Adaptive Logics and the Integration of Induction and Deduction

In this paper, I argue that it is typical of many scientific reasoning processes that they involve the integrated use of inductive and deductive steps. I moreover illustrate with examples from the sciences that the distinction between induction and deduction is context-dependent— an inference treated in one context as deductive may in a different context may be treated as inductive—and that their integration leads to interesting forms of dynamics. The main example concerns Clausius’ derivation of Carnot’s theorem from an inconsistent set of premises. Although this reasoning process involves no other inference rules than those validated by Classical Logic, it nevertheless exhibits many of the characteristics traditionally associated with inductive reasoning processes. Finally, I show how the integrated use of induction and deduction can be explicated in terms of adaptive logics, and illustrate this with adaptive logics for three main types of scientific reasoning: an inconsistency-adaptive logic, a logic of induction, and a logic of abduction.