List, Michael: Am I to conclude that your post and logic separates CSP's realism of structuralism from a nominalistic philosophy of structuralism?
Am I further to conclude that a syntagm is to be excused from the logic of relatives? (progressions?) If I am taking your linguistic terminology out of the your "habits", please be so kind as to explain your usuage. As for the term, "artificial", I am simply using the normal dictionary definition: "made or produced by human beings" 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
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