Classical Recapture

Details Classical Recapture Classical Recapture

2003-03-25

arxiv.org/abs/math/0303313v1

Mathematics

Logic

8 pages, 1 figure. Published in Logica e filosofia delle scienze: Atti del sesto convegno triennale, V. Fano, M. Stanzione & G

Scientific paper

The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former system which exhibits the same patterns of inference as the latter system. In particular if a relationship of this kind can be shown to exist between a non-classical logic and classical logic, the non-classical system is said to exhibit classical recapture. This has been invoked by several proponents of non-classical logics to argue that their system retains classical logic as a limit case, and is therefore a methodologically progressive successor to classical logic. In this paper I advance and defend a new and more precise account of recapture and the character of its reception by the proponents of the recapturing system. I then indicate some of the applications of classical recapture which this account makes possible.

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