Sets, properties, and unrestricted quantification

In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press (2006)
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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Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Semantic Values in Higher-Order Semantics.Stephan Krämer - 2014 - Philosophical Studies 168 (3):709-724.
Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.

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