The Commens Dictionary
Quote from ‘Truth and Falsity and Error’
These characters equally apply to pure mathematics. [—] The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. His hypotheses are creatures of his own imagination; but he discovers in them relations which surprise him sometimes. A metaphysician may hold that this very forcing upon the mathematician’s acceptance of propositions for which he was not prepared, proves, or even constitutes, a mode of being independent of the mathematician’s thought, and so a reality. But whether there is any reality or not, the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails.
‘Real’ (pub. 09.03.13-17:40). Quote in M. Bergman & S. Paavola (Eds.), The Commens Dictionary: Peirce's Terms in His Own Words. New Edition. Retrieved from http://www.commens.org/dictionary/entry/quote-truth-and-falsity-and-error.