Philosophy Induction

Hume's Problem Of Induction

David Hume is known as one of the foremost skeptics and humanists of his time, who exalted in mankind's ability to transform the world through science. Somewhat ironically, then, one of his most far-reaching philosophical contributions was to phrase the problem of induction which today is often thought to deny scientific knowledge. Just a couple chapters of a single book, Hume posed a question which has yet to be satisfactorily answered, despite the great intervening time. In its most simple form, Hume's problem merely asked what evidence there was to support the instinctive understanding that the future would resemble the past, and then pointed out that since he could see no logical reason why this should be the case, then he could not with reasonably say that it must be so. And despite attempts to dismiss his challenge, it seems no one has yet come up with a simple logical response. So the challenge to find some straightforward reason to trust our instinctual inductions still stands, and though a number of alternatives have been posed, none stand up to theoretical perusal. If it is possible to argue from experience (which is to say, to use induction) to get at empirical truth, this seems to be more a coincidence than a rationally determined outcome -- for according to purely logical thought, there is no indisputable evidence that the future will resemble the past or that observed instances can predict new instances.

Before going any farther into the indefensibility of induction, it would be well worth while to take a moment to explain the difference between deduction and induction. Deduction is understood to be the method by which knowledge of specificities is gleaned from knowledge of generalities. It is based entirely on internal reasoning and thought, and does not depend on the existence of an external world to validate its conclusions. So long as its premises are true, and the steps in logic are legitimate, its conclusions will follow per force. Inductive reasoning, on the other hand, is understood to be the method by which (perceived) knowledge of general rules and principles can be gleaned from surveying specific cases and examples. It depends on the assumption that some causal link can be found between what has occurred and been observed, and depends on external evidence for its conclusions.

For some reason, the traditional example of how inductive reasoning works is to ask how it can be known that the sun will rise tomorrow. It is certain that every day as far back as one can remember or research, the sun has risen every day. How does this prove, however, that it will rise tomorrow? Even barring a super nova or an asteroid hit that took Earth off its axis, how could we know that the so-called laws of physics will be still active tomorrow? Mere deduction cannot prove that the sun will rise, though it may be able to explain how it rises. One depends rather on past experience to predict the future. The sun will rise, we believe, because it has always risen in the past.

However charming this example may be, it seems slightly misleading in its implications. The sun has risen 100% of the time from now back to the beginning of recorded history, and so it seems a very good inductive bet. However, inductive reasoning can also apply to categories where there is merely a high percentage of correlation. For example, one might reason inductively that a certain car is able to go approximately a specific maximum speed under equal conditions, even though that speed may vary slightly from test to test. Induction deals both with events that repeat without fail, and with probabilities.

The problem which Hume proposes for inductive reasoning is that while it seems like commonsense to trust it (and he never indicates that one should not live one's life according to the common sense of induction), there is no philosophic or logical reason to think it is trustworthy. A chicken who has been fed every morning by the same farmer and so inductively comes to expect food and kindness from that feeding hand may in fact be exercising common and even reasonable sense, but she is not actually being logical -- as she will discover on the day that the farmer kills her for dinner instead of feeding her. In the same way, perhaps, all our common place conclusions about the universe may one day be absolutely crushed, because while we had instinctive justification for those conclusions we did not have logical evidence for them.

There are two sorts of inductions which are commonly made, and both have flaws. The first sort is to generalize about the properties (Hume calls them the "powers") of an certain kind of object based on previous observations of specific examples of that kind of object. For example, one might say that "all swans we have ever seen or heard of are white, therefore all swans are white." This would be reasonable, perhaps, save that there is no evidence for its conclusion. Indeed, this is one example of a historically common induction that has failed, since the discovery of black swans in Australia. (Through inductive reasoning itself, then, it might be seen that inductive reasoning is prone to failure) The other sort of conclusion which might be reached through induction is one where it is suggested that a certain event or sequence of events will occur in the future because it has occurred reliably in the past. An example is the way in which Newton's Law of Gravity is assumed to be universal, or that the sun will rise, or on a more intimate level that one's spouse will continue to be loving or trustworthy.

