Plural Logicism

Erkenntnis 78 (5):1051-1067 (2013)
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Abstract

PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of logicism which is radically alternative to Frege’s and which is grounded on the existence of individuals rather than on the existence of concepts

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Francesca Boccuni
University Vita-Salute San Raffaele

Citations of this work

Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
Logicism and Neologicism.Neil Tennant - 2013 - Stanford Encyclopedia of Philosophy.

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References found in this work

Introduction to logic.Patrick Suppes - 1957 - Mineola, N.Y.: Dover Publications.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.

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