more from Penelope Maddy

Single Idea 17614

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism]

Full Idea

Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics.

Gist of Idea

The connection of arithmetic to perception has been idealised away in modern infinitary mathematics


Penelope Maddy (Defending the Axioms [2011], 2.3)

Book Reference

Maddy,Penelope: 'Defending the Axioms' [OUP 2013], p.53

A Reaction

Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor.

Related Idea

Idea 17612 Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]