Three Principles of Inference and Deliberation Matthew Kotzen UNC Chapel Hill Department of Philosophy Draft of May 9, 2012 1 Introduction Here is a principle of deductive inference. Reasoning By Cases A ∨ B. If A then C . If B then C . Therefore, C . Here is a principle of decision theory. The Dominance Principle S knows that (A ∨ B). If S were to know that A, then S should φ. If S were to know that B, then S should φ. Therefore, S should φ. Here is a principle of inductive inference. The Partition Principle P A and P B are two subpopulations of population P that partition P . Within P A , C is evidence for D. Within P B , C is evidence for D. Therefore, within P , C is evidence for D. Almost everyone accepts Reasoning By Cases, including advocates of various prominent non-Classical logics such as Intuitionism, Relevance Logic, and Paraconsistent Logic. The Boolean-valued semantics for Classical Logic (for Boolean algebras of more than two elements), of which Supervaluational 1