Single Idea 8311

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

If 2 is a particular, 'adding' it to itself can, it would seem, only leave us with 2, not another number. (If 'Socrates + Socrates' denotes anything, it most plausibly just denotes Socrates).

Gist of Idea

If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2

Source

E.J. Lowe (The Possibility of Metaphysics [1998], 10.7)

Book Reference

Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.224


A Reaction

This suggest Kant's claim that arithmetical sums are synthetic (Idea 5558). It is a nice question why, when you put two 2s together, they come up with something new. Addition is movement. Among patterns, or along abstract sequences.

Related Ideas

Idea 5558 7+5=12 is not analytic, because 12 is not contained in 7 or 5 or their combination [Kant]

Idea 9974 Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]