Sets, properties, and unrestricted quantification

In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press (2006)

Authors
Øystein Linnebo
University of Oslo
Abstract
Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical.
Keywords absolute generality  set theory  properties
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Unrestricted Quantification and the Structure of Type Theory.Nicholas K. Jones & Salvatore Florio - 2021 - Philosophy and Phenomenological Research 102 (1):44-64.
Plurals and Mereology.Salvatore Florio & David Nicolas - 2021 - Journal of Philosophical Logic 50 (3):415-445.
Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.

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