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Single Idea 14103

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism]

Full Idea

Pure mathematics is the class of all propositions of the form 'p implies q', where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants.

Gist of Idea

Pure mathematics is the class of propositions of the form 'p implies q'

Source

Bertrand Russell (The Principles of Mathematics [1903], §001)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.3


A Reaction

Linnebo calls Russell's view here 'deductive structuralism'. Russell gives (§5) as an example that Euclid is just whatever is deduced from his axioms.