The Principle of Ecthesis in Hypothetical Reasoning

In this paper I hope to effect at least two changes in the way logicians think about their subject. The first has to do with the notion of validity; the second has to do with how we parse out the different modes of reasoning. I shall argue that, once we separate the concept of formal validity from the more restricted notion of deductive validity, we can discover distinct systems of non-deductive argumentation such that, beginning with a characteristic axiom, we can derive further related argument forms. These forms may not be deductive, but they are still clearly argument forms of the same type as the axiom from which they were derived. For this paper I shall focus on the type of reasoning that Charles S. Peirce called ‘abduction’. Many logicians are still struggling with the idea that abduction is a mode of reasoning distinct from induction. I hope to show that there is a formal basis for the distinction.