Plural Logicism

Authors: Francesca Boccuni

Publish Date: 2013/03/23

Volume: 78, Issue: 5, Pages: 1051-1067

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Abstract

PG Plural Grundgesetze is a consistent secondorder system which is aimed to derive secondorder 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 conceptsI wish to thank the British Academy which generously funded a Visiting PostDoctoral Fellowship for me to work on this paper at the Philosophy Department University of Bristol I also wish to thank both the Philosophy Department UoB and Prof Øystein Linnebo for providing the sponsorship needed to obtain the funding and most of all I sincerely thank Prof Linnebo for his valuable supervision I am grateful to the participants of the ParisNancy workshop in Philosophy of Mathematics Paris 2011 In particular I wish to thank Andrei Rodin Marco Panza Simon Hewitt Sean Walsh Patricia Blanchette Ignasi Jané John Burgess Brice Halimi and Sebastien Gandon for their questions and remarks I also wish to thank two anonymous reviewers whose very detailed and valuable comments helped me to improve this paper dramatically Last but not least I wish to thank Paola Cantù for an amusing and particularly useful conversation on the topic of this paper in front of a pint of beer in Nancy

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