Studia Logica 96 (2):289-313 (2010)

Massimiliano Carrara
University of Padua
Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite à la Dedekind, as the unique non-logical axiom. We will also sketch a virtual interpretation of the classical continuum involving no other infinite than a countable plurality of individuals
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-010-9282-2
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References found in this work BETA

Naming and Necessity.Saul A. Kripke - 1980 - Harvard University Press.
Naming and Necessity.Saul Kripke - 1980 - In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge. pp. 431-433.
Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.

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Citations of this work BETA

Plural Logicism.Francesca Boccuni - 2013 - Erkenntnis 78 (5):1051-1067.
Plural Grundgesetze.Francesca Boccuni - 2010 - Studia Logica 96 (2):315-330.
Arbitrary Reference, Numbers, and Propositions.Michele Palmira - 2018 - European Journal of Philosophy 26 (3):1069-1085.

View all 7 citations / Add more citations

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