  Peirce held that the continuity of space, time, ideation, feeling, and perception is an irreducible deliverance of science, and that an adequate conception of such continua is an extremely important part of all the sciences. The doctrine of the continuity of nature he called “synechism,” a word deriving from the Greek preposition that means “(together) with.” In mid-1892, somewhat under the influence of reading Cantor’s works, Peirce defined a (linear) continuum to be a linearly-ordered infinite set C such that (1) for any two distinct members of C there exists a third member of C that is strictly between these; and (2) every countably infinite subset of C that has an upper (lower) bound in C has a least upper bound (greatest lower bound) in C. The first property he called “Kanticity” and the second “Aristotelicity.” (Today we would likely call these properties “density” and “closedness,” respectively.) The second condition has the corollary that a continuum contains all its limit points, and sometimes Peirce used this property in conjunction with “Kanticity” to define a continuum.