Philosophical Studies:1-22 (forthcoming)

Authors
Thomas Schindler
University of Amsterdam
Abstract
Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is assumed. However, the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. This alternative emerges very naturally by reflecting on the features on which the type-theoretic solution of the problem of unrestricted quantification relies. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way. The ideas developed in this paper make crucial use of Russell’s notion of range of significance.
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DOI 10.1007/s11098-022-01776-8
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References found in this work BETA

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Saving Truth From Paradox.Hartry Field - 2008 - Oxford, England: Oxford University Press.
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Truth and Meaning.Donald Davidson - 1967 - Synthese 17 (1):304-323.
Truth and Meaning.Donald Davidson - 1967 - Synthese 17 (1):304-323.

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