Abstract
AbstractMost philosophers hold that the use of our deductive powers confers an especially strong warrant on some of our mathematical and logical beliefs. By contrast, many of the same philosophers hold that it is a matter of serious debate whether any inductive inferences are cogent. That is, they hold that we might well have no warrant for inductively licensed beliefs, such as generalizations. I argue that we cannot know that we know logical and mathematical truths unless we use induction. Our confidence in our logical and mathematical powers is not justified if we are inductive sceptics. This means that inductive scepticism leads to a deductive scepticism. I conclude that we should either be philosophical sceptics about our knowledge of deduction and induction, or accept that some of our inductive inferences are cogent.
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