more from Michael D. Resnik

Single Idea 6295

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

Full Idea

If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects.

Gist of Idea

There are too many mathematical objects for them all to be mental or physical

Source

Michael D. Resnik (Maths as a Science of Patterns [1997], One.1)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [OUP 1999], p.3


A Reaction

No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology.