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A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic

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Abstract

If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be the truth-value that had to be preserved under the substitution of co-extensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ‘Vulcan rotates’, are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are state-of-affairs-as-extension-related extensional. This implies (in accordance with the basic idea of state-of-affairs semantics) that such sentences are also truth-value-related extensional in Quine’s sense, but not truth-value-as-extension-related extensional.

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Acknowledgements

I am indebted to Karel (Joe) Lambert for his improvements of a longer version of the paper as well as to two anonymous referees for their helpful comments. Also, I would like to thank Rodrigo Leeb and Kevin Thompson for proof-reading.

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  1. Department of Philosophy, University of Salzburg, Franziskanergasse 1, 5020, Salzburg, Austria

    Hans-Peter Leeb

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  1. Hans-Peter Leeb
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Correspondence to Hans-Peter Leeb.

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Leeb, HP. A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic. J Philos Logic 49, 1091–1109 (2020). https://doi.org/10.1007/s10992-020-09550-z

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