The Logic of Conditionals: An Application of Probability to Deductive Logic.

TLDR

The logic of conditionals has traditionally relied on truth conditions, but this chapter argues that a probabilistic foundation is needed to capture the ambiguity of true/false in conditionals and to provide a more adequate representation of conditional inference. The authors develop a probabilistic calculus to better represent conditional inferences than the propositional calculus. The calculus formalizes conditional statements and their truth-functional components, providing rules for determining the validity of symbolized inferences. The chapter articulates the core philosophical idea that conditional inference should be grounded in probabilistic reasoning.

Abstract

Publisher Summary This chapter provides a rigorous mathematical foundation for a theory of the logic of conditionals based on probabilistic concepts that are informally presented by Adams. This theory involves a formal calculus analogous to the propositional calculus for symbolizing conditional statements and their truth-functional components, and it gives rules for determining the formal validity of inferences symbolized within the calculus. The objective of setting up this calculus is to give a more adequate representation of inferences involving conditionals than does the propositional calculus. The main philosophical idea upon which the theory is based is stated in the chapter. An adequate understanding of inferences involving conditionals must take into consideration other things besides their truth conditions. This is connected with the fact that in ordinary parlance, the words “true” and “false” have no unambiguous sense as applied to conditional statements whose antecedents prove to be false.