To Be is to Be the Object of a Possible Act of Choice

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

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

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Massimiliano Carrara
University of Padua

References found in this work

Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.

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