Single Idea 10231

[catalogued under 18. Thought / E. Abstraction / 7. Abstracta by Equivalence]

Full Idea

Perhaps we can introduce abstract objects by abstraction over an equivalence relation on a base class of entities, just as Frege suggested that 'direction' be obtained from parallel lines. ..Properties must be equinumerous, but need not be individuated.

Gist of Idea

Abstract objects might come by abstraction over an equivalence class of base entities

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 4.5)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.124


A Reaction

[He cites Hale and Wright as the originators of this} It is not entirely clear why this is 'abstraction', rather than just drawing attention to possible groupings of entities.