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person1970s-present

Stewart Shapiro

Disciplines:
logic
philosophy of mathematics

Summary

American philosopher of mathematics who developed ante rem structuralism — mathematical objects are positions in structures that exist independently of their instantiations — and has written on philosophy of logic.

Core Contribution

Ante rem structuralism: mathematics is the science of structure; mathematical objects are positions in structures; structures exist as abstract objects prior to any instantiation. Defended second-order logic as genuine logic against Quine's objections.

Key Spikes & Highlights

  • Ante rem structuralism holds that the natural number structure exists as an abstract object — the specific set-theoretic representatives of numbers are arbitrary, vindicating Benacerraf's indeterminacy.
  • Argues that second-order logic is legitimate despite Quine's accusation that it is set theory in disguise — the expressive power difference from first-order logic is philosophically significant.

Notable Works & Achievements

Foundations without Foundationalism

Philosophy of Mathematics: Structure and Ontology

Thinking about Mathematics

Historical Influences

Paul Benacerraf Michael Dummett W. V. O. Quine

Intellectual Lineage

Analytic Philosophy Philosophy of Mathematics

Contemporaries & Peers

Penelope Maddy Hartry Field Kit Fine

Minds Influenced

No recorded minds influenced.

Intellectual Posterity

Structuralism in Philosophy of Mathematics

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