Is Sinechism Necessary?

Abstract

As Murray Murphey observed over fifty years ago. Peirce´s apparent failure to finish his theory of continuity threatens to reduce his late philosophical system to "a castle in the air". In this paper I begin by arguing that Peirce did indeed fail to develop the rigorous theory of the continuum that he thought he needed. I then take a first stab at the question of whether he really did need it by examining the role of continuity in the 1903 Harvard lectures on pragmatism. While continuity comes into play in those lectures in a surprisingly small number of relatively brief passages, I find two whose doctrinal importance makes them worthy of detailed examination. That examination reveals that the argumentaire force of these passages is much diminished by the lack of a fully worked out theory of continuity; it also reveals how consistently Peirce was led astray by the errors and lacunae in the theory he had partially worked out. But there is good news as well as bad. Peirce has other arguments, not reluing on his failed theory of continuity, for many of the central claims he advances in the harvard lectures. When we are as skeptical as we should be about Peirce´s grand claims about continuity, the result is not to vaporize the castle altogether, but to scale it back to something more modest, but habitable nonetheless.