Jon, list After further comparison of notation between the DNLR and 1880 AOL, I have tentatively set this up. small case (f,h) letters denote collections of individuals. A coefficient attached in front of the letter gives the number of the collection. ( for instance,"[3]a") Capital case letters are difficult. If they have a superjacent mark ( F',F'')they are individuals but if they have a subjacent number because the number of the collection is missing, then they function either as the number of the collection (usually for absolute terms) or as the number of additional places. (for relatives) But, even for absolute terms, the subjacent number can be used for number of additional places. The sign "+," seems to have been dropped. So... 1st try: [3}a = A',A'',A'''.......... etc. number of collection with three individuals. I find this preferable for reasons of calculating. a = A1 + A2 + A3....etc. "logical sum of individuals" with the number of the collection as alternatives. (One of my takes on 1880) Finally, taking "A1 + A2 + A3" as shorthand symbol for A1= A' A2= (A' + A'')A3= ( A' + A'' + A''') etc. you get a= A' + (A' + A'') + (A' + A'' + A''') = (A1 + A2 + A3) ....... There are some suggestions for ordering obviously, but no compulsion. I am toying with XOR between collection numberssuch as ...XOR (_ + _) XOR ( _ + _ ) XOR.......... 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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