The Epistemic Understanding of Natural Deduction (original) (raw)

We often think of a logic as a three-part system composed of an uninterpreted language, a semantic system, and a deductive system. Keeping the language fixed, different logics can be produced by changing the semantic system or the deductive system or both. Choosing a logic is not just a matter of convenience. Although two logics that differ only in deductive system can be equivalent in the sense of always deriving the same conclusions from the same premises, it is often true that each system corresponds to a specific approach to logic. Natural deduction, specifically, corresponds to approaching logic as a mathematical model of correct deductive reasoning. In natural deduction, the flow of reasoning is not just a linear sequencing in which each formula in each step is derived just from its previous lines. Rather, natural deduction involves, in addition to steps derived just from their previous lines, also steps derived from subderivations that may contain further subderivations, each subderivation starting from a supposition. In natural deduction, the actual deductive process is more explicitly analyzed than in other deductive systems—with the same language and semantic system. This paper also investigates some consequences of understanding natural-deduction systems in an epistemological framework.