List: Today I came across two interesting passages that bear on the subject of this thread, the first of which is by Peirce himself.
CSP: Synechism is a doctrine I have long held but have never had an opportunity to expound. The logic of relations sets everything in logic in a new light and greatly enlarges & metamorphizes every conception. Corresponding to *generality* in *nonrelative* logic is *continuity* in *relative* logic, and the development of the principle of continuity in the light of that logical view & the adoption of it as the central principle of metaphysics is an indication of what I mean by synechism. (RL 390; 1905 May 12) This is in a draft letter addressed to F. C. S. Schiller. A current graduate student at Indiana University, Jimmy J. Aames, quotes a portion of it (among other passages) and then states the following in a 2015 paper that he has posted online ( https://www.academia.edu/12635422/Peirces_Extreme_Realism_and_Supermultitudinous_Conception_of_Continuity ). JJA: The difference between continuity and non-relative generality is the difference between generality *qua* continuity and generality *qua* possibility (potentiality; cf. CP 1.427, c. 1896). A possibility, being a First, is absolutely *sui generis*. It has no reference to any other possibility. A continuum, on the other hand, has reference to a whole range of possibilities--it embodies the rules for the determination of a possibility. Thus we should say that a continuum is a system of relations between the possible and the actual. It is a Third, a connection between a First and Second. It dictates what *would be* actualized given the relevant conditions. A possibility in itself, however, is a mere *may-be*. For me, the key insight here is that "a continuum is a system of relations between the possible and the actual." In mathematical terminology, a continuum is a system of relations between (indefinite) infinitesimals and (distinct) points. In Peirce's helpful terminology of R 144, a continuum is a system of relations between *portions *of the same dimensionality as the whole and *limits *of lesser dimensionality. In his later terminology, a continuum is a system of relations between (unmarked) material parts and (marked-off) actual parts. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >
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