Mathematicians prove all sorts of truths about numbers, truths that often assert the existence of certain numbers {for example, given two rational numbers, there exists a rational number between them} and sometimes the non-existence of certain numbers {for example, there exists no largest prime number}. But what does this talk of mathematical existence amount to? Do these proofs really have to do with existence in the same way that tables and chairs, the moon and the sun, and you and me exist? Or is mathematical existence something like saying that a particular move exists in chess-say, when a pawn has moved completely across the board to a square on the opponent's back row and can be exchanged for any piece, not just a piece that your opponent has captured, which can result in your having, say, two queens on the board?
( Rebecca Goldstein )
[ Plato at the Googleplex: Why ]
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