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.

Turning now to your other example, one sees that Peirce will use capitalization in most any way he pleases, here given ALL CAPS to his terms defined as well as to the relationships (TO & FOR) he wants to emphasize. Here the ordinals are again preceded by an article as he means to emphasize the categorial nature of R-O-I.
CP 1.541 A REPRESENTAMEN is a subject of a triadic relation TO a second, called its OBJECT, FOR a third, called its INTERPRETANT, this triadic relation being such that the REPRESENTAMEN determines its interpretant to stand in the same triadic relation to the same object for some interpretant.
You are correct in writing that in the following quote "Peirce uses 'First', 'Second' and 'Third' as adjectives":
A Representamen is the First Correlate of a triadic relation, the Second Correlate being termed its Object, and the possible Third Correlate being termed its Interpretant,
As I see it Peirce both respects the Hegelian dialectical order and, as the "Logic of Mathematics" paper shows, gives it a kind of primacy so that, yes, one must even as one, say, turns from dialectical to involutional analysis (i.e. starting at thirdness which involves the other two categories) say,  "First one has thirdness which involves secondness which involves firstness". This is first used as 'firstly', in the ordinary non categorial sense of the ordinal 'first'. The point is that one is required even in involution to employ Hegel's order (or if one doesn't care to consider "The Logic of Mathematics" discussion, a simple ordinal progression). Now, admittedly, "First one has thirdness" may seem a peculiar locution, but it makes perfect sense within the context of Peirce's involutional analysis (which, by the way, is employed to generate the three categories once one assumes the reduction thesis is correct). [cf CP 1.490-1]

Gary

Jean-Marc Orliaguet wrote:

For the record, here some more definitions where the use of English grammar is not entirely consistent.

Is it a question of prestige or can't anyone who was so 100% positive that these cannot be ordinal labels comment on this?


1) we have the terms 'second', 'third' (without capital letter) without referent.

1903 - C.P. 1-541 - Lowell Lectures: Lecture III, vol. 21, 3d Draught .
My definition of a representamen is as follow:
A REPRESENTAMEN is a subject of a triadic relation TO a second, called its OBJECT, FOR a third, called is INTERPRETANT, this triadic relation being such that the REPRESENTAMEN determines its interpretant to stand in the same triadic relation to the same object for some interpretant. -----

2) here Peirce uses 'First', 'Second' and 'Third' as adjectives:

1903 - C.P. 2_242 - Nomenclature and Divisions of Triadic Relations, as far as they are determined .
A Representamen is the First Correlate of a triadic relation, the Second Correlate being termed its Object, and the possible Third Correlate being termed its Interpretant,

-----

3) here Peirce uses 'first', 'second', 'third' as adjectives with a noun: 'something', a 'second something', a 'third something',

1906 - MS 292. Prolegomena to an Apology for Pragmaticism .
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


source: http://www.univ-perp.fr/see/rch/lts/MARTY/76defeng.htm

/JM
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