수학적 대상의 존재와 우연성

초록

According to Field, mathematical objects do not exist but they might have existed. In this paper I examine how persuasive this 'contingent' nominalism could be. For this I give a detailed analysis of the recent debate on the contingency of mathematical objects. I argue that the putative connection between contingency and explanation could still be sustained, but an independent argument is needed in order to support a general principle underlying the connection. I show that the attacks based on the anti-insularity principles already reflect their own positionson the modal status of the existence of mathematical objects.

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