Agustín Rayo, Gabriel Uzquiano
Clarendon Press, Nov 23, 2006 - Philosophy - 408 pages
Is it possible to quantify over absolutely all there is? Or must all of our quantifiers range over a less-than-all-inclusive domain? It has commonly been thought that the question of absolute generality is intimately connected with the set-theoretic antinomies. But the topic of absolute generality has enjoyed a surge of interest in recent years. It has become increasingly apparent that its ramifications extend well beyond the foundations of set theory. Connections include semantic indeterminacy, logical consequence, higher-order languages, and metaphysics. Rayo and Uzquiano present for the first time a collection of essays on absolute generality. These newly commissioned articles — written by an impressive array of international scholars — draw the reader into the forefront of contemporary research on the subject. The volume represents a variety of approaches to the problem, with some of the contributions arguing for the possibility of all-inclusive quantification and some of them arguing against it. An introduction by the editors draws a helpful map of the philosophical terrain.
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2 Relatively Unrestricted Quantification
3 Context and Unrestricted Quantification
4 Against Absolutely Everything
Universal Quantification in the Universal Sense of Universal Quantification
6 Sets Properties and Unrestricted Quantification
7 Theres a Rule for Everything
8 The Problem of Absolute Universality
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absolutely everything absolutely unrestricted all-inclusive domain argue argument assignment atomic atomistic extensional mereology background domain Boolos Cantor cardinal characterization claim concept conﬂict deﬁned deﬁnition difﬁculty discussion domain of discourse Dummett everything axiom example existence expression ﬁnd ﬁnite ﬁrst ﬁrst-level ﬁrst-order ﬁrst-order language ﬁxed formal formula framework full schemes G¨odel hierarchy higher-order identity indeﬁnitely extensible individuals inﬁnite instance interpretation iterative Liar Paradox mathematical McGee mereological sum modal naďve natural numbers notion objects ontological ordinals Oxford paradox Philosophy Philosophy of Mathematics plural quantiﬁcation possible predicate principle problem proper classes properties quantiﬁer domains quantify question range Rayo relevant rules Russell’s satisﬁes second-order logic second-order quantiﬁers semantic category semantic value sense sentence set theory set-theoretic speciﬁc theorem things Timothy Williamson tion transﬁnite true truth universal quantiﬁer universe of discourse University Press unrestricted quantiﬁcation urelements Uzquiano variables well-foundedness well-ordering Williamson 2003 ZFCSU ZFCU