Hi Jon, Lists, I have been comparing the steps Peirce takes in the 1870 "Notation for Logic of Relatives" to the path he lays out in the 1880 "On the Algebra of Logic." Your notes on the earlier essay are quite helpful to me, but they stop at CP 3.77 where he introduces the sign of involution. I'd like to ask if you have a set of notes for the remaining sections of the essay that you would be willing to share.
The discussion of the doctrine of individuals that starts at CP 3.93 throws considerable light on his account of individuals in the later essay. As such, I would like to get a better grasp on what he is doing, for example, when he makes the transition from individual relatives to infinitesimal relatives. (CP, 3.100) I'm also interested in getting a better handle on the way he is modeling the relations involved in the logical quaternion on Hamilton's conception of the algebraic quaternion. (CP 3.125; W2, 409-10) James Van Evra offers some suggestions for thinking about the general impetus behind Peirce's moves. He says that, at this point in the essay, "strange things begin to appear." Peirce employs a wide range of mathematical devices in the development of the system of algebraic logic, including "logarithms, derivatives, complex numbers, quaternions, transcendental equations, non-Euclidean geometry, and more, all within a strictly logical context and without regard to the limits of interpretability." (Studies in the Logic of CSP, 149-50) My sense is that this describes the general impetus for Peirce's moves in too strong of terms. Peirce does not think it strange to apply this wide range of mathematical conceptions to the development of a notation for a mathematical logic of relatives, and he is thinking quite hard about the limits of the interpretability of the notation he is describing. After all, he is trying to develop a system of logical relatives that will be sufficiently rich to analyze the conceptions used and inferences made in these areas of mathematical inquiry. So, if Jon (or anyone else) has suggestions for reading these parts of the 1870 essay, I'd like to see them. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]] Sent: Friday, February 13, 2015 9:02 PM To: Jim Willgoose; Jerry LR Chandler; Peirce List Subject: Re: [PEIRCE-L] Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 4 Re: Jim Willgoose At: http://permalink.gmane.org/gmane.science.philosophy.peirce/15677 Jim, List, These are some of the reasons that I prefer "elementary relative" to "individual relative" and "absolute", "monadic", or "non-relative" to "term of singular reference", since the words "individual" and "singular" have too many meanings in too many different contexts. Regards, Jon On 2/13/2015 10:21 PM, Jim Willgoose wrote: > Jon, > > Yes. You are right. I should have stayed out of that one on reference. The > question of generality is open though. > > Jim W > >> Date: Fri, 13 Feb 2015 18:04:13 -0500 >> From: [email protected] >> To: [email protected]; [email protected]; [email protected] >> Subject: Re: [PEIRCE-L] Peirce’s 1880 “Algebra Of Logic” Chapter 3 • >> Selection 4 >> >> Jim, List, >> >> No, I think that is incorrect. >> >> "A non-relative term may be called a term of singular reference." >> >> I don't think that leaves any room for A:B to be a term of singular >> reference. >> >> The series singular, dual, plural here describes the arities 1, 2, ≥ 3. >> >> A non-relative term is also known as an absolute term. >> >> The letters A, B, C here refer to individuals, not classes. >> >> All the concepts and distinctions treated in this chapter, modulo the usual >> variations in notation and terminology, are discussed in much greater detail >> in the 1870 Logic of Relatives. See the following article, where I added >> much >> in the way of illustrative examples: >> >> http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives >> >> Regards, >> >> Jon >> -- 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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