A random thought–the problem of induction, popularized by Hume, is one of those long-standing issues in philosophy. The gist is roughly:
Inductive reasoning works by taking some set of observations and generalizing their characteristics to a larger set of phenomena. A typical example is this–How do we know the sun will rise again tomorrow? It has always done so in the past, so it will do so again tomorrow. We can take a step back and ask–How do we know that, just because something has always happened in a certain way in the past, that it will also happen that way in the future? Or, more generally, how do we know that we can take observations of some subset of a class of phenomena and then assume that the observed characteristics also hold for the whole class? Hume’s contention was that any answer to this question will, itself, rely on inductive reasoning (e.g.–Yesterday I predicted, on the basis of past events, that the sun would rise today, and it did! Therefore, the same reasoning will work again tomorrow.), and that’s circular, so we can’t get anywhere. Apparently, no one has found a way out of Hume’s problem of induction. We simply have to take inductive reasoning on faith, or give it up.
The alternative to inductive reasoning is deductive reasoning, in which we simply work in the opposite direction. We infer the characteristics of a particular individual from characteristics known to hold for the class of individuals to which it belongs. A typical example is this–All men are mortal; Socrates is a man; therefore, Socrates is mortal. Responses to Hume’s problem of induction focus on trying to provide a deductive proof for inductive reasoning. Nobody seems to have any qualms about deductive reasoning itself; there is no corresponding “problem of deduction” to complement the “problem of induction”. But we might ask:
So, OK, we can’t provide a deductive argument establishing that inductive reasoning works. What about the opposite? Can we provide an inductive argument establishing that deductive reasoning works? It is not intuitively obvious how we would go about this. For instance, we might pull out the old chestnut about Socrates and say, “Well, he died, so the deductive argument for his mortality works!” However, all this tells us is that the conclusion of that particular argument happens to be true, not that the reasoning works. If we followed that line, we’d end up having to say that any reasoning that happens to lead to a true conclusion is valid, and any reasoning that leads to a false conclusion is invalid… but that is in direct opposition to the operations of deductive reasoning. I can’t really think of a way around this problem. Maybe someone has done it, I don’t know. Maybe deductive reasoning just feels so right that we can’t imagine giving it up; but, then, we’re in no danger of giving up inductive reasoning, either, whether it can be justified or not.