List, Jon: Jon, a central problem of deciphering CSP logic of relatives in assigning meaning to the terms he uses as compared to how logic-mathematical terms are used today.
Your interpretations of his meanings are only one of many possible meanings, and, as you are well aware, we often differ on such matters. >>> Taking dual individual relatives, >>> for instance, we may arrange them all in an infinite block, thus, >>> >>> A:A A:B A:C A:D A:E etc. >>> B:A B:B B:C B:D B:E etc. >>> C:A C:B C:C C:D C:E etc. >>> D:A D:B D:C D:D D:E etc. >>> E:A E:B E:C E:D E:E etc. >>> etc. etc. etc. etc. etc. etc. >>> >>> In the same way, triple individual relatives may be arranged >>> in a cube, and so forth. The table of pairs and triples of terms in THIS paper are ORDER relations in a plane or cube. The interpretation as a "set" is a reduction of meaning from "ordered symbols" to "members of a set" (for example , Venn diagrams). Nothing wrong with such a the reduction of meaning to a simpler meaning, it is just that it is a different meaning. The reason we differ is clear to me. I insist that CSP was educated as a chemist and that he would, THEREFORE, use a logic which was consistent with the logic of chemistry as it was known in his time. Set theory is not adequate to represent the polar opposites of electricity as used in the chemical dualism of mass and electricity. During the period of 1860-1900, the logic of chemistry changed dramatically and CSP notion of relatives also changed. Compare his use of chemical terminology in the 1860/1870's with that in his long paper C. S. Peirce (1897 Jan.), "The Logic of Relatives", The Monist, v. VII, n. 2 pp. 161-217. The interpretation I gave is consistent with his usage of the term "relative" in this paper in the discussion of the bonding of logical terms in a medad. Perhaps we are merely looking at his changes of meaning of "relative" with time. As the above paper shows, the transition of meanings of the term "relative" from a chemical relative to a logical relative to a mathematical relative are subtle. As mathematics is taught today, there are literally dozens of different meanings for the notion of a "relation" as a logical operation. The reader of mathematical texts must select the logic operation signified by the term "relation" from a set of terms used in context of that text. On a different but adjacent topic, it should be noted that the treatment of the six ways to express the ORDER relation between three terms, A, B, and C, is analogous to a general mathematical structure of a group. The order of three of the six sentences express a group rotation operation on a triangle and the other three sentences express a reflection in the plane. Thus, the concept of a mathematical group provides simple logical diagrams to express differences in the grammatical order of these "relative?" terms. Cheers Jerry On Feb 12, 2015, at 11:48 PM, Jon Awbrey wrote: > Inquiry Blog > http://inquiryintoinquiry.com/2015/01/30/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-preliminaries/ > http://inquiryintoinquiry.com/2015/02/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-1/ > http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/ > http://inquiryintoinquiry.com/2015/02/11/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-3/ > http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-4/ > > Peirce List > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15566 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15607 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15608 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15616 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15624 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15634 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15636 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15639 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15641 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15646 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15657 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15659 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15660 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15664 > JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15665 > > Jerry, List, > > When in doubt, please refer to my blog versions where > I can use the appropriate math formatting and typefaces. > > Peirce uses roman (non-italic) typeface for constants or > individuals, that is, proper names of individual entities. > So I use LaTeX \mathrm{A}, \mathrm{B}, \mathrm{C}, etc. > for these. Think "Ann", "Bob", "Cal", etc. for these. > > Math style sheets dictate italics for variables, > so this is the