o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
On 2/6/2017 9:31 AM, Jon Alan Schmidt wrote: JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-02/msg00043.html Is it right to say that “generals are constituted of individuals”? For Peirce, generality is continuity, and my understanding is that no continuum is “constituted of individuals”, since no collection of individuals is truly continuous. o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o Jon, List, I would be content to say that, in the same vein I might say, “the real line is a continuum constituted of individual points”. If it's merely the word “constituted” that is causing difficulty then I would substitute “consisting” and it would mean the same thing for all practical mathematical and scientific purposes: “the real line is a continuum consisting of individual points”. Continuity is a matter of the relations among individual points not a matter of their ontologies per se. An adequate discussion of mathematical continua and their relation to physical continua and whether there really are such things would make for a long and diverting digression at this point, but it's not really called for since the concept of continuity that Peirce relates to logical generality does not demand the full power of those sorts of continua but only a logical sort of continuity that is more general or simply weaker, depending on your point of view. I know I've remarked on this point before ... so let me go hunt that up ... o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o JA:https://inquiryintoinquiry.com/2014/11/09/continuity-generality-infinity-law-synechism-1/ The concept of continuity that Peirce highlights in his synechism is a logical principle that is somewhat more general than the concepts of either mathematical or physical continua. Peirce’s concept of continuity is better understood as a concept of lawful regularity or parametric variation. As such, it is basic to the coherence and utility of science, whether classical, relativistic, quantum mechanical, or any conceivable future science that deserves the name. (As Aristotle already knew.) Perhaps the most pervasive examples of this brand of continuity in physics are the “correspondence principles” that describe the connections between classical and contemporary paradigms. The importance of lawful regularities and parametric variations is not diminished one bit in passing from continuous mathematics to discrete mathematics, nor from theory to application. Here are some further points of information, the missing of which seems to lie at the root of many recent disputes on the Peirce List: It is necessary to distinguish the mathematical concepts of continuity and infinity from the question of their physical realization. The mathematical concepts retain their practical utility for modeling empirical phenomena quite independently of the (meta-)physical question of whether these continua and cardinalities are literally realized in the physical universe. This is equally true of any other domain or level of phenomena — chemical, biological, mental, social, or whatever. As far as the mathematical concept goes, continuity is relative to topology. That is, what counts as a continuous function or transformation between spaces is relative to the topology under which those spaces are considered and the same spaces may be considered under many different topologies. What topology makes the most sense in a given application is another one of those abductive matters. o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey isw: http://intersci.ss.uci.edu/wiki/index.php/JLA facebook page: https://www.facebook.com/JonnyCache
----------------------------- 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 .
