heifer, etc.) or whether most Jews practiced a more modern (in the sense of “post-Diaspora”) mikveh (ritual bath) purification.
Preparing a body for burial — washing it, wrapping it — is now (and I don’t know how recent it is) a primarily male obligation, ideally a male family member.
Even when you accept them as “reliable” I guess they still leave a lot to be desired. Just half to hate those small disparities. What is Jesus’ lineage again?
Kuliniewicz is right, his ignorance of biblical criticism reveals itself in that second sentence asserting Matthew as the first Gospel while his ignorance of archeology and history reveals itself in the first. I think it’s been shown that we are long past the time when we could accept the New Testament as reliable in any sense.
This is Bittinger’s brain (e.g. calculus text); this is Bittinger’s brain on religion (e.g. Faith Equation).
I heard this guy in a radio interview the other day. He claims (as you quote) to try to convince a nonbeliever, but he just seems to be pandering to the (non-mathematician) believers. Especially “Assuming you accept the reliability of the New Testament…”! How is assuming the ancient text to be true a convincing argument for faith?
He was also talking about all the studies that have been done supporting the reliability of prayer.
I came across a seven page equation last week for a simple probability term in a wireless communication system. Yet faith = mind + heart + will. That IS amazing!
The corrosive effects of Christianity on the intellect (*sigh*)…
I’ve got a post up about “empty tomb” apologetics over at Evangelical Realism. One point I raised that you don’t hear much about: did you know that, according to the Bible, the Pharisees did not go to Pilate to ask for a guard until after the Passover? Jesus was famous for “bending” the restrictions against doing certain things on holy days, and here his disciples (and anyone else) had over a day to get in and do whatever they wanted in the tomb.
This equation begs a lot of questions. Philosophers and many others have written a few libraries full of books and papers trying and failing miserably to answer the question what is mind. An equally large number of trees have been sacrificed for paper in attempts to explain what will is and whether we have a free one or not. This just leaves the term heart. Are we talking about stuffed ox heart or fried slices of lamb’s heart? Or what exactly are we supposed to understand by the usage here?
Mark, if you ever happen to have time to look over the following, it would be really great. I do not have your grip on mathematics and logic in particular to make heads or tails of how to discern this material. It would be interesting to hear you piece this one out.
If “Faith = Mind + Heart + Will” then “Faith – Heart – Mind = Will” is the definition of ‘Will’. No, there is no equation here. It is not even a formula, strictly speaking. It is a recipe, and a badly incomplete one, very much like “Breakfast = Bacon, Eggs, Toast”, which is a list, and the list leaves out the plate, the fork, and does not resolve the issue of whether anything goes on the toast.
Empty-tomb apologetics seem to be the quintessential example of a failure to understand modern standards of evidence. Just because a story says that a tomb is empty, it doesn’t mean that another part of the story really happened. Does the testimony of the alcoholic crop-duster pilot in the movie Independence Day mean that thirteen-mile-wide flying saucers really destroyed half the cities of the United States?
Be still, my foolish heart.
Still, I have to give the grand prize to Frank Tipler’s explanation of the Resurrection:
And here I thought sphaleron fields only existed in Star Trek: Voyager.
Watt de Fawke: the egg, goes on the toast.
This just reminded me of the Meyer-Putnam Proof of the existence of God, which can be found at http://www9.georgetown.edu/faculty/ap85/papers/MeyerProof.html
and I thought I’d share.
One has to wonder whether Tipler was trying for the Templeton Prize.
I have to disagree with MarkCC about “faith axioms.” I think it’s an inherently bad concept. In math and science, axioms should be kept to an absolute minimum. If you can derive something from other axioms, you do not make it an axiom in itself. You keep them to a minimum, and even your axioms should be open to re-appraisal. For example, look at how Einstein’s theories of relativity have affected our willingness to consider the real world as being appropriately represented by a Euclidian space.
I wonder what Bittinger thinks of Dembski?
My idea of faith axioms isn’t what Bittinger ends up with – it’s the mathematical version. The basis of your understanding
of the world, reduced down to the bare essentials from which
everything else can be derived logically. And *of course* they should always be open to revision!
Bittinger uses the term “axiom” for something that is in no way, shape, or form an axiom. His faith axioms aren’t axioms. They’re not even theorems. They’re just totally random arbitrary statements.
If it’s a soft boiled egg the toast gets cut into strips which are then dipped into the egg.
Mary Magdalene is not the prostitute: this is a common error.
Thanks for the correction. I’m Jewish, and I’ve never spent any time actually learning much about Christianity, so all of the figures tend to get muddled up.
As may be seen in the above comments Mark, you make the same error that Bittinger does about second guessing the writer(s) of the Gospel. Neither you nor he really has any idea about the motives for having one person rather than another do anything in the story. As with all literature, the interpretation is left to the reader. Since we are all completely out of the context that they were written, it is highly doubtful that any of us can determine the reasoning any more. So, to use these dubious arguments as indicators of either the truth or falsehood of the story is likewise dubious. I think the much more glaring issue is in the line “Assuming you accept the reliability of the New Testament”.
