List, Michael: On Nov 11, 2014, at 8:06 AM, Michael DeLaurentis wrote: > Jerry -- It’s not that Peirce didn’t accept Cantorian set theory* [he did] – > he didn’t think any aleph approached a true continuum [as he conceived it], > just as any integer raised to the power of the integers [aleph null] will get > you to aleph-1 only. The third sentence of my post, I think, is pretty clear > on that. So your counting is still stuck in the Cantorian alephs. > > *For overview, see Kelly Parker, The Continuity of Peirce’s Thought, pp. 79 > ff: “For the most part, Peirce embraced Cantor’s discoveries. He welcomed > Cantor’s work as opening the way to a mathematically rigorous investigation > of an ancient and intractable set of philosophical problems concerning the > infinite.” For some late elaboration on the points above, see CPS’s “On > Multitudes [ca. 1897], considering equivalents of Dedekind cuts and the > alephs, and concluding, inter alia [and epigrammatically], “Number cannot > possible express continuity.’ >
Parsing and commenting on Michael's message: ML: It’s not that Peirce didn’t accept Cantorian set theory* [he did] - JLRC: Do you mean to infer that CSP accepted Cantorian set theory in its entirety? Or did he not accept part of it? Did he accept Cantorian notation and Cantorian symbols and Cantorian alephs and use them rather than his own expressions? ML: The third sentence of my post, I think, is pretty clear on that. JLRC: I concurred with this aspect of your post. ML: So your counting is still stuck in the Cantorian alephs. JLRC: I concurred with respect to the counting. Infinity -1 is less than infinity, is it not? I used this sloppy representation solely because most of the contributors to this list are not into higher mathematics and it's highly specialized usage of terms. Your response omits mention of the relation among relatives as a basis for extension of graphs (diagrams.) The question I was seeking to address, at a higher level of abstract, was the relation between CSP's quote on continuity and branching (as a simpler term that is directly related to graph theory and diagrammatic logic.) In 4.179, CSP deploys the concept of two collections of M's and N's as rows, such that individuals of M and N are relatable by an r. (In current mathematical terminology, this would be expressed in combinatorial language). How do you think this passage (4.179) corresponds with Cantorian set theory? How do you think this passage (4.179) corresponds with graph theory? How would you relate the logical diagrams of the two potential correspondences? These are questions of interest to me… both questions are important for understanding CSP logic of relatives (including the triadic triad) to bio-semiotics, biochemistry and chemistry under the restriction of the meaning of atomic numbers. From this restriction, one can infer that a collection of atoms form a molecule. The diagrams of molecules obviously include branching. Cheers Jerry
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
