History and Philosophy of Logic 34 (1):53-67 (2013)

Authors
Edwin Mares
Victoria University of Wellington
Abstract
This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.
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DOI 10.1080/01445340.2012.733269
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References found in this work BETA

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Reconsidering Logical Positivism.Michael Friedman - 1999 - Cambridge University Press.
An Analysis of Knowledge and Valuation.Clarence Irving Lewis - 1946 - La Salle, IL, USA: Open Court.

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