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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