Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective

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Journal of Philosophical Logic 48 (4):685-707 (2019)
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Abstract

Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.

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10.1007/s10992-018-9490-1

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Author Profiles

Stanislav Speranski
St. Petersburg State University
Leon Horsten
Universität Konstanz

Citations of this work

Generic Structures.Leon Horsten - 2019 - Philosophia Mathematica 27 (3):362-380.
Modelling Afthairetic Modality.Giorgio Venturi & Pedro Yago - 2024 - Journal of Philosophical Logic 53 (4):1027–1065.
Generic reasoning: A programmatic sketch.Federico L. G. Faroldi - forthcoming - Logic Journal of the IGPL.

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References found in this work

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.

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