Logic and Formalization

In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger, Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press (forthcoming)
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Abstract

This chapter focuses on formalizing understood as the practice of assigning formulas to ordinary-language arguments and sentences with the aim of representing logical forms transparently and making it possible to give formal proofs and theoretically respectable explanations of validity. This practice raises the question of how the adequacy of formalizations can be assessed. The relatively few attempts at explicating criteria of adequacy for formalizations have mostly focused on two ideas. Either formalizations are required to correctly represent inferential properties of sentences, or they are expected to correspond to sentences with respect to truth-conditional structure. This chapter analyses how such criteria function, what presuppositions they rest on, and what their limitations and problems are. Issues raised by equivalent sentences and equivalent formalizations show that these criteria still permit formalizations that lead to unnecessarily trivial or wrong explanations of validity. What is missing is that adequate formalizations must be the result of assigning formulas to sentences in a systematic way. This links criteria of adequacy to compositionality and procedures of formalizing.

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Georg Brun
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