Re: [PEIRCE-L] How do we formalize the triadic sign?

[Jerry LR Chandler]

Robert; List-

> On Jan 8, 2024, at 9:18 AM, robert marty  wrote:
> 
> You know very well that we don't mention "what goes without saying" in 
> mathematics. For example, when Peirce names the classes of signs, he doesn't 
> note that symbols are legisigns, any more than he mentions that the three 
> iconic signs are rhematic.

After further thought, I find these sentences to be problematic.

Within mathematics, if a sentence is not placed in a specified contact, then 
the reader is open to multiple potential assignments of meanings and possibly 
multiple possible arrangements of consequences.  

In the case of “signs”, I would suggest that without specification of the 
location of the sign, both the 2nd and 3ns are open to the reader’s mind (seme).

This example of seeking to category theory as a generic form of absolute 
vagueness is remote from the trichotomy.  Legisssign is a direct consequence of 
genesis from “argument” and symbol. 

Further, the sequence of 
O—>S—> I
As an implicative sequence would not be an causal axiomatic sequence as a 
consequence of the multiple possible meanings of a sign or the context in which 
the sign occurs. 

BTW, are you aware of CSP’s reference to Maxwell’s equations? 

Cheers
Jerry_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] How do we formalize the triadic sign?

[robert marty]

Jon, List,

One more effort ... if you take the definition of a mathematical category,
you'll see that you only need to "flatten" your diagram a little to get the
category O → S → I. To do this, we'll consider the abstract category X → Y
→ Z with three abstract objects X, Y and Z and not two but three morphisms
in addition to the three identities. Indeed, the compound morphism X → Z
exists by definition . There's no need to mention it.  It doesn't need to
be, since an axiom assures us of its existence. By implementing this
abstract form on the definition of the sign, we obtain the diagram O → S →
I, and its validation as a diagram of the triadic sign depends only on the
nature of the arrows which, in the triadic sign, are determinations. Now,
Peirce defines a determination as follows:

*renders definitely to be such as it will be* (CP 8.361, 1908)



and if O *renders definitely  S to be such as it will be**  and S renders
definitely I to be such as it will be, *then* O renders definitely I  to be
such as it will be . *This results from the semantics of determination
according to Peirce (and according to common sense).

Peirce himself notes:

*I define a Sign as anything which on the one hand is so determined by an
Object and on the other hand so determines an idea in a person's mind, that
this latter determination, which I term the Interpretant of the Sign, is
thereby mediately determined by that Object. A sign, therefore, has a
triadic relation to its Object and to its Interpretant. *(n° 47 bis – 1908
- Letter to Lady Welby in  CP 8.343 ).

This is how the Peircian sign can be apprehended by this mathematical
object; and of course, there's more to come...


Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le lun. 8 janv. 2024 à 16:01, Jon Alan Schmidt  a
écrit :

> List:
>
> Here is a modified version of my EG with the two dyadic relations of
> determining now included. Erasing them in accordance with the usual
> transformation rules gives the other version of my original EG as posted on
> Friday, its only difference from the one below being the convention for
> where to locate the three correlate lines of identity around the relation
> name. Erasing "mediating" instead gives my EG for "the object determines
> the sign, which determines the interpretant," which again is not false but
> could be misleading--although the genuine triadic relation of mediating (or
> representing) *involves *those two dyadic relations, it is not *composed *of
> them in the sense that it is not built up from them nor reducible to them.
>
> [image: image.png]
>
> Regards,
>
> Jon
>
> On Sun, Jan 7, 2024 at 1:39 PM Jon Alan Schmidt 
> wrote:
>
>> Ben, List:
>>
>> I share your concern about describing the *genuine *triadic relation of
>> mediating (or representing) with its three correlates (sign, object,
>> interpretant) as if it were reducible to dyadic relations of determining,
>> which could only be true if it were a *degenerate *triadic relation. It
>> is not *false *to say, "the object determines the sign, which determines
>> the interpretant," but it could be misleading because it omits the *mediation
>> *of the sign by which the object *also *determines the interpretant.
>> Indeed, it is more accurate to say, "the object determines the sign to
>> determine the interpretant." Peirce expresses this even more precisely as
>> follows, in what I consider to be one of his very best definitions of a
>> sign.
>>
>> CSP: I will say that a sign is anything, of whatsoever mode of being,
>> which mediates between an object and an interpretant; since it is both
>> determined by the object *relatively to the interpretant*, and
>> determines the interpretant *in reference to the object*, in such wise
>> as to cause the interpretant to be determined by the object through the
>> mediation of this "sign." (EP 2:410, 1907)
>>
>>
>> That is why I call the relation "mediating" in my Existential Graph (EG)
>> that I posted on Friday, rather than "representing," although the latter
>> could be substituted with some loss of generality. Here is that EG again.
>>
>> [image: image.png]
>>
>> Peirce himself apparently never scribed this EG, but he did scribe the
>> one for the genuine triadic relation of *giving *with its three
>> correlates (giver, gift, recipient). As one would expect for *any *genuine
>> triadic relation, it is isomorphic with the EG above, except that instead
>> of three heavy lines of identity with the correlate names attached, the
>> relation name has three dots (also called "hooks" or "pegs" in other
>> writings) to which Peirce assigned those names in the subsequent text. Here
>> is an image of that handwritten sentence in R 670 (1911).
>>
>> [image: image.png]
>>
>> Regards,
>>
>> Jon Alan Schmidt - Olathe, Kansas, USA
>> Structural Engineer, Synechist Philosopher, Lutheran Christian
>> 

Re: [PEIRCE-L] How do we formalize the triadic sign?

