This line of thought assumes the self is a congruent object. This assumption has been explicitly held to be false in multiple universes of discourse, such as Psychoanalysis and Buddhism.
----- Original Message ----- From: "charles murray" <[email protected]> To: "Jeffrey Brian Downard" <[email protected]> Cc: "Peirce List" <[email protected]> Sent: Tuesday, May 3, 2016 8:29:24 AM Subject: Re: [PEIRCE-L] Topology, the Gamma Graphs, and representations of self 3 May 2016 Jeff, all: In my March 24 post I expressed interest in your remarks about Peirce's mathematics and theory of the self. With a hint from your March 29 response I have located what I'm curious about in your post dated 4 July 2014 from the De Waal Seminar. You write: "My first suggestion is that we start by thinking about the self as a relationship between representations. In Euclidean geometry, for instance, we say that one figure is congruent with another if we can move one around and superimpose it on top of another. The basic ways in which figures can be moved in a diagram is by translation, rotation and reflection. It turns out that reflection is the fundamental kind of symmetry on a Euclidean surface because we can achieve the same effect as translation by reflecting over two lines. The same is true of rotation (but the lines cross). [quotation continued:] Before we introduce any ideas from projective geometry, how might we use this geometric notion of reflection to think about the symmetries that hold between one representation and another representation that is, in some sense, 'congruent' with it? Or, if you prefer a weaker relation, how is one representation similar to another? In what ways might one representation mirror another?" In my rudimentary understanding of reflection as an operation upon graphs on a Euclidean surface, certain facts about points on the reflected graph necessitate certain facts about points on the reflecting graph. For example, given a coordinate system with the graph A of a 1-1 function, there is a reflecting graph B such that for any point on A specified by the x coordinate _a_ and the y coordinate _b_, there is a point on B specified by the x coordinate _b_ and the y coordinate _a_. This gives reflection about the graph of the function y = x. Graphs of other relations give other reflections, e.g., reflections about the x axis, y axis or the origin. There are conditions on whether there is a reflection and if so what it is like. First, there are conditions on the algebraic properties of that which is being graphed. It matters whether it is a relation, whether the relation is a function, what results from negating the function, or negating the function's argument, and whether the function is many to one or one to one. There are corresponding conditions on graphic representation, which include provision for a coordinate system with an x and y axis, their intersection at a point of origin, points specifiable by x and y coordinates, and the possibility of various symmetries between graphs with respect to this system. Extending these rudimentary remarks, I suppose reflection _might_ be best understood as conditioned by the movement of a point from one place to another, represented graphically by having a point on the graph maintain its identity through changes in facts about it, such as having one or both its coordinates change value from positive to negative or vice versa, or having its x coordinate become its y coordinate and vice versa. More needs to be said to account for preservation of identity through such changes. It also seems important to be more careful than I am above in keeping straight whether one is speaking of a graph as a legisign or a sinsign; it should be recognized that reference to "points" as part of a sinsign may be misleading. Are we on the same page so far? Best, Charles [Text File:message-footer.txt]
----------------------------- 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 .
