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Plural Quantification and Classes (2003)
| Venue: | Philosophia Mathematica |
| Citations: | 5 - 1 self |
BibTeX
@INPROCEEDINGS{Uzquiano03pluralquantification,
author = {Gabriel Uzquiano},
title = {Plural Quantification and Classes},
booktitle = {Philosophia Mathematica},
year = {2003},
pages = {3--67}
}
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Abstract
1. George Boolos has extensively investigated plural quantification in Boolos [1984] and Boolos [1985]. He observed that such locutions as the Geach and Kaplan’s sentence “There are some critics who admire only one another ” are not adequately formalized in the language of first-order predicate logic, but rather in the language of monadic second-order logic. Indeed, Boolos showed in Boolos [1984] that plural quantification is interdefinable with second-order quantification. This is an indisputable technical result, but its philosophical significance depends on the ontological status of plural quantification. What is crucial for Boolos is that plural quantification requires neither metalinguistic ascent nor ontological commitment with sets, classes or Fregean concepts. Boolos persuasively argued that plural quantification is not singular quantification in grammatical disguise. The Geach and Kaplan’s sentence involves ontological commitment with critics, but not with sets, classes, or Fregean concepts under which critics fall. The observation that second-order quantification is interdefinable with plural quantifica-tion is of special interest for the philosophy and the foundations of set theory. There are
Keyphrases
plural quantification ontological commitment fregean concept second-order quantification first-order predicate logic singular quantification critic fall ontological status plural quantifica-tion special interest indisputable technical result philosophical significance metalinguistic ascent george boolos set theory monadic second-order logic grammatical disguise
