Jerry - That you can endlessly, and apparently recursively, add any number of elements means only that you have a potentially countably infinite collection. Cantor's power-set operation allows increasing magnitude beyond the limit of countability. CSP is effectively saying no operation can move beyond the cardinality of any rank, no matter how constructed, that arrives at his conception of a true continuum. Certainly, the m-value branching of any number N of elements doesn't get you there.
From: Jerry LR Chandler [mailto:jerry_lr_chand...@me.com] Sent: Monday, November 10, 2014 11:59 AM To: Benjamin Udell Cc: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Re: Continuity, Generality, Infinity, Law, Synechism, etc. Ben, list: On Nov 10, 2014, at 9:33 AM, Benjamin Udell wrote, quoting CSP: A true C <http://psychclassics.yorku.ca/Baldwin/Dictionary/defs/C4defs.htm#Continuum> ONTINUUM (q. v.) is something whose possibilities of determination no multitude of individuals can exhaust. A minor comment with respect to this definition of a continuum. The concept of "can exhaust" is a weak concept of continuity relative to the notion of a mark on a line or the welding of points together. A simple counterexample of this definition arises in chemical logic. The conjunction of chemical elements creates molecules containing all the parts of each element. Such conjunctions beget spatial objects. An element may serve as a branching point for the graph of the molecule, it may signify 1,2,3,4,... branches into 3D space. The additions of further conjuncts is not exhaustible; no multitude of individual atoms exhausts the individuals. Yet, the branched structure, as a consequence of valence, is a set of nodes and lines representing the parts of the atoms. It is not necessarily a circle but circles are not excluded. Does this concept of conjunction conform to CSP's definition of a continuum based on the concept of exhausting individuals? Cheers Jerry _____ No virus found in this message. Checked by AVG - www.avg.com Version: 2015.0.5315 / Virus Database: 4189/8475 - Release Date: 10/29/14 Internal Virus Database is out of date.
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
