Inductive reasoning (December 2003):
Deductive reasoning is fairly straightforward, and the results of a deductive argument are guaranteed to be 100% accurate (assuming the same is true of the argument's premises). That is, if we can be said to know (really know) the premises, we can also be said to know the conclusion. Can the same be said for inductive reasoning?
Well, what is inductive reasoning? Inductive reasoning involves concluding a generalization from a number of instances. Here are some examples of inductive reasoning: I've observed thousands of tomatoes and every single one of them had seeds; therefore, I conclude by inductive reasoning, that all tomatoes have seeds. Every morning the sun rises (okay, it appears to rise); the sun will rise tomorrow.
These sounds like ordinary (non-philosophical) things to say. I do expect that the sun will rise tomorrow, and the reason I believe it will do so is because it has reliably done so in the past. Similarly, if someone were willing to bet me $100 that the next tomato I cut open would be seedless, I'd think they were foolish and I would happily accept the bet. I think it's clear that inductive reasoning does provide justification for its conclusions.
The question in my mind isn't whether inductive reasoning provides justification, but whether it provides good enough justification for knowledge. After all, isn't it conceivable that somewhere there is a seedless tomato that I just haven't come across yet? Or perhaps that in a few years such a tomato will have been engineered? I still think I'm justified in my belief about tomatoes, and yet I still have a very miniscule amount of doubt about my generalization. Inductive reasoning does not seem to have the same guarantee as deductive reasoning.
Here's one statement of the (Humean) problem of induction: Why should inductive inferences be considered rationally justified from a philosophical/epistemic standpoint? From an ordinary standpoint, accepting inductive inferences seems rational; inductive inferences give us the right results. But this turns out to be circular reasoning. Why do we think inductive inferences give us the right results? Because they have given us the right results in the observable cases. That is, if we assume the principle of induction, the principle of induction is true.
Hume considers this problem (or rather a subset of this problem at length). When all observed As are B, is the conclusion that all As are B rational? His answer is no; inductive inferences are the result of an a-rational process, a belief in constancy and habit. Hume challenges his dissenters to present a demonstration that the principle of induction is justified. Hume says that such a demonstration would have to either accept the principle of induction a priori or rely on either empirical reasoning (in which case it falls prey to circularity in assuming the principle).
I won't go into the details of arguments in defense of induction, but the fall roughly into these categories: (1) a priori justification of induction is possible (Russell, BonJour), (2) induction can be inductively justified without the circularity we've seen above, (3) ordinary language justifies induction (Strawson), and (4) pragmatic reasons justify induction (Reichenbach).
Finally, another problem of induction (known as the new riddle of induction) was introduced by Goodman. It goes as follows: Suppose that prior to some specified time t a large number of emeralds were observed and they were all found to be green. By inductive reasoning, we can conclude that all emeralds (including those to be examined after time t) are green. So far, so good. But consider the (admittedly strange-sounding) term "grue", defined to mean "green if examined before time t and blue if examined after time t". Since all emeralds observed before time t were found to be grue, it seems we should be able to conclude by induction that all emeralds are grue. This means we should be able to conclude that all emeralds after time t are blue. But then we've concluded that all emeralds after time t are both green and blue, and this can't be right.
How do we explain why the inductive reasoning is valid (or at least more valid) in the green case, but not the grue case? Goodman's answer is that some properties are more projectible (also more entrenched) than others, and that "green" is more projectible than "grue".