Jean-Marc, List,

Please see my most recent post addressed to Jim for what should serve as a response to your question. My argument there in a nutshell is that in a genuine trichotomic relationship all elements do in one sense mediate between the others and even necessarily so or it would not be a genuine trichotomic relationship; but as soon as one begins to take into consideration categorial associations in some context, then a particular order (one of six possible ones, which I call trikonic vectors following Parmentier)   matters, both as to categorial association and their logical and/or temporal movement. However there are frequently several orders (vectors) of possible importance once could consider. For example, and since I just mentioned him, I'll offer Parmentier's example. He opposes the vector of determination (epitomized by "the object determines a sign for an interpretant") with what he (and I) see to be the reverse the vector of representation (some interpreter, say an artist or scientist, creates a symbol (say, a poem or a diagram) meant to reveal certain significant  relationships which exist in the world (an imaginary or "real" one) and which diagram observation (the reading of the novel or the observation and, perhaps, manipulation of the diagram) reveals. This is seen as vectorial movement from secondness through firstness to thirdness in the first case (the object, 2ns, determines the sign, 1ns, for the interpretant, 3ns) reversing this order in the second (the experienced interpreter of signs, the artist or scientist, 3ns, creates a novel or diagram, 1ns, revealing some poetic or scientific 'truth' about the world, 2ns)
.See Section 5 of my paper Outline of trikonic:  Diagrammatic Trichotomic on the Arisbe site for a very brief discussion of trichotomic vector analysis.
http://members.door.net/arisbe/menu/library/aboutcsp/richmond/trikonic.htm

Now I know, Jean-Marc, that you do no even agree upon this categorial associations of sign/object/interpret. All I can say is that Parmentier and I do (as far as I can tell--and even if he sees the categorial matter somewhat differently, order does matter for both of us).

Gary

Jean-Marc Orliaguet wrote:
Gary Richmond wrote:
Jean-Marc,

You wrote:
1) we have the terms 'second', 'third' (without capital letter) without referent.
The text which originally prompted this discussion is:
1. 274. A Sign, or Representamen, is a First which stands in such a genuine triadic relation to a Second, called its Object, as to be capable of determining a Third, called its Interpretant, to assume the same triadic relation to its Object in which it stands itself to the same Object. 
It is quite true that Peirce doesn't always capitalize ordinals. As I've contemplated the structure of the above passage what strikes me, however, as most significant is the combination of the article 'a' connected to the capitalized _expression_, for example "a Third". In all the English speaking world if one simply wanted to say "this follows this follows this" one would say something like "A Sign stands, first, in relation to x, second in relation to, etc."  never "a First". A First here  means a categorial something, one of the three elements of a "genuine triadic relation" at this level of analysis.


although this is not how I understand it either -- they are not adverbs like "first", "secondly", "thirdly". I understand it as:

    A Sign, or Representamen, is a first [thing] which stands in such a genuine triadic relation to a second [thing] ....


as it is written in:

    A sign may be defined as something (not necessarily existent) which is so determined by a second something called its Object that it will tend in its turn to determine a third something called its Interpretant


would you say in the sentence above that "a second something" and a "third something" are categorial (whatever "categorial" might mean to you)?


/JM ---
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