more from Kathrin Koslicki

### Single Idea 17312

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

Full Idea

Being the successor of the successor of 0 is more explanatory than being predecessor of 3 of the nature of 2, since it mirrors more closely the method by which 2 is constructed from a basic entity, 0, and a relation (successor) taken as primitive.

Gist of Idea

It is more explanatory if you show how a number is constructed from basic entities and relations

Source

Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4)

Book Reference

'Metaphysical Grounding', ed/tr. Correia,F/Schnieder,B [CUP 2012], p.199

A Reaction

This assumes numbers are 'constructed', which they are in the axiomatised system of Peano Arithmetic, but presumably the numbers were given in ordinary experience before 'construction' occurred to anyone. Nevertheless, I really like this.

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