In order to be justified in believing in the output of inductive inference and reasoning, one must be justified in believing the inductive rule (that the future resembles the past) is truth conducive. That is to say, inductive reasoning seems valid because people instinctively feel that the inductive rule is reliable and yields accurate results. Instinct, as Hume and others after him have agreed, does have its place. However, in order to actually be logically justified in believing in the inductive rule, one would be required to produce a valid argument supporting it. One might either produce a deductively valid argument, or an inductively valid argument. Unfortunately for our peace of mind, this seems to be impossible.

As far as developing a deductively valid argument goes, Hume assures us that this is impossible. Deductive reasoning depends on a priori definitions and contradictions to assure its logic. If a thing can be stated without internal contradiction -- if it could be true within a void, as it were -- then there is no reason why it may not be deductively true. Hume explains that there is no contradiction in saying that the course of nature might change, or that an object which is in all other ways like those we have seen in the past might have one or two significantly different traits. (He gives the example of snow that has the feel of fire to it, and recent experiences with acid or atomic precipitation suddenly bring this argument into a new sort of relief as something which is indeed quite conceivable). He says it is no more intelligible to say that the trees will flourish in December and decay in May than vice versa -- and that whatever makes sense within the imagining mind is not false on a deductive level but only on a practical and experiential level. If anything, the idea that the future will not resemble the past may make more sense deductively, as the very definition of time hinges on the idea of subtle change that marks off one moment from the next -- and so to say that the future will be the same as the past might seem contradictory to some. So the only other option to prove the inductive rule must be through inductive rather than deductive reasoning.

What those who depend on induction and past experience fail to realize, and what Hume points out, is that no matter how much sense this line of thought may make -- and no matter how many times it may show itself to be an adequate predictor of the future -- and no matter how large the sample of observations may be, these elements can only be taken as premises towards a conclusion about the future if the inductive rule itself works. If the only way we can argue that the inductive rule works is by attempting to show its validity inductively, then a problem arises. Until induction itself can be justified, it cannot simply be said that induction works to predict the future because it has always worked in the past -- that is the very inductive sort of reasoning which is being called into question. In short, the inductive rule is considered valid and truth conducive through a process of induction, but induction can only be considered reliable if the rule is valid.

However, arguing for the inductive rule on the basis of (unproven) induction is a circular argument which cannot be considered valid. If, as Hume suspects, induction does not work, than how can anything be proved inductively -- let alone the theory of induction itself? The conclusion that induction is valid is only true if the premises that proceed it are true, and if one of those premises is that "induction is valid" we are still left unsure of the validity of the conclusion because that statement itself has not been proven.

One might say that many instances of inductive reasoning had proven to be valid -- but these are only instances, and not evidences. There are still infinitely more instances where induction might prove false (and indeed, there have in the past been many instances where it has shown itself false in one way or another, as with the black swans, or the existence of red emeralds and theories of relativity). So through its vicious circularity and through its failure to show conclusive evidence to the contrary, the inductive justification for induction is even less promising than attempts to show deductive justification.

Since there cannot be evidence supporting induction, we cannot logically be justified in believing its conclusions. Of course Hume himself admits that "none but a fool or madman will ever pretend to dispute the authority of experience." (Hume, IV, II, 7) He is not so much asking whether or not a sane and ordinary person would function as if induction were true as he is asking whether or not they would be logically (rather than practically) justified in doing so. After all, generations of animals have operated according to inductive reasoning, which is why training technique can be used with them. Does the dog learn to expect a reward for doing some trick or other because he has a logical reason to believe that past rewards predict future rewards -- or does he merely have faith in the constancy of his master? One could very well argue that following the practice of inductive reasoning, for a human, should be a similar process. One should not pretend that this induction is logical or even reasonable, but understand that on the contrary it is merely a natural adaptive response to a difficult environment.

