Jon, list I am still working on this passage at end of sec. 3 (W:4 p. 198) I + J + K = 1 + L + M but does not imply (I + J + K)l = (1 + L + M) l The left side suitably rearranged is similar in number and degree to a dual relative such as the "block" from sec 2. The right side subsumes the left but adds a degree. The sign "=" doesn't shift but rather "l ( )" changes the identity of the structure.(?) I can't help but think of divisors of 6. Peirce is also intermingling "not" in here in a way that leaves me wondering occasionally how to think about "non-lovers of women," " lovers of non-women" and " lovers of women but not from Paris." Which ones are the simple negatives? Whats in the group? I am chasing "e." But thats just me. Jim W Jim W
> Date: Thu, 12 Mar 2015 14:40:21 -0400 > From: [email protected] > To: [email protected] > Subject: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 8 > > Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 8 > http://inquiryintoinquiry.com/2015/03/12/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-8/ > Date : March 12, 2015 at 2:00 pm > > Peircers, > > Here's the next selection from Peirce's 1880 "Algebra of Logic". > > <blockquote> > > Chapter 3. The Logic of Relatives (cont.) > > §4. Classification of Relatives (cont.) > > 227. These different classes have the following relations. > Every negative of a concurrent and every alio-relative is > both an opponent and the negative of a self-relative. > Every concurrent and every negative of an alio-relative is > both a self-relative and the negative of an opponent. > > There is only one relative which is both a concurrent and the > negative of an alio-relative; this is ‘identical with ──’. > > There is only one relative which is at once an alio-relative and > the negative of a concurrent; this is the negative of the last, > namely, ‘other than ──’. > > The following pairs of classes are mutually exclusive, > and divide all relatives between them: > > Alio-relatives and self-relatives, > Concurrents and opponents, > Negatives of alio-relatives and negatives of self-relatives, > Negatives of concurrents and negatives of opponents. > > No relative can be at once either an alio-relative or > the negative of a concurrent, and at the same time > either a concurrent or the negative of an alio-relative. > > 228. We may append to the symbol of any relative a semicolon > to convert it into an alio-relative of a higher order. Thus > (l;) will denote a ‘lover of ── that is not ──’. > > </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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