Jon,list. It sounds good. By the way, I like your choice of "tuple" or maybe "n-element" as a means to sort out the number of individuals from the number of the relative, and both from the number of relations etc. I figured out that a 3-tuple monad is equivalent to a 3-tuple dual relative in "number." But in the former case, it the number of relations. (Apparently Peirce proves this in 1882.) In any case, I get the whole 0,1 thing from PL. I was just bothered by the idea that "b" is up above when "a" collapses leaving only "x" to go infintely down +/- > 0 . I also wondered whether the stated parameters are actually countably finite or not. Last aside, Peirce could use a distinct quantifier as well as an individual variable symbol. This is probably unfair. Jim W > Date: Thu, 19 Feb 2015 09:46:53 -0500 > From: [email protected] > To: [email protected]; [email protected] > Subject: Re: Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 6 > > 1880 Algebra Of Logic : Logic Of Relatives > •••:http://comments.gmane.org/gmane.science.philosophy.peirce/15566 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15698 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15699 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15701 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15703 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15706 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15709 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15714 > > 1870 Logic Of Relatives : Doctrine Of Individuals > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15673 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15679 > > Jim, List, > > At this point we need to go back to the 1870 Logic of Relatives > and review what Peirce wrote about the "Doctrine of Individuals". > This passage represents one of the most radical insights in all > of Peirce's thought and it is crucial to understanding the way > he managed to finesse the whole debacle of nominal thinking. > > But I know I've reviewed and we've discussed this many times before, > so I'm thinking I might save a few quanta of mental effort by going > back and looking up some of the previous visitations. > > May take a while to collect the links ... > > Jon > > On 2/17/2015 11:05 PM, Jim Willgoose wrote: > > > > jon, list I changed my mind. "The simple is the negative of the > > individual." This is the last line of section 1. I took the sign "~a" as > > 0 on the grounds that the product of negated individuals would be 0 if "a" > > is the logical sum of individuals. I then assumed you could introduce > > something else, say "b," and if not, then a single algebra is defined. > > That may be ok. But that is not the problem. Rather, both limits collapse > > forcing a redescription of what is individual and what is simple. Thus, > > what is in an individual up to N comes unglued in R. Correspondingly, what > > is a simple in R requires more flexibility in the definition of an > > individual. > > > > Jim W> Date: Mon, 16 Feb 2015 11:00:06 -0500 > >> From: [email protected] > >> To: [email protected] > >> Subject: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection > >> 6 > >> > >> Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 6 > >> http://inquiryintoinquiry.com/2015/02/16/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-6/ > >> Posted : February 16, 2015 at 10:30 am > >> > >> Peircers, > >> > >> As long as I've got the WordPress warmed up, > >> I might as well post the last paragraph of > >> the present section, CP 3.222. And then > >> I think it's probably time to balance, > >> or ballast, these flighty abstractions > >> with a few bags of concrete examples. > >> > >> Regards, > >> > >> Jon > >> > >> <blockquote> > >> > >> Chapter 3. The Logic of Relatives (cont.) > >> > >> §2. Relatives (concl.) > >> > >> 222. Instead of considering the system of a relative as consisting > >> of non-relative individuals, we may conceive of it as consisting of > >> relative individuals. Thus, since > >> > >> A = A:A + A:B + A:C + A:D + etc., > >> > >> we have > >> > >> A:B = (A:A):B + (A:B):B + (A:C):B + (A:D):B + etc. > >> > >> But > >> > >> B = B:A + B:B + B:C + B:D + etc.; > >> > >> so that > >> > >> A:B = A:(B:A) + A:(B:B) + A:(B:C) + A:(B:D) + etc. > >> > >> </blockquote> > >> > >> References > >> > >> • Peirce, C.S. (1880), “On the Algebra of Logic”, > >> American Journal of Mathematics 3, 15–57. > >> Collected Papers (CP 3.154–251), > >> Chronological Edition (CE 4, 163–209). > >> > >> • Peirce, C.S., Collected Papers of Charles Sanders Peirce, > >> vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), > >> vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, > >> Cambridge, MA, 1931–1935, 1958. Volume 3 : Exact Logic, 1933. > >> > >> • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, > >> Peirce Edition Project (eds.), Indiana University Press, Bloomington > >> and Indianapolis, IN, 1981–. Volume 4 (1879–1884), 1986. > >> > >> Resources > >> > >> • Peirce’s 1870 Logic Of Relatives > >> http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives > >> > > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache
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