Jon, list Went back and took notes on sec 1. As an aside, I did a little reading from Dr B Peirce's lecture in 1870 in D.C where he spoke of a single, double, triple, up through sextuple algebras. Interesting stuff. (Negative integers are nilpotent with odd powers and idempotent with even powers!#? There is a block diagram which I am trying to understand.) The lecture is available in pdf fascimile online. Further aside, I am new to thinking in blocks and cubes. I am trying to think in terms of a carpenters square with m x n on the two edges such that they transpose when you move 90 degrees. But you can also turn it over and thus orientation of i,j come into play. I need to master m,n,i,j so that I think less concretely. But to the point. Peirce sets ideal limits on the individual term A and the simple term a. The formula "~a" suggests the destruction of all the individuals A. Yet in light of the notation on the previous page, "b" is lurking out there and "x" is back in play such that: ~a= 0 + b. If ~a = 0 + 0, then you have defined a single algebra. 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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