Single Idea 8693

[catalogued under 18. Thought / E. Abstraction / 7. Abstracta by Equivalence]

Full Idea

Hume's Principle has a structure Boolos calls an 'abstraction principle'. Within the scope of two universal quantifiers, a biconditional connects an identity between two things and an equivalence relation. It says we don't care about other differences.

Clarification

Hume's Principle says numbers are identical through one-to-one correspondence

Gist of Idea

An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect

Source

George Boolos (Is Hume's Principle analytic? [1997]), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 3.7

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.75


A Reaction

This seems to be the traditional principle of abstraction by ignoring some properties, but dressed up in the clothes of formal logic. Frege tries to eliminate psychology, but Boolos implies that what we 'care about' is relevant.