Hume asks on what grounds we come to our beliefs about the unobserved on the basis of inductive inferences. He presents an argument in the form of a dilemma which appears to rule out the possibility of any reasoning from the premises to the conclusion of an inductive inference. There are, he says, two possible types of arguments, “demonstrative” and “probable”, but neither will serve. A demonstrative argument produces the wrong kind of conclusion, and a probable argument would be circular. Therefore, for Hume, the problem remains of how to explain why we form any conclusions that go beyond the past instances of which we have had experience. Hume stresses that he is not disputing that we do draw such inferences. The challenge, as he sees it, is to understand the “foundation” of the inference—the “logic” or “process of argument” that it is based upon. The problem of meeting this challenge, while evading Hume’s argument against the possibility of doing so, has become known as “the problem of induction”.

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