Jerry, List, We might add that category theory, as it has been developed in mathematics in the 20th century, is a generalization upon the conception of a mathematical group. Peirce was quite familiar with Klein's use of group structure as a basis for exploring the relations between different areas of mathematics. As such, we should not assume that the general idea of what is involved in the conception of mathematical category is entirely foreign to Peirce.
Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jerry LR Chandler [[email protected]] Sent: Tuesday, April 29, 2014 7:38 AM To: Peirce List Cc: Michael Shapiro Subject: Re: [PEIRCE-L] continuing the discussion re Structuralism List, Michael: Further comments on your unusual posts concerning your linguistic perspectives on CSP's "structuralism". 1. Do you accept the fact that the concept of continuity is a geometric concept, as in CSP's example of the LINE and the separation of the line from the surface? Continuity as a concept is historically grounded in Greek philosophy, isn't it? 2. Category theory is an algebraic theory. It originated about 1941. It is exceedingly abstract form of infinities of associative relations on graphs. Linguistically, the terms are clearly separate and distinct, are they not? In addition, many. many philosophies of categories have been described. Michael, when you write: I can't say anything about mathematical category theory, are you referring as well to the algebraic form of continuity intrinsic to category theory? In other words, are you excluding the Peircian logic of continuity and representing continuity from set theory as your basis for interpreting of your linguistic "habits"? Cheers Jerry On Apr 29, 2014, at 3:38 AM, Michael Shapiro wrote: Jerry, List, I can't say anything about mathematical category theory, but I would certainly advocate applying Peirce's categoriology to the structure of the syntagm. Apropos of the latter, in what sense do you mean that my understanding of the syntagm is "artificial?" M. -----Original Message----- From: Jerry LR Chandler Sent: Apr 28, 2014 7:44 PM To: Peirce List Cc: Michael Shapiro Subject: Re: [PEIRCE-L] continuing the discussion re Structuralism List, Michael A brief comment, the purpose of which is to sharpen the differences between scientific structuralism and your usage of the term with respect to linguistic continuity. On Apr 28, 2014, at 8:21 AM, Michael Shapiro wrote: “so space presents points, lines, surfaces, and solids, each generated by the motion of a place of lower dimensionality and the limit of a place of next higher dimensionality” (CP 1.501). This quote is not a purely mathematical notion. This quote infers that the concept of "motion" is necessary for shifting (transitivity) between lower and higher dimensions. The notion of motion infers changes of positions with time, a progression of durations. This is a physical concept, independent of mathematical systems of axioms and of formal symbolic logics. This quote excludes the notion of an icon as a real dimensional object - for example, a molecule or the anatomy of our bodies. "Every element of a syntagm is to varying extents both distinct (bounded) and conjoined with every other. (In “The Law of Mind” [1892] Peirce uses the example of a surface that is part red and part blue and asks the question, “What, then, is the color of the boundary line between the red and the blue?" [CP 6.126). His answer is “half red and half blue.”) With this understanding we are reinforced in the position that the wholes (continua, gestalts) of human semiosis are simultaneously differentiated and unified." This is a brilliant example of the conundrum of continuity as it relates to the logic of relatives and the individuality of "real" objects in the "real world". CSP ducks the basic issue by asserting that it is "half red and half blue" The scientific approach to this conundrum is to label a real object (that which is presented to our senses) as an individual, and to give the identity of this separate and distinct object a name that distinguishes it from other objects. Philosophically, scientific realism demands this. Thus it is the concept of identity that clearly separates the presentative image of a part from the entire image of the whole blackboard. "To conclude and sum up, this is the kind of structuralism I mean when I speak of "structuralism properly understood" and impute it, moreover, to Peirce." It appears to me that your conclusion is not about structuralism as in the sense of anatomy or chemistry, but about the continuity of a meaning of a progression of symbols that you wish to give meaning to. I do not find this view of Peircian rhetoric to be consistent with CSP's notion of a medad as a central concept of his logic of relatives. The chemical concept of structuralism forms an exact spacial progression (topological) that generates a smooth transfer of meaning from atoms to molecules and to higher order structures, such as human anatomy. BTW, would you extend this analysis of Peircian rhetoric about continuity to mathematical category theory? To any of the several philosophical theories of categories? It is not that I disagree with your artificial understanding of the concept of "syntagm", rather it is the representation of the signs that you choose to represent the continuum. Cheers Jerry ----------------------------- 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]<mailto:[email protected]> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected]<mailto:[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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