Mathematics is not a positive science

From "The Regenerated Logic", _The Monist_, vol. 7, pp. 19-40, (1896)

From CP 3.428 & Monist v. 7 p. 24

Mathematics is not a positive science; for the mathematician holds himself free to say that A is B or that A is not B, the only obligation upon him being, that as long as he says A is B, he is to hold to it, consistently. But logic begins to be a positive science; since there are some things in regard to which the logician is not free to suppose that they are or are not; but acknowledges a compulsion upon him to assert the one and deny the other. Thus, the logician is forced by positive observation to admit that there is such a thing as doubt, that some propositions are false, etc. But with this compulsion comes a corresponding responsibility upon him not to admit anything which he is not forced to admit.