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Frege on the Real Numbers

Eric Snyder and Stewart Shapiro

in Essays on Frege's Basic Laws of Arithmetic

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198712084
eISBN:
9780191780240
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198712084.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper is concerned with Gottlob Frege’s theory of the real numbers as sketched in the second volume of his masterpiece Grundgesetze der Arithmetik. It is perhaps unsurprising that Frege’s theory ... More


Enacting Infinity: Bringing Transfinite Cardinals into Being

Rafael E. Núñez

in Enaction: Toward a New Paradigm for Cognitive Science

Published in print:
2010
Published Online:
August 2013
ISBN:
9780262014601
eISBN:
9780262289795
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262014601.003.0012
Subject:
Philosophy, Philosophy of Mind

This chapter argues that cases wherein an empirically observable physical reality is lacking—when there is no pregiven world to be mentally re-presented—are provided by mathematics. In particular, it ... More


Neo-Fregeanism and the Burali-Forti Paradox

Ian Rumfitt

in Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198792161
eISBN:
9780191866876
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198792161.003.0010
Subject:
Philosophy, Moral Philosophy

This chapter considers what form a neo-Fregean account of ordinal numbers might take. It begins by discussing how the natural abstraction principle for ordinals yields a contradiction (the ... More


Numerals: Earrooyn

in Practical Manx

Published in print:
2008
Published Online:
May 2014
ISBN:
9781846311314
eISBN:
9781781380680
Item type:
chapter
Publisher:
Liverpool University Press
DOI:
10.5949/UPO9781846315596.009
Subject:
Society and Culture, Cultural Studies

Manx cardinal and ordinal numerals can occur with or without a noun. This chapter discusses cardinal numbers; cardinal numbers with noun; duals; nouns of measure after numeral; numerals preceding ... More


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