Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective

&
Journal of Philosophical Logic 48 (4):685-707 (2019)
  Copy   BIBTEX

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.

Categories

Keywords

Reprint years

DOI

10.1007/s10992-018-9490-1

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

On the ordered Dedekind real numbers in toposes.Marcelo E. Coniglio & Luís A. Sbardellini - 2015 - In Edward H. Haeusler, Wagner Sanz & Bruno Lopes (eds.), Why is this a Proof? Festschrift for Luiz Carlos Pereira. College Publications. pp. 87-105.
Generic Structures.Leon Horsten - 2019 - Philosophia Mathematica 27 (3):362-380.
From magnitude to natural numbers: A developmental neurocognitive perspective.Roi Cohen Kadosh & Vincent Walsh - 2008 - Behavioral and Brain Sciences 31 (6):647-648.
On arbitrary sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.
Kant and Finitism.W. W. Tait - 2016 - Journal of Philosophy 113 (5/6):261-273.
Carnapian Structuralism.Holger Andreas - 2014 - Erkenntnis 79 (S8):1373-1391.
Why Numbers Are Sets.Eric Steinhart - 2002 - Synthese 133 (3):343-361.
Arbitrary reference.Wylie Breckenridge & Ofra Magidor - 2012 - Philosophical Studies 158 (3):377-400.
On the Essence and Identity of Numbers.Mario Gómez-Torrente - 2015 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 30 (3):317-329.
Induction, Normality and Reasoning with Arbitrary Objects.Markos Valaris - 2017 - Ratio 30 (2):137-148.
Induction, Normality and Reasoning with Arbitrary Objects.Markos Valaris - 2016 - Ratio 29 (4).
An argument concerning the unknowable.Leon Horsten - 2009 - Analysis 69 (2):240-242.
Reference to numbers in natural language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
Frege-Russell numbers: Analysis or explication?Erich Reck - 2007 - In The Analytic Turn. London: Routledge. pp. 33-50.
The innate schema of natural numbers does not explain historical, cultural, and developmental differences.Marie-Pascale Noël, Jacques Grégoire, Gaëlle Meert & Xavier Seron - 2008 - Behavioral and Brain Sciences 31 (6):664-665.

Analytics

Added to PP
2018-10-25

Downloads
48 (#323,919)

6 months
7 (#411,886)

Historical graph of downloads
How can I increase my downloads?

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.

Add more citations

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.
The principles of mathematics revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.

View all 18 references / Add more references