Jon A., List: It does not seem right to me to say that, from Peirce's perspective, a continuum is "constituted of individuals" or that a truly continuous line "consists of individual points." My impression is that instead he saw the continuum or line as the more fundamental entity, such that its parts are not individuals or points, but themselves also continua; hence the notion that all of reality is general (i.e., continuous) to some degree. Between any two *actual *individuals in a continuum or points on a line are *potential *individuals or points exceeding all multitude. A continuum or line thus far outruns any collection of individuals or points within it. The direction of "composition," so to speak, is then from the continuum or line to individuals or points, rather than the other way around. Am I missing something?
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Feb 6, 2017 at 1:10 PM, Jon Awbrey <[email protected]> wrote: > 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-gene > rality-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 >
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