[robert marty]

That's okay Jerry ... I'm just trying to stay within the framework of exact
philosophy as Peirce sees it :

*The doctrine of exact philosophy, as I understand that phrase, is, that
all danger of error in philosophy will be reduced to a minimum by treating
the problems as mathematically as possible,** that is, by construction some
sort of a diagram representing that which is supposed to be open to the
observation of every scientific intelligence, and thereupon
mathematically,--that is, intuitionally,--deducing the consequences of that
hypothesis. *(NEM IV:12, unidentified fragment)


Regards,
Robert

Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le lun. 8 janv. 2024 à 17:11, Jerry LR Chandler <
jerry_lr_chand...@icloud.com> a écrit :

>
>
> On Jan 8, 2024, at 9:18 AM, robert marty  wrote:
>
> Jerry, List
>
> You know very well that we don't mention "what goes without saying" in
> mathematics.
>
>
> Sorry, Robert.
> Interesting but hardly compelling response.
>
> Human communications in multidisciplinary forums such as this are open to
> misunderstandings.  To “invoke” such a phrase is meaningless to your
> readers.
>
> In applied mathematics, the calculations are contained to the
> interpretations of the symbols asserted in the formula.
>
> In philosophy, each individual philosopher assigns symbols and asserts
> premises ad hoc with an intended “unit of meaning.”  Isn’t that what
> philosophical discourse is all about?
>
> Cheers
> Jerry
>
>
>
>
_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] How do we formalize the triadic sign?

[Jerry LR Chandler]

> On Jan 8, 2024, at 9:18 AM, robert marty  wrote:
> 
> Jerry, List
> 
> You know very well that we don't mention "what goes without saying" in 
> mathematics. 
> 

Sorry, Robert.
Interesting but hardly compelling response.

Human communications in multidisciplinary forums such as this are open to 
misunderstandings.  To “invoke” such a phrase is meaningless to your readers.

In applied mathematics, the calculations are contained to the interpretations 
of the symbols asserted in the formula.  

In philosophy, each individual philosopher assigns symbols and asserts premises 
ad hoc with an intended “unit of meaning.”  Isn’t that what philosophical 
discourse is all about?

Cheers
Jerry 



_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] How do we formalize the triadic sign?

[robert marty]

Jerry, List

You know very well that we don't mention "what goes without saying" in
mathematics. For example, when Peirce names the classes of signs, he
doesn't note that symbols are legisigns, any more than he mentions that the
three iconic signs are rhematic. Since my diagram represents a category, an
axiom assures us that identity morphism exists for every object. They are
rarely mentioned. That's why I didn't worry about it when I realized they'd
disappeared. I thought it would lighten the load without doing any damage.

For the same reasons, the diagram shows that there are not two but three
arrows in O  * →*  S  * →*   I, simply because we know or affirm that it
represents a category. The third morphism is the compound of the two. It is
also, by definition, for those who know what the word "category" means
(i.e., for those who know the category axioms). There's no metaphor here;
it's a formalization of the triadic sign, implicitly validated by Peirce:

*I define a Sign as anything which on the one hand is so determined by an
Object and on the other hand so determines an idea in a person's mind, that
this latter determination, which I term the Interpretant of the Sign, is
thereby mediately determined by that Object. A sign, therefore, has a
triadic relation to its Object and to its Interpretant. *(n° 47 bis – 1908
- Letter to Lady Welby in  CP 8.343 ).

All because for Peirce "determination" means:

*renders definitely to be such as it will be* (CP 8.361, 1908)


 Regards,
Robert Marty
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le lun. 8 janv. 2024 à 06:07, Jerry LR Chandler <
jerry_lr_chand...@icloud.com> a écrit :

