Where do the natural numbers come from?

DOI10.1007/BF00485187zbMath0757.03001OpenAlexW2320236514MaRDI QIDQ1202499

Harold T. Hodes

Publication date: 2 February 1993

Published in: Synthese (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00485187

zbMATH Keywords

cardinality quantifiersontological commitmentmodel-theoretic semanticshigher- order logicsMathematical-Object Theorysecond-order predicate logic

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Second- and higher-order arithmetic and fragments (03F35) Second- and higher-order model theory (03C85)

Related Items (8)

Where do sets come from? ⋮ Cardinality logics. I: Inclusions between languages based on ``exactly ⋮ RELATIVE CATEGORICITY AND ABSTRACTION PRINCIPLES ⋮ LOGICISM, INTERPRETABILITY, AND KNOWLEDGE OF ARITHMETIC ⋮ THE POTENTIAL IN FREGE’S THEOREM ⋮ Natural numbers and natural cardinals as abstract objects: A partial reconstruction of Frege's \textit{Grundgesetze} in object theory ⋮ Frege's unofficial arithmetic ⋮ Realism and paradox

Cites Work

• On the logic of demonstratives
• Axioms for actuality
• On modal logics which enrich first-order S5
• Cardinality logics. I: Inclusions between languages based on ``exactly
• Three-valued logics: An introduction, a comparison of various logical lexica, and some philosophical remarks
• Cardinality logics. Part II: Definability in languages based on ‘exactly’
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