The Rationality of Induction — David Stove

Is deductive logic empirical? (No) Is inductive logic also empirical? (No) Is induction justified and, if so, is it just an extension of logic? (Yes)

Stove takes Hume (and his nuttier current-day followers such as Popper) to task and shows that, yes, induction is rational. He also shows that the common belief that ordinary is formal is a myth. Knowledge of the validness of certain arguements must come from intution, as Carnap argued, and Stove proves. He shows that certain forms of logical arguments do not always give valid conclusions, and that all arguments must be judged individually. In his words, “Cases Rule”.

This is another in a series of books that I think are largely unknown by most statisticians and probabilists, especially those who tend toward so-called pure mathematics. But this book, like Jaynes and Cox, argue the case for logical, as opposed to subjective, probability forcefully and conclusively. They deserve to be more widely read because, I believe, they have a great deal to say on the foundations of our field.

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