How May the Propositional Calculus Represent?

South American Journal of Logic 3 (1):173-184 (2017)
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Abstract

This paper is a conceptual study in the philosophy of logic. The question considered is 'How may formulae of the propositional calculus be brought into a representational relation to the world?'. Four approaches are distinguished: (1) the denotational approach, (2) the abbreviational approach, (3) the truth-conditional approach, and (4) the modelling approach. (2) and (3) are very familiar, so I do not discuss them. (1), which is now largely obsolete, led to some interesting twists and turns in early analytic philosophy which will come as news to many contemporary readers, so I discuss it in some detail. The modelling approach is, to the best of my knowledge, newly introduced here. I am not presenting it as a rival to the other approaches, but as a philosophically interesting possibility.

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Tristan Grøtvedt Haze
University of Melbourne

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References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Tractatus Logico-Philosophicus.Ludwig Wittgenstein - 1956 - Revista Portuguesa de Filosofia 12 (1):109-110.
On sense and reference.Gottlob Frege - 1960 - In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge. pp. 36--56.

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