If he means that the reliability as “accurately describes events”. then the conclusion was assumed in the premise. Of by reliable, he means “reliably reflects what was written by the author”, then it doesn’t seem to offer any proof for the reason I just gave above.
Isn’t the conclusion from the negation of an unlikely event of a more unlikely event a kind of a logical fallacy? (as in “If the disciples were attempting a hoax, wouldn’t they have sent men to discover the empty tomb?”)
Who cares what their motives were? Who cares how unlikely it is that everybody lied about everything? You just can’t conclude something spectacularly more unlikely from such things.
Natural vs. Supernatural, Deism vs. Theism, Believing vs. Questioning, Passing a treadmill test vs. five weeks later having a heart attack. Anyone out there think that any of those are paradoxes? He moves on to another set of examples: a bunch of people who he asked “What’s the best and worst part of your job?”. He took the best parts and the worst parts from their answers, and said that each of those was a personal paradox.
I … guess… maybe there’s commonality between these pairs in that they’re all examples of things that cause cognitive dissonance when you contrast them in that particular way? I guess? Maybe? Although I’m not sure what is gained by sitting down and listing them out.
Just to be clear, he says that reaching a state of “paradox” in this way is a good thing?
This post started out as if it was going to analyze a work of apologetics, so I had a hard time understand why we should bother. For reasons discussed in comment #19 for example, it is error prone and not especially valuable as such. Except perhaps to uncover Bad Math. Halfway down is the point that pisses you and me off for different reasons, in my case that it is really an evangelical text. So I’m aboard.
As a physicist I choose to reject Bittinger’s (and yours) model.
Axioms, however revisable, are supposed to formalize achieved knowledge. And they seldom or never captures information inherent in “we don’t know yet” or other forms of more or less incomplete knowledge.
My experience with methods and processes makes me prefer methodological principles, such as science methods and Occam’s razor, as a basis and let the results dynamically be what they may.
It is also more coherent with daily life and its variation and contingencies. In practice we don’t often have the opportunity to use rigorous methods though, and in any case our mind works by making up a narrative of what we already did, so we resort to adaptable game strategies, relative morals, et cetera to cope with events.
I have a vague memory of having this discussion here before. In any case I think it is consistent, those views of mine seem to be methodological principles and not “axioms”. (And in case they can be meaningfully appropriated as the later, beware that they may change with short notice. :-P)
I like this: Faith = Mind + Heart + Will. It uses symbols in order to clarify the expression. And why do we use symbols? When we first learn them they are abbreviations, and they clarify our expressions. But soon our expressions become extremely obscure, when we put them into logical or symbolic form, so that to work out what our symbolic expressions mean, we have to translate them back into words!
Now, there is a use of symbols where they have a special, relatively precise meaning, in maths and logic. But those are not the usual “+” and “=” that non-specialists work with. Is it OK to write £2 + £2 = £4? But those symbols are not precisely defined. We do use the same symbols in ZFC (or math), and in Peano’s axiomatic system, and in Heyting’s, and so forth, but that use of mine (which is quite normal) was none of those…
…and although we do use symbols other than “+” for things resembling, but different to, addition, e.g. logical conjunctions and set unions, nonetheless we often use “+” for mereological summation, which is not the same as arithmetical (or analytical, or vectorial, and so forth) addition, but is more like the “+” in “Breakfast = Bacon + Eggs + Toast”
It can also be used for the parts of concepts, e.g. Knowledge = True Belief + Justification (which may be false, but is not nonsense), or K = JTB + anti-luck, where “anti-luck” does not name something like a gremlin, or a curse, but something (details undiscovered) that stops the JB being T as a matter of luck. A similar process of abbreviation (or symbolization) may be in play with “Mind” and “Heart” etc.
(although having said that, the neatness of Bittinger’s equation is about the only thing I liked of his; whereas I did enjoy MarkCC’s analysis, whence I’d apologise for being a little pedantic:)
Charles, re: the Putnam/Meyer “Proof” (comment 12), it looks to me like you could take that text, substitute “Flying Spaghetti Monster” for “God” and “noodly creator” for “divine creator” and have just as firm a “proof” for the existence of the FSM…
“Assuming you accept…” has got to be the worst starting point for any scientific examination unless the thing you are supposed to be assuming to accept is something which has been or will be (in the work) shown to be correct. Using it marks the user as one who’s not applying his brain to the subject at hand, and that always kinda spoils a hypothesis for me.
Hey, Mark! Isn’t there a “Carnival of Mathematics” due from you today?
Science is encapsulated by the scientific method. It’s a operational system for increasing the predictibility of our empirical observations; it’s not a belief system about mysterious ultimate absolutes.
What’s so daggone difficult for so many to understand about that?
Oh, yes, you can. The proof is amusing, but not really of any special value. In fact, it’s just a rephrasing of the “first cause” argument that goes back to Aquinas (I think). It’s just gibberish in the same sort of vein as this book.
I prefer a product representation:
log breakfast = a*log bacon + b*log egg +c*log toast + d*log …
But these are subscripted coefficients and variables, since sometimes toast is replaced by biscuits or pancakes, and the egg may be prepared in a variety of ways, and sometimes the “bacon” may be ham or sausage (link or patty?) and so on.