How May the Propositional Calculus Represent?

Authors
Tristan Haze
University of Sydney
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.
Keywords philosophy of logic  propositional calculus  applied logic  interpretation of logic  proof-theory  modelling
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References found in this work BETA

On Sense and Reference.Gottlob Frege - 2010 - In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge. pp. 36--56.
On Concept and Object.Gottlob Frege, P. T. Geach & Max Black - 1951 - Mind 60 (238):168-180.

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