default in LaTeX math settings. > The only variable used in CP 3.220 is ''x''. > > A general term is one that denotes any and all the elements of a set. > Peirce uses terms like "aggregate" or "logical sum" to refer to sets. > > General terms and variables are not exactly the same thing, > although there is a relation between them in some contexts > since a variable ranges over the members of a set. > > So if Bob and Cal and Don each love only Ann, > but Ann loves only Don, then the dual relative > ℓ = lover of = B:A + C:A + D:A + A:D. > > I think the problem is that "member" has two meanings. > It can mean "member of a set" or "member of a tuple". > > Regards, > > Jon > > On 2/12/2015 11:55 PM, Jerry LR Chandler wrote: >> List, Jon: >> >> If read from a technical perspective, this passage (CP 3.220) can be >> interpreted as nearly self-contradictory or utterly ambiguous. It appears >> that CSP is unable to distinguish between nouns as Proper Nouns and nouns as >> generals. But this can be a perplex gloss. >> >> Contrast: >>> Every relative, ..., is general; >> (seemingly inferring that a relative is a general, that is, a mathematical >> variable.) >> >>> An individual relative refers >>> to a system all the members of which are individual. >> >> (seemingly inferring that and INDIVIDUAL relative is not a general (!) >> and further, requiring that the concept of "an individual relative" also >> makes necessary a system of relations such that only individuals (that is, >> perhaps non-generals? ) are the only members allowed.) >> >>> The expressions >>> >>> (A : B) >>> >>> (A : B : C) >>> >>> may denote individual relatives. >> >> are expressions of pairings of symbols that are not to be interpreted as >> variables, at least as I read it. >> (The notation is NOT the usual notation for variables for multiplication or >> addition. Nor is the subsequent table of extensions...) >> >> Nevertheless, I find the meaning of CP3.220 to clear and straight forward. >> It is analogous to the meaning of natural relations among atomic relatives. >> >> "Individual relative" may refer to the Proper Name of an individual chemical >> element. >> >> It is also consistent with his later paper on the logic of relatives in >> relation to graph theory: >> C. S. Peirce (1897 Jan.), "The Logic of Relatives", The Monist, v. VII, n. 2 >> pp. 161-217. >> >> In short, in CSP's terminology, the nature of addition and of >> multiplication, differ for general relatives and individual relatives, >> vaguely similar to Boolean notions. >> >> Cheers >> >> Jerry >> >> >> >> On Feb 12, 2015, at 3:28 PM, Jon Awbrey wrote: >> >>> Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 4 >>> http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-4/ >>> Posted : February 12, 2015 at 4:00 pm >>> >>> <blockquote> >>> >>> Chapter 3. The Logic of Relatives (cont.) >>> >>> §2. Relatives (cont.) >>> >>> 220. Every relative, like every term of singular reference, is general; >>> its definition describes a system in general terms; and, as general, it >>> may be conceived either as a logical sum of individual relatives, or as >>> a logical product of simple relatives. An individual relative refers >>> to a system all the members of which are individual. The expressions >>> >>> (A : B) >>> >>> (A : B : C) >>> >>> may denote individual relatives. Taking dual individual relatives, >>> for instance, we may arrange them all in an infinite block, thus, >>> >>> A:A A:B A:C A:D A:E etc. >>> B:A B:B B:C B:D B:E etc. >>> C:A C:B C:C C:D C:E etc. >>> D:A D:B D:C D:D D:E etc. >>> E:A E:B E:C E:D E:E etc. >>> etc. etc. etc. etc. etc. etc. >>> >>> In the same way, triple individual relatives may be arranged >>> in a cube, and so forth. The logical sum of all the relatives >>> in this infinite block will be the relative universe, ∞, where >>> >>> x ─< ∞, >>> >>> whatever dual relative x may be. It is needless to distinguish >>> the dual universe, the triple universe, etc., because, by adding >>> a perfectly indefinite additional member to the system, a dual >>> relative may be converted into a triple relative, etc. Thus, for >>> ''lover of a woman'', we may write ''lover of a woman coexisting >>> with anything''. In the same way, a term of single reference is >>> equivalent to a relative with an indefinite correlate; thus, >>> ''woman'' is equivalent to ''woman coexisting with anything''. >>> Thus, we shall have >>> >>> A = A:A + A:B + A:C + A:D + A:E + etc. >>> >>> A:B = A:B:A + A:B:B + A:B:C + A:B:D + etc. >>> >>> </blockquote> >>> > > -- > > 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 > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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