Wednesday, August 7, 2013

The Ontological Argument and the Limits of Philosophy

If you find an argument in a philosophy text which is left deliberately shrouded in obscure terminology, chances are it is because it is transparently fallacious and disobeys the fundamental principles of philosophic reasoning.  Ontological arguments are a family of arguments for the existence of God which belong in this category.  Put simply, they take the form: "God, by definition, is perfect.  One of the qualities of perfection is existence.  Therefore, God exists."

As with a lot of ingenious philosophical arguments, like the ones which try to prove that motion isn't real or that we exist inside some video game designed by hyper-intelligent aliens from the future, I suspect most people's reaction to this argument is something like: "That's patently ridiculous and unconvincing, but I couldn't tell you why."  Philosophers, on the other hand, train themselves to value reason over insight, so it took them quite a few millennia to get around to this point of view, and a great many intelligent people have been taken in along the way.  Even Bertrand Russell recalled an experience as an undergraduate flirting with Hegelianism in which: "one day in 1894, as I was walking along Trinity Lane, [...] I saw in a flash (or thought I saw) that the ontological argument is valid. I had gone out to buy a tin of tobacco; on my way back, I suddenly threw it up in the air, and exclaimed as I caught it: 'Great Scott, the ontological argument is sound.'"

When some philosophers did get around to disproving the ontological argument, they attempted it by rather more elaborate means than your average person would be likely to employ.  Kant thought the error in the ontological argument lay in its contention that existence could be a predicate.  If existence were a predicate, after all, then everything to which we could attach any other predicate would also have to exist.  Antony Flew elaborated on the point in a classic refutation.  Suppose I employ the concept of a tame tiger, said Flew.  For a tiger to be tame, or for it to be anything else, he pointed out, it would have to exist.  Therefore, tame tigers exist, according to the logic of the ontological argument.  If you had a religion worshipping the elusive beasts, its theologians could therefore content themselves that they had settled the eternal veracity of their religion via its means.  (See here for Flew's original "tame tiger" argument.)

All of this is true enough, but it seems rather like using a hippopotamus to pick up a pea, as H.G. Wells would have put it.  The ontological argument can be dispelled by less labor-intensive means than talking about predicates and nominatives.  Namely, one can ask of it as of any philosophical argument: what facts about reality and existence entered into it at the beginning?  And what facts about reality and existence came out at the end?  If the answers to both are not substantially the same, you have an invalid argument-- this is what is known as Hume's fork, and neglect of it for most of the history of philosophy is responsible for most, if not all, of the errors of metaphysics. (See this article, also written by Antony Flew, for a good primer on the fork and its uses.)

I would appear to be saying that philosophy cannot generate new knowledge.  This is true, if by knowledge we mean new information about the world.  This cannot in fact be "generated" by philosophy.  It is false, however, if by "knowledge" we mean the implications of information we already possess, but had not yet reasoned out fully to ourselves.  All deductive reasoning takes this form.  If all men are mortal and Socrates is a man, then Socrates is mortal, as the old example goes.  You will see at once that nothing is known by the end of the syllogism that was not known at the outset-- but something new may have been realized, or grasped, or comprehended.

Deductive reasoning, therefore, is made up exclusively of definitions—of tautologies, in other words.  It cannot make available to us new knowledge; it is simply a process whereby we come to understand the knowledge we already possess.  This is true even of the most elaborate mathematical reasoning.

Some, especially mathematicians, may object at this point.  In a desire to defend the honor of their discipline, many will credit mathematics, as they have credited it in the past, with working wonders of scientific inquiry.  To realize that this is not quite what math does can be a disillusioning experience.  As Bertrand Russell once put it in an essay called “My Mental Development”: “I thought of mathematics with reverence and suffered when Wittgenstein led me to regard it as nothing but tautologies.”  Meanwhile, the superhuman complexity of many mathematical operations seems to suggest that they must be revealing fundamentally new truths not already implicit in the axioms from which they began.  It has also meant that mathematicians, brilliant reasoners though they are, are sometimes prevented by the intellectual demands of their craft from reasoning about what they are doing.  This, coupled with its ability to find the implications of things in the real world by chains of deduction far too complicated to be grasped intuitively (as we ordinarily do with our day-to-day deductions) has endowed mathematics with an almost mystical quality.  Such things account for why Philip Joudain, an associate of Russell's, once accused his fellow mathematicians of being "bad philosophers," even if they are very good other things.  He illustrates the point with an anecdote about an eminent medieval mathematician who was asked by his student how one could reach conclusions about quantities in the real world by using the fictitious concept of negative numbers and was told “Go on, and faith will guide you.”

