Relative Interpretations and Substitutional Definitions of Logical Truth and Consequence

In Igor Sedlár & Martin Blicha (eds.), The Logica Yearbook 2019. London, Vereinigtes Königreich: College Publications. pp. 33 - 47 (2020)
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Abstract

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

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Mirko Engler
University of Vienna

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References found in this work

Philosophy of logic.Willard Van Orman Quine - 1970 - Cambridge: Harvard University Press. Edited by Simon Blackburn & Keith Simmons.
Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Philosophy of Logic.W. V. Quine - 2005-01-01 - In José Medina & David Wood (eds.), Truth. Blackwell.
On second-order logic.George S. Boolos - 1975 - Journal of Philosophy 72 (16):509-527.
The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.

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