more from Willard Quine

Single Idea 9556

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics]

Full Idea

Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects.

Gist of Idea

Nearly all of mathematics has to quantify over abstract objects

Source

Willard Quine (Word and Object [1960], §55)

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.269


A Reaction

Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually).