The Commens Dictionary
Quote from ‘A Sketch of Logical Critic’
Personally, I agree entirely with James, against Dedekind’s view; and hold that there would be no actually existent points in an existent continuum, and that if a point were placed in a continuum it would constitute a breach of the continuity. Of course, there is a possible, or potential, point-place wherever a point might be placed; but that which only may be is necessarily thereby indefinite, and as such, and in so far, and in those respects, as it is such, it is not subject to the principle of contradiction, just as the negation of a may-be, which is of course a must-be, (I mean that if “S may be P” is untrue, then “S must be non-P” is true), in those respects in which it is such, is not subject to the principle of excluded middle.
‘Continuum’ (pub. 30.03.15-18:04). 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-sketch-logical-critic.