more from E Reck / M Price

### Single Idea 10174

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'.

Gist of Idea

Mereological arithmetic needs infinite objects, and function definitions

Source

E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)

A Reaction

Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad.