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.

CP 5.567
‘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
Mar 09, 2013, 17:40 by Sami Paavola
Last revised: 
Jan 07, 2014, 00:58 by Commens Admin