more from Michael D. Resnik

Single Idea 6301

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism]

Full Idea

Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position.

Clarification

'Congruence' is identity of shape

Gist of Idea

Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest

Source

Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [OUP 1999], p.209


A Reaction

This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component?