But of course, mathematicians need not fear Hume’s fork.  It does not make even their simplest arithmetical operations superfluous.  Suppose one needed to add 45789 oranges to 596 oranges.  You have 46385 oranges at the beginning, just as you have 46385 oranges at the end, though without employing a mathematical technique, you would not have realized it.  

The point here is simply that you have no more oranges at the end as you had at the beginning.  You do not know anything about reality that could not be known beforehand.  If all of this is now starting to seem painfully trite and obvious to you, it is only because you live in an enlightened age.  It was the conventional wisdom in the 19th century, for instance, that mathematics was actually a series of inductive reasonings, and its conclusions a collection of empirical generalizations.  This idea was reproduced, for instance, in John Stuart Mill's Logic, the standard text of the era.  Mill would have us believe that those 45789 oranges were added to those 596 oranges enough times to demonstrate that, in most cases, this operation will yield 46385 oranges.  If you are willing to accept that this is not in fact what is happening in an arithmetic operation, then you are ready to accept Hume’s fork.

All of this is by way of saying that philosophical reasoning, like mathematics, cannot generate new information.  Philosophers are not scientists, and they have no members of their profession out in the field.  Therefore, all they are equipped to do is to draw inferences from the data which has already been made available to them by scholars in other disciplines.  What does this mean? It means that we should not allow ourselves to be beguiled by a chain of purely deductive reasoning starting from a set of ideas, because no matter how appallingly complex and byzantine it may be, it cannot ever tell us anything other than what was already implicit in the ideas with which it began.  It may therefore be a perfectly valid line of reasoning, but if we are not prepared to accept the ideas with which it started, then the complexity of its inferences cannot tell us anything new about “matters of fact and real existence,” as Hume put it.  So beware the libertarian who aims to prove to you by mathematics alone that every time the government employs someone it is effectively removing a job from the private sector.  There may be a lot of math involved, but chances are that one of the ideas with which our libertarian began is an implauisble one which he would reject in any other context: that the national wealth is a fixed sum.  Beware likewise any mathematical “proof” of God’s existence, even if it comes from the World’s Smartest Man.

And finally- beware the ontological argument.  You will see plainly now that it is not a valid deductive argument, because you didn’t go into it with oranges and come out with oranges—you went in with an idea, “God,” and you came out with a purported “matter of fact and real existence”—and a rather big and extraordinary one at that.  This is faulty reasoning.  The only way to make the argument valid would be to argue from ideas to the consequences of holding those ideas—to say, in other words, that if you are willing to accept that the notion of a perfect Being has reference to some really existing entity, then you must believe God exists.  In short, if you believe God exists, then you believe God exists.  This is airtight, to be sure.  But, like all deductions, it is a tautology.

Of course, theists are not the only ones responsible for arguments of this sort—they invariably dog any philosophical attempt, from any school or persuasion, to derive real conclusions about the outside world.  This is thanks to that wretched fork again.  Philosophy, like foreign intervention, has a long track record as an instrument of destruction, but not as one of creation.  This is immediately clear from any sustained acquaintance with a given philosophical school.  Its representatives are always at their clear-headed and incisive best when they are pulling down the idols of their opponents.  They turn suddenly opaque and starry-eyed, meanwhile, when they have to defend some positive claim of their own about the nature of metaphysics and ultimate reality.  Your most ruthless and bloodthirsty logical positivist can sound like a no-nonsense attorney when he’s at the throat of Heidegger, yet he will turn into the most sublime and transcendent mystic as soon as you ask him to answer Hume’s problem of induction.  The same positivists who declare, with reason, that the ontological argument is faulty because one cannot derive facts about the world from the mere definitions of words as they are used in Western languages will respond on another occasion to the problem of induction by invoking the meaning of the word “knowledge” and saying that one of the things to which it refers is in fact inductive conclusions.  This is called reasoning to a foreordained conclusion, and before climbing onto any high horses, let me say with certainty: we all do it.

