Frege meets Dedekind: A neologicist treatment of real analysis

DOI10.1305/ndjfl/1038336880zbMath1014.03013OpenAlexW1984542683MaRDI QIDQ1860971

Stewart Shapiro

Publication date: 24 March 2003

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1305/ndjfl/1038336880

zbMATH Keywords

logicismsecond-order logicnatural numbersreal numbersintegerssecond-order arithmeticrational numbersneologicismHume's PrincipleDedekind cutsabstraction principlesfoundations of real analysisneo-Fregean programpairs of numberssecond-order real analysis

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Philosophical and critical aspects of logic and foundations (03A05) Foundations of classical theories (including reverse mathematics) (03B30) Foundations: limits and generalizations, elementary topology of the line (26A03) Second- and higher-order arithmetic and fragments (03F35)

Related Items

Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics, Abstracting propositions, LOGICISM, INTERPRETABILITY, AND KNOWLEDGE OF ARITHMETIC, Identity and the cognitive value of logical equations in Frege's foundational project, HUME’S PRINCIPLE, BAD COMPANY, AND THE AXIOM OF CHOICE, FREGE’S CONSTRAINT AND THE NATURE OF FREGE’S FOUNDATIONAL PROGRAM, Coalgebra and abstraction, Second-order logic: properties, semantics, and existential commitments, Hume's big brother: Counting concepts and the bad company objection, Bad company tamed, Bad company generalized, Neo-Fregean foundations for real analysis: Some reflections on Frege's constraint, The fruits of logicism, DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES

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