The Commens Dictionary
Quote from ‘The Logic Notebook’
A continuum is a system of relations determined by a general rule, which by virtue of its perfect generality does not suppose any ultimate units (indeed such a unit would involve a breach of the continuity, because introducing something not general), but which yet not only permits the distinction of units but provides relations by which any multitude of ultimate units would be perfectly distinguished from one another.
Ah! I had better say a system of connections rather than a system of relations.
‘Continuum’ (pub. 30.03.15-13:34). 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-logic-notebook-2.