The best arguments that every school of philosophy can marshal are those which defeat the claims of their rivals, not those which justify their own.  The theist’s finest hour is when she compels the scientific materialist to admit that empirical knowledge is incapable of justifying itself.  Meanwhile, the atheist is similarly well advised to battle the theist on her own territory—to redirect the conversation away from her own positive beliefs about the world and back to the problem of evil or to the paradox of an omniscient Being which exists outside of time and knows in advance everything that will occur in history which nonetheless endows its creatures with “free will.”  

I hope by now you can see why superior force of arms always belongs to the philosophical weapons of destruction.  It is no cruel coincidence—philosophy is simply not equipped to tell us about “matters of fact and real existence,” but only of “relations of ideas.” (Hume's terms again.) Its primary task remains an important one—that of clearing up misconceptions and of unraveling the implications of those ideas which more empirical disciplines have been able to establish with greater or lesser certainty.  But it is also a limited one.

I would be remiss if I didn’t briefly address the rather ingenious “modal” variant of the ontological argument forwarded in recent times by Alvin Plantinga.  It is certainly an impressive piece of work and my first response to it was something like the half-envious revulsion I mentioned at the outset: “That must be wrong, but I don’t know why.”  Let’s see if I can do better here.

As I understand it, and I could well be mistaken, the argument is supposed to proceed as follows:
(1)  According to modern theoretical physics, there is an infinite number of worlds.  The universe we perceive around us is only one of them.
(2)  Given (1), then any possible world exists.
(3)  A world in which a Perfect Being exists is possible.
(4) Given (1), (2), and (3), there is a Perfect Being in at least one of the worlds.
(5)  One of the characteristics of a truly Perfect Being would be that it would exist in all worlds.
(6)  Therefore, a Perfect Being exists in our world and in every other.

Like I said, ingenious—but too clever by half.  The problems with this argument are manifold: first of all, I’m not at all sure that (1) is a proposition which would win universal assent from theoretical physicists and applied mathematicians.  I know very little about this subject, except for the fact that philosophers and other humanists often receive their information about “parallel universes” and the like from popularizers of string theory and other catchy-sounding cosmologies-- the very people who are often regarded with suspicion by their less proselityzing colleagues.  But supposing that (1) is true, it’s by no means evident that (2) follows from it logically.  There could be an infinite number of worlds without them embracing every conceivable world, just as there are an infinite number of points of space on a line between point A and point B without that line taking up all of space-- or just as there is an infinite number of positive integers but not a single one of them is -3.3.  Similarly, there may be an infinite number of worlds without any of them containing God.

But the fundamental problem with Plantinga’s argument (unless—and I am open to the possibility—I have profoundly misunderstood it) is one which the philosopher Walter Kaufmann found in all versions of the ontological argument—and that is this business about “perfection.”  The universe, Kaufmann pointed out, has no objective or independent standard of “perfection.”  The "perfection" concept is simply a product of human vocabularies, and it was invented to refer to the utmost capacity to perform a certain function useful to human beings.  The perfect razor is one which never leaves any hair behind and never breaks the skin, says Kaufmann, the perfect sandwich one which leads to superlative ecstasies of alimentary satisfaction, and so forth.  The notion of a perfect Being, perfect in itself, may simply be incoherent-- rhetorical and sentimental nonsense at best.  Of course, the theist or Platonist may object that this insistence that qualities of goodness and perfection have no objective reality, and only make sense in reference to human values and needs, is deplorable and blasphemous.  This may well be—but it seems like precisely the sort of thing which is supposed to be proven by things like the “modal” ontological argument.  It therefore cannot be assumed at the outset as one of the premises of that argument.

This post cannot tell us whether or not God exists, but I hope that it has helped to close one popular and misguided avenue to answering the question.  I hope it may also inspire skepticism in our readers when they are confronted with a deductive argument which begins with apples and ends with pears—the numbers may be pretty, but trust me, something is amiss.  When deciding on the merits of a philosophical argument, we can still scarcely improve on the operation recommended by Hume at the end of the Enquiry:
“If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion."

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