To be is to be the object of a possible act of choice

Studia Logica 96 (2):289-313 (2010)
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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References found in this work BETA
Saul Kripke (2010). Naming and Necessity. In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge 431-433.
Stephen Yablo (2001). Go Figure: A Path Through Fictionalism. Midwest Studies in Philosophy 25 (1):72–102.

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Francesca Boccuni (2013). Plural Logicism. Erkenntnis 78 (5):1051-1067.

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