Listers,
It might be useful at this point in the discussion for me to try to be more specific about what I consider to be structuralism "properly understood." Perhaps I can clarify my understanding by casting it in terms of Peirce's synechism, the doctrine of continuity that qualifies as the all-embracing framework for Peirce's whole philosophy.
The general characterization of continuity in Peirce can be reified by seeing how he aligns it with his mathematics, specifically with what comes to be called topology or non-standard analysis. Speaking of topological space, Peirce qualifies it as continuous in the event it meets either of two conditions: it must return to itself or contain its own limits. If it is “unbroken,” it must return to itself; if it has limits, such limits represent a breach of continuity, manifested as “topical singularities” of a lower dimensionality than that of the continuum itself. In two-dimensional space the limits can be either points or lines. In the case of a line, the topical singularity is itself continuous, but it is a continuum of a lower dimensionality than that of the space that contains it: “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).
In this manner a whole series of continua of varying dimensionalities can be envisaged, embedded within one another, with any continuum of N dimensions having as its limit, in the form of a topical singularity, a continuum of not more than N-1dimensions. Dimensionality, then, is conceived as a topological characteristic of continua.
Applying these topological ideas to the analysis of the hierarchical structure of simultaneous syntagms in semiosis, such as that of phonemes or tropes, we can identify syntagms with continua and rank relations with dimensionalities. (This matches, in a shorthand version, some of the late Kenneth Pike’s main ideas about language structure.) The segmentation of the continuum into elements that are organized hierarchically is attended by boundaries between them, corresponding to the idea of limits in topological space.
Language and culture are organized into continua that illustrate Aristotle’s conception of a continuum as containing its own limits. 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.
But perhaps the question we really need to ask is: what is simultaneity as such? And more precisely: does simultaneity have parts? We know that in visual perception the parts of a whole (gestalt) are presented simultaneously and can be apperceived totally, severally, or serially, depending on the particular focus prompted by interest and attention. But in non-spatial terms, again, is simultaneity as such stratifiable into levels or components?
One of the examples Peirce cites by way of exploring the relation between time and continuity suggests a positive answer. In “The Law of Mind” Peirce says: “what is present to the mind at any ordinary instant, is what is present during a moment in which that instant occurs. Thus, the present is half past and half to come.” (CP 6.126) This idea about time is congruent with his fundamentally Aristotelian position concerning the properties of a line––which for Peirce was any line, not necessarily a straight line, and for Aristotle an irreducible geometrical object. Thus if a line is divided into two halves, called line intervals, then the endpoints of both segments are loci; and “a line interval by the mere fact of existing as a line interval ‘defines,' as it were, its endpoints.They are abstract properties of the line interval itself, and the notion of a line interval with no endpoints is senseless” (Ketner & Putnam in RLT: 40). When the original line is reconstituted, the two middle endpoints once again coincide at the point of division as one point. This point which is capable of splitting into two corresponds exactly to the moment of the present that is simultaneously half past and half future.
We can perhaps get a firmer grasp on the nature of simultaneity by looking at the continuum from a slightly different point of view, suggested by another of Peirce’s examples (from his eighth and final Cambridge Conferences Lecture of 1898, “The Logic of Continuity”), which deserves to be cited in full (RLT 261-2):
"Let the clean blackboard be a sort of Diagram of the original vague potentiality, or at any rate of some early stage of its determination.This is something more than a figure of speech; for after all continuity is generality. This blackboard is a continuum of two dimensions, while that which it stands for is a continuum of some indefinite multitude of dimensions.This blackboard is a continuum of possible points; while there is a continuum of possible dimensions of quality, or is a continuum of possible dimensions of a continuum of possible dimensions of quality or something of that sort.There are no points on this blackboard.There are no dimensions in that continuum. I draw a chalk line on the board.This discontinuity is one of those brute acts by which alone the original vagueness could have made a step toward definiteness.There is a certain element of continuity in this line.Where did this continuity come from? It is everything upon it continuous. What I have really drawn there is an oval line. For this white chalk-mark is not a line, it is a plane figure in Euclid’s sense, a surface, and the only line [that] is there is the line which forms the limit between the black surface and the white surface. Thus discontinuity can only be produced upon that blackboard by the reaction between two continuous surfaces into which it is separated, the white surface and the black surface. But the boundary between the black and white is neither black, nor white, nor neither, nor both. It is the pairedness of the two. It is for the white the active Secondness of the black; for the black the active Secondness of the white."
In this image of blackboard and chalk mark we have the perfect visual analogue of the simultaneous syntagm in human semiosis, which is a continuum ramified by discontinuities that are themselves continua. In this structure,the boundary between the components of the syntagm is not only necessarily present but plays the crucial role of binding and separating simultaneously.
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.
Michael
----------------------------- 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 .
