more from David Bostock

Single Idea 18146

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

Full Idea

If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle.

Gist of Idea

If Hume's Principle is the whole story, that implies structuralism


David Bostock (Philosophy of Mathematics [2009], 9.A.2)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.272

A Reaction

Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely.

Related Idea

Idea 18145 Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock]