Quantificational Logic and Empty Names

Philosophers' Imprint 13 (2013)
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Abstract

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia.

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2013-05-31

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Andrew Bacon
University of Southern California

Citations of this work

Classical Opacity.Michael Caie, Jeremy Goodman & Harvey Lederman - 2019 - Philosophy and Phenomenological Research 101 (3):524-566.
Conversational Exculpature.Daniel Hoek - 2018 - Philosophical Review 127 (2):151-196.
Asymmetries in the Value of Existence.Jacob M. Nebel - 2019 - Philosophical Perspectives 33 (1):126-145.
An Argument For Necessitism.Jeremy Goodman - 2016 - Philosophical Perspectives 30 (1):160-182.

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References found in this work

The Varieties of Reference.Gareth Evans - 1982 - Oxford: Oxford University Press. Edited by John Henry McDowell.
Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.

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