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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