>
>
> On Jan 7, 2024, at 9:10 AM, robert marty  wrote:
>
> It's clear, then, that the composition of the two determinations gives
> rise to the triadic relation for Peirce. That's why I've underlined
> "therefore." Consequently, the formalization is simplified considerably,
> without any loss of information, by :
>
> O  à S à I
>
> The arrows represent determinations, and this diagram reads:
>
> O determines S, which determines I
>
> Referring to the Peircean conception of a determination:
> *We thus learn that the Object determines (i.e. renders definitely to be
> such as it will be) the Sign in a particular manner. *(CP 8.361, 1908)
>
> We can see that O determines I by transitivity. Peirce verified this in MS
> 611 (Nov. 1908).
>
> This diagram has the considerable advantage of being equivalent to the
> mathematical object below:
>
> Schematic representation of a category with objects *X*, *Y*, *Z* and
> morphisms *f*, *g*, *g* ∘ *f*.
> 
> (click)
>
> It's an algebraic category, the simplest there is (non-trivial). This one
> is the archetypal example of a category on the
>
>
> Robert:
>
> You may want to check your mathematical conclusions.
>
> While I understand that the following details are highly technical in
> nature, it is important that mathematics NOT be treated as merely a
> symbolic metaphor when an inquiry into the meaning of symbols is under the
> microscope.
>
> The sequence O—> S —> I. as three alphabets symbols and two arrows.
>
> The schematic diagram referenced by the “click," (which is, by the way,
> only a partial representation of a mathematical category,) has three arrows
> and repeats the function labels and even composes the two functions.
>
> In addition, the identity arrows necessary to define a mathematical
> category are missing. These notational constraints are essential for the
> additional property of closure, which is far beyond the simple property of
> transitivity illustrated by the simple sequence of three alphabetic symbols
> and two arrows.
>
>
> Cheers
> Jerry
>
>
>
>
>
_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] How do we formalize the triadic sign?

[Jon Alan Schmidt]

List:

Here is a modified version of my EG with the two dyadic relations of
determining now included. Erasing them in accordance with the usual
transformation rules gives the other version of my original EG as posted on
Friday, its only difference from the one below being the convention for
where to locate the three correlate lines of identity around the relation
name. Erasing "mediating" instead gives my EG for "the object determines
the sign, which determines the interpretant," which again is not false but
could be misleading--although the genuine triadic relation of mediating (or
representing) *involves *those two dyadic relations, it is not *composed *of
them in the sense that it is not built up from them nor reducible to them.

[image: image.png]

Regards,

Jon

On Sun, Jan 7, 2024 at 1:39 PM Jon Alan Schmidt 
wrote:

> Ben, List:
>
> I share your concern about describing the *genuine *triadic relation of
> mediating (or representing) with its three correlates (sign, object,
> interpretant) as if it were reducible to dyadic relations of determining,
> which could only be true if it were a *degenerate *triadic relation. It
> is not *false *to say, "the object determines the sign, which determines
> the interpretant," but it could be misleading because it omits the *mediation
> *of the sign by which the object *also *determines the interpretant.
> Indeed, it is more accurate to say, "the object determines the sign to
> determine the interpretant." Peirce expresses this even more precisely as
> follows, in what I consider to be one of his very best definitions of a
> sign.
>
> CSP: I will say that a sign is anything, of whatsoever mode of being,
> which mediates between an object and an interpretant; since it is both
> determined by the object *relatively to the interpretant*, and determines
> the interpretant *in reference to the object*, in such wise as to cause
> the interpretant to be determined by the object through the mediation of
> this "sign." (EP 2:410, 1907)
>
>
> That is why I call the relation "mediating" in my Existential Graph (EG)
> that I posted on Friday, rather than "representing," although the latter
> could be substituted with some loss of generality. Here is that EG again.
>
> [image: image.png]
>
> Peirce himself apparently never scribed this EG, but he did scribe the one
> for the genuine triadic relation of *giving *with its three correlates
> (giver, gift, recipient). As one would expect for *any *genuine triadic
> relation, it is isomorphic with the EG above, except that instead of three
> heavy lines of identity with the correlate names attached, the relation
> name has three dots (also called "hooks" or "pegs" in other writings) to
> which Peirce assigned those names in the subsequent text. Here is an image
> of that handwritten sentence in R 670 (1911).
>
> [image: image.png]
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
>
> On Sun, Jan 7, 2024 at 11:54 AM Ben Udell  wrote:
>
>> Hi, Robert, all,
>>
>> I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that
>> you quote in your message,
>>
>> *The conceptions of a First, improperly called an "object," and of a
>> Second should be carefully distinguished from those of Firstness or
>> Secondness, both of which are involved in the conceptions of First and
>> Second. A First is something to which (or, more accurately, to some
>> substitute for which, thus introducing Thirdness) attention may be
>> directed. It thus involves Secondness as well as Firstness; while a Second
>> is a First considered as (here comes Thirdness) a subject of a Secondness.
>> An object in the proper sense is a Second.* (EP 2: 271)
>>
>> We had some long arguments many years ago at peirce-l about what Peirce
>> meant by "First" etc., when he wasn't explicitly tying those adjectives to
>> the categories.  Joe Ransdell, Gary Richmond, I, and probably others,
>> argued that, yes, Peirce was alluding to his categories.
>>
>> I also remember a whole lot of discussion about Peirce's shift to viewing
>> the sign as not only determining the interpretant but also being determined
>> by the object.  At the time, