The principle of continuity is the idea of fallibilism objectified. For fallibilism is the doctrine that our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy. Now the doctrine of continuity is that all things so swim in continua.
C. S. Peirce, CP 1.171 (c. 1897)
Chapter 13 of Turning Signs (the netbook), on meaning spaces, has now been revamped for the 2nd edition. Now included is a sketch of Peirce’s Existential Graph system, which illustrates one of the paradoxes of inquiry: in order to learn how a whole system works, we usually have to analyze it and study how its parts are related.
Peirce did this with the continuous thought process, and his graph system was his favorite method of analysis. He did not limit himself to the human thought process, but tried to model the thought process of any being capable of learning by experience – even the “thought” of Nature herself. (What do those quotation marks around “thought” mean? The newly revised chapter delves into that as well.) Anyway, i hope it helps to give some fallible inkling of why we’re all swimming in a continuum of indeterminacy.