Where do the natural numbers come from?
type: Item
instance of: scholarly article
title: Where do the natural numbers come from?
zbMATH Open document ID: 0757.03001
DOI: 10.1007/BF00485187
author: Harold T. Hodes
published in: Synthese
publication date: 1993-02-02T00:00:00Z
review text: This paper offers a model-theoretic development of the ideas presented in the author's paper: ``Logicism and the ontological commitment of arithmetic'' [J. Philos. 81, No. 3, 123-149 (1984)]. In Section 1, Section 5 and Section 10 I will discuss the philosophical motivation for this project. For more, see the author [loc. cit.; ``Ontological commitment, thick and thin'', in: G. Boolos (ed.), Meaning and method: Essays in honour of Hilary Putnam (Cambridge, 1990)]. More information about some of the higher-order logics that will be introduced below may be found in the author's papers: ``Cardinality logics. I, II'' [Ann. Pure Appl. Logic 39, No. 3, 199-238 (1988; Zbl 0653.03023); J. Symb. Logic 53, No. 3, 765-784 (1988; Zbl 0668.03003)].
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B15
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03C85
zbMATH DE Number: 109028
zbMATH Keywords: cardinality quantifiers
zbMATH Keywords: second-order predicate logic
zbMATH Keywords: model-theoretic semantics
zbMATH Keywords: Mathematical-Object Theory
zbMATH Keywords: ontological commitment
zbMATH Keywords: higher- order logics
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00485187
OpenAlex ID: W2320236514
description: scientific article; zbMATH DE number 109028