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concept19th-20th century

Abstractionism

Disciplines:
logic
philosophy of mathematics

Summary

The view in philosophy of mathematics that abstract objects (numbers, sets) are obtained by abstracting from concrete instances — identifying equivalence classes under abstraction principles like Hume's Principle.

Core Contribution

Provides a neo-logicist foundation for arithmetic: numbers are defined via abstraction principles (the number of Fs = the number of Gs iff there is a one-to-one correspondence between F and G things), deriving arithmetic without explicit definitions.

Historical Influences

Gottlob Frege G. Boolos

Intellectual Lineage

No conceptual lineage found.

Allied Works

The Limits of Abstraction Principia Mathematica Die Grundlagen der Arithmetik

Contemporaries & Peers

No recorded contemporaries.

Minds Influenced

No recorded minds influenced.

Intellectual Posterity

No conceptual posterity found.

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