Second-order languages and mathematical practice

DOI10.2307/2274326zbMath0596.03003OpenAlexW2062506884MaRDI QIDQ3727947

Stewart Shapiro

Publication date: 1985

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2274326

zbMATH Keywords

arithmeticanalysisset theorysemanticssecond-order logiccategoricityLöwenheim-Skolem theoremsadequacy of first-order languages

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Classical first-order logic (03B10)

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A defense of second-order logic ⋮ The Significance of a Categoricity Theorem for Formal Theories and Informal Beliefs ⋮ WHAT CAN A CATEGORICITY THEOREM TELL US? ⋮ Toward a modal-structural interpretation of set theory ⋮ Putnam’s Constructivization Argument ⋮ Axiomatizations of arithmetic and the first-order/second-order divide ⋮ The challenge of many logics: a new approach to evaluating the role of ideology in Quinean commitment ⋮ Putnam and constructibility ⋮ A critical appraisal of second-order logic ⋮ A model for science kinematics ⋮ IMPS: An interactive mathematical proof system

Cites Work

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• Which logic is the right logic?
• Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory
• Categoricity