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…