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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

Source

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)).