Robert, List:
On the contrary, I am not putting the trichotomy for the final interpretant
(If) *itself *in any position whatsoever--only the one for its *relation *with
the sign (S-If), which appears in both Peirce's 1903 taxonomy as
rheme/dicisign/argument and his later taxonomies as seme/pheme/delome.
Again, my purpose in not introducing any of the *other *interpretant
trichotomies is to avoid revisiting our longstanding disagreement about
their logical order for classifying signs, especially since it is not
pertinent to the thread topic of indexicality. Anyone who would like to
discuss the interpretants is welcome to start a new thread accordingly.
Peirce himself postulated the arrangement of the three trichotomies in his
1903 taxonomy as S → Od-S → S-If, and you obviously agree with this since
you have repeatedly employed it in your mathematical lattice approach. In
this thread, I have simply added the two preceding trichotomies from
Peirce's later taxonomies, in the same order that he likewise postulated,
so I do not understand your objection to the Od-S trichotomy coming after
both the Od and S trichotomies. Peirce ultimately identifies a trichotomy
for each of the six correlates *itself*--the sign, its two objects, and its
three interpretants--as well as a *different *trichotomy for each of the
four *external* relations that the sign has with other correlates (Od-S,
S-If, S-Id, Od-S-If). These are the ten trichotomies that yield 66 sign
classes, and he already includes both kinds--one for a correlate (S) and
two for relations (Od-S, S-If)--in his 1903 taxonomy that yields ten
classes.
Peirce marks only two of the ten trichotomies to indicate his level of
confidence about them. The one for the mode of apprehension of the sign
itself as potisign/actisign/famisign is {sigma}, although he adds, "I think
I might as well have marked this division {delta} instead of {sigma},
except that perhaps the question may arise whether I ought not to have
recognized a division according as the sign is a *natural sign*, which has
no party to the dialogue as its author, or whether it be an *uttered sign*,
and in the latter case, is the very sign that is getting uttered or
another. But it seems to me that this division turns upon the question of
whether or not the sign uttered is a sign of a sign as its Object" (CP
8.348, EP 2:484). The one for the mode of presentation of the immediate
object as descriptive/designative/copulant is {mu}, although he adds, "I
would mark it {delta} if I were satisfied with the distinction between
Descriptives and [Designatives]" (CP 8.352, EP 2:485).
I take no issue with your Venn diagram and accompanying remarks, which
continue to address only the three 1903 trichotomies that are
uncontroversial. What I am questioning is Peirce's initial classification
of the *word *"beauty"--not the *quality *of beauty--as an *abstractive*,
which according to the same draft letter can *only *be an iconic
qualisign/tone; but as I said before, the only *words *that are (at least
arguably) iconic qualisigns/tones are onomatopoeia, such as "buzz" and
"tick tock." Again, in my view, the quality of beauty *itself *can be an
abstractive iconic qualisign/tone, with some *other *quality as its
dynamical object; the *word *"beauty" as a *type *is a rhematic symbolic
collective copulant, with the *general concept* of beauty as its dynamical
object; and the *word *"beauty" as a *token *is often a rhematic iconic
designative concretive, with the quality of beauty as *actually embodied*
in something as its dynamical object.
In the end, I agree that "readers can judge for themselves" whether my
comments about speculative grammar are reasonable in light of Peirce's
pioneering work, as well as whether the last paragraph below is an accurate
characterization of our exchanges.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
On Tue, Oct 7, 2025 at 12:59 PM robert marty <[email protected]>
wrote:
> Jon, List,
>
> I can now see that your approach is dominated by your desire to place the
> interpretant If in a position that conforms to your views, which I have
> shown to be on the fringes of the fundamentals of Peirce's semiotics. Our
> readers can judge for themselves. By omitting (a) what we disagree on and
> then pronouncing (b) a kind of default prohibition on the use of
> interpretants in this thread (even though you yourself retain If in your
> personal construction), you are demonstrating your intention to confine the
> debate to a field that you have chosen by proposing a new pentadic sign.
>
> It is incorrect to say that my approach concerns only the ten classes of
> signs. In the past, I employed a method derived from Category Theory, which
> enabled me to identify the ten classes of triadic signs and their lattice
> structure. With the same method (my trichotomic machine[1]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn1>),
> I obtained the 28 classes of hexadic signs and their lattice. This method
> is applicable to any other sequence of n trichotomies with (n-1)
> determinations, and therefore also to n = 10 (if there were agreement on
> their integration into a sequence of nine successive, well-defined
> determinations, which is far from being the case). And if the approach you
> propose were valid, your 21 classes would immediately be organized into a
> lattice that you can obtain by going to the lattice generator[2]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn2>
> designed by Patrick Benazet and marking the number 5 in the indicated
> location.
