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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