Models for Counterparts Authors Original Paper

First Online: 08 October 2010 Received: 01 August 2010 Accepted: 08 September 2010 DOI :
10.1007/s10516-010-9120-1

Cite this article as: Torza, A. Axiomathes (2011) 21: 553. doi:10.1007/s10516-010-9120-1
Abstract
Lewis proposed to test the validity of a modal thesis by checking whether its possible-world translation is a theorem of counterpart theory. However, that criterion fails to validate many standard modal laws, thus raising doubts about the logical adequacy of the Lewisian framework. The present paper considers systems of counterpart theory of increasing strength and shows how each can be motivated by exhibiting a suitable intended model. In particular, perfect counterpart theory validates all the desired modal laws and therefore provides a way out of the logical objection. Finally, a weakening of perfect counterpart theory is put forward as a response to some metaphysical objections.

Keywords
Counterpart theory
Modal logic
Identity
Intended model

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