Single Idea 10005

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

Full Idea

That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns.

Gist of Idea

Arithmetic doesn’t simply depend on objects, since it is true of fictional objects


Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2)

Book Reference

-: 'Philosophical Review 114' [Phil Review 2005], p.215

A Reaction

This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them.