>
> However, it turns out that your approach is not well-defined because your
> construction contains a tautology that renders it inconsistent. In fact,
> your proposition is presented by the diagram. Od → Oi → S → Od-S → S-If in
> which each element mentioned, Od, Oi, S, and If, is defined by Peirce. The
> order of the first three trichotomies, as well as the first two
> determinations represented by arrows, and the order of the three elements
> in the letter to Lady Welby dated December 23, 1908. Od-S and S-If are
> your notations for the 7th trichotomy in Peirce's list of 10 trichotomies
> (8.344) and S-If for the 9th. The other two arrows, therefore, each
> represent a relation of determination that you postulate between S and Od-S
> and between Od-S and Od-If.
>
> My argument requires recalling a concept that is taught in high schools.
> It is "function composition."[3]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn3>The
> general diagram is as follows:
>
> [image: Une image contenant noir, obscurité Le contenu généré par l’IA
> peut être incorrect.]
>
> where h = g o f represents the function h that results from concatenating
> f and g, I refer to your first two arrows, Od → Oi → S, calling here for
> the first arrow and g the second. Then, since the determination relation is
> transitive, we have h = g o f, which is therefore well defined, and we
> can write Od → S, where the arrow represents the determination h of Od by
> S.
>
> Next, you continue with a determination relation S → Od-S where, in your
> own words, "The Od-S trichotomy is according to the sign's relation with
> its dynamical object." However, we have just seen that Od already
> determines S; therefore, according to you, the sign S should determine a
> relation in which this same Od already determines it. At the very least,
> this is a tautology, and your chain of determinations therefore ends here.
>
> I'm not sure if you evaluated Peirce's assertions based on this model. If
> so, the errors you attributed to him would have been wrong.
>
> Furthermore, I believe you have read the following item (CP 8.445, EP2:
> 483) in which Peirce expresses some certainties and many doubts about
> certain trichotomies:
>
> The ten divisions appear to me to be all Trichotomies, but it is possible
> that some of them are not properly so. Of these Ten Trichotomies, I have a
> clear apprehension of some, (which I mark {d} for {délos}), an
> unsatisfactory and doubtful notion of others (which I mark {a} for
> {adélos}), and a tolerable but not thoroughly tried conception of others
> (which I mark {m} for {metrios}, {s} for {schedon}, almost clear, {ch} for
> {chalepös} hardly better than {a}).
>
>
> *Délos* means that something has become clear or obvious.
> *Adélos*, which is its opposite, means unclear, obscure, indistinct,
> uncertain, vague, and random.
> *Métrios: *average, common, standard, even mediocre.
> *Shedon: *almost, nearly, approximately, close to, near
> *. Chalepös:* with difficulty, with great effort, reluctantly; generally
> expresses the idea of something difficult to accept or deal with.
>
> Unfortunately, I have not been able to find this marking by Peirce; it
> does not appear in Irvin Lieb's edition of Letters, nor in Charles
> Hardwick's Semiotics and Significs. However, it may be found in the paper
> edition of Collected Papers, which I no longer have access to.
>
> Finally, for "beauty," I took the trouble to design a Venn diagram in my
> previous post, which took me a lot of work. Have you considered my
> arguments? I never find any reasoned criticism from you. You oppose me with
> what you believe to be an alternative truth that I am compelled to analyze.
> It is an asymmetrical dialogue in which I am the only one observing the
> precepts of scientific debate. I am not leaving the arena, but I will
> henceforth limit my responses to the bare minimum.
>
> Regards,
>
> Robert Marty
> ------------------------------
>
> [1]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref1>
> The
> trichotomic machine, *Semiotica*, vol.2019, n°228, may 2019, p.173-192.
>
> [2]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref2>
> http://patrick-benazet.chez-alice.fr/treillis_en_ligne/lattices/
>
> [3]
> <#m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref3>
> https://en.wikipedia.org/wiki/Function_composition
>
> Honorary Professor ; PhD Mathematics ; PhD Philosophy
> fr.wikipedia.org/wiki/Robert_Marty
> *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
>
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