more from James Robert Brown

Single Idea 9622

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers]

Full Idea

'There are two apples' can be recast as 'x is an apple and y is an apple, and x isn't y, and if z is an apple it is the same as x or y', which makes no appeal at all to mathematics.

Gist of Idea

'There are two apples' can be expressed logically, with no mention of numbers


James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.53

A Reaction

He cites this as the basis of Hartry Field's claim that science can be done without numbers. The logic is ∃x∃y∀z(Ax&Ay&(x=y)&(Az→z=x∨z=y)).