Tuesday, October 8, 2019

On The Problem of Induction

The problem of induction is a legacy of David Hume even though he never used the word “induction” in his works. In a series of works, the first of which is his A Treatise of Human Nature, Hume offers his arguments against induction. He shows that the truth of the premises of an inductive argument, even if it enjoys a great deal of evidential support, do not necessarily lead to the truth of the argument’s conclusion.

Hume points out that for you to have the reason to believe the result of your inductive inference, you must have the reason to believe that the uniformity principle—which states that unobserved instances resemble observed instances—is true. We can have an inductive argument only when past performances resemble future results in ways that will allow us to make generalizations about those future results. But the reason to believe in the uniformity principle is not self-evident.

Hume divides claims into two categories — “relations-of-ideas claims” and “matter-of-fact claims”. The matter-of-fact claims, he points out, can be either true or false based on the facts in reality that can be observed directly. However, the relations-of-ideas claims are true or false by virtue of the concepts, or ideas, that they involve—to establish the truth or falsehood of such claims you have to go out into the world and verify.

Now the uniformity principle is not a relations-of-ideas claim because there is nothing in the concepts involved in the claim that will guarantee its truth. But if all claims are either relations-of-ideas claims or matter-of-fact claims, and the uniformity principle is not a relations-of-ideas claim, then it must be a matters-of-fact claim.

The uniformity principle is a claim about the unobserved since it talks about unobserved instances resembling observed instances. But since the uniformity principle is itself a matter-of-fact claim about the unobserved, it means that you can have a reason to believe that the uniformity principle is true, only if you already have the reason to believe that the uniformity principle is true.

But this means that the justification for the uniformity principle comes from the uniformity principle—the argument is circular and therefore it is invalid. Thus Hume has reached the conclusion that he wants—he has shown that there cannot be any non-circular logical argument for believing in the answers that we derive from inductive arguments.

There are several ways by which Hume’s argument against induction can be rejected. I am not getting into those arguments in this post—but it is worth noting that while there can be any number of arguments to establish a particular view of induction, there cannot be any ultimate solution to the problem. It is not necessary that there should be a solution to every philosophical problem—the problem of induction is one of those problems for which there is no solution.

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