If inductive reasoning is understood as faith, rather than as logic, it makes a great deal more sense. Modern man hesitates to say, "I believe the sun will rise tomorrow because I have faith in a solar deity" -- so instead he prefers to say that "I believe the sun will rise tomorrow because I have faith in the law of gravity and rotation of the earth and so forth." However, it is part of Hume's point to say that the later is actually no more logically justifiable than the former. In the responses of his critiques, who frequently argue for a "pragmatic" or even "best bet" sort of approach to induction, one is not infrequently reminded of the idea of Pascal's wager that it is better to believe in God and risk being wrong (in which case nothing happens) than to fail to believe in him and risk being wrong (in which case on is punished eternally). Likewise it is a better bet to believe in the law of gravity because it has always proved true in the past than to risk jumping off a cliff in hopes that one will start flying.

Which brings us around to those who have chimed in with their opposition or possible solution to this problem of induction. One possible response would be to deny that inductive support of induction is inherently viciously circular, and to say instead that it makes a certain kind of sense. Another response would be to suggest that it does not matter whether or not induction can be logically proven, for it is equally valid even if it is illogical common sense.

One such response that denied the vicious circularity of an inductive argument for induction was that of Laurence BonJour. He proposed that while in cases where there is "no convergence on a limiting value" it is appropriate to reject the standard inductive conclusion. However, he also suggests that in many cases there is such a convergence. The only explanations of an apparent convergence between cause and effective is chance or the existence of some value upon which the results can converge.

The more that convergent results persist, the higher the possibility that it is not a mere matter of chance. The likelihood of this limiting value becomes more and more apparent with increasing numbers of results, and the possibility of it all being chance becomes "exponentially lower...so the only explanation that remains for such convergences is that they do in fact approach a real value...some regularity in nature." He argues for embracing a best fit model for the facts, and seems to suggest that since induction is the only possible way to study induction, it is also a viable way. However, there are certain objections to BonJour's claim, including the idea that if inductive reasoning is only sometimes valid then that is hardly better than not being valid at all, and the idea that observation of results may skew the apparent way in which they point to a convergent point.

Other responses have argued that induction does not need to be logically valid to be valid. These arguments may be phrased as "pragmatic" arguments, or the "common language" or "common sense" arguments. While they have different focuses, they are all essentially the same. One such pragmatist solution, offered by Hans Reichenbach, rejects both deductive and inductive attempts to prove induction, and instead claims that one must have a pragmatic justification. Induction is valid because it is, essentially, a good bet. By believing in induction, we are better able to deal with our world, predict the future with a fair degree of accuracy, and function like sane people. In short, he seems to claim that the only thing more foolish than believing in a principle without logic is to fail to believe in a principle which is central to our survival. One might say this is an almost Darwinian approach, which treats induction as a logically indefensible but realistically adaptive mutation of the mind.

The major flaw with Reichenbach's argument is that the pragmatist says nothing Hume did not already admit. Hume regularly agreed that he would have to be mad to say that one should not pragmatically live according to the rules of induction, and simply claimed that there was no epistemological support for those uniquely nonsensical but necessary rules. Whether or not they work, the rules of induction make no logical sense, and Reichenbach's argument doesn't change that.

A similar (and similarly weak) argument draws from the common-speech definitions of "reasonable" and "knowing." Philosophers such as Strawson argue that the cultural definitions of "reasonable" and "justified" and so forth include the idea of conforming to inductive standards. So, for example, a scientific theory will not be seen as reasonable --no matter how neat the math is-- if it does not line up with the way the world has worked up till now and if it does not seem to follow inductively with our general expectations. So to ask, he says, if induction is reasonable is like asking if the law is legal. It is simply confusing. However, what these ordinary language enthusiasts fail to notice is that ordinary language cannot truly dictate logic. Yes, induction may be reasonable, but it is not Reason (ie, logic). There could conceivably be many reasonable things that are not logical, because in the common speech many emotional and biological pressures are considered to be reasonable. For example, believing in God may seem very reasonable, but God cannot necessarily be proved with logic and reason.