Rejoinder to Skyrms and Salmon

Abstract

I would like to make some general remarks about my paper ‘Some Problems of Inductive Logic’ in view of the commentary by Brian Skyrms printed here and in view of additional commentary on the paper by Richard Cartwright.¹ My remarks are not so much intended to rebut specific criticisms as to make it clearer what I am trying to do in the paper, and why I consider its general line of attack important. The fundamental claim of the paper is that the probability calculus, intelligently used, may serve as the sole formal calculus required to represent the valid inductive inferences important for scientific method. (Of course, deductive inference would also be involved.) This is not a novel claim and it has been made in various places by Sir Harold Jeffreys, L. J. Savage, and I. J. Good. But these defenders of the claims are primarily statisticians, and they may quite reasonably be suspected of bias. Nor is the claim very precise, since the probability calculus can receive a great many interpretations. Nonetheless, any attempt to defend it philosophically seems to fall awkwardly between the formal rigorism of the Carnapians, and the formal nihilism of various positions committed to the denial of the relevance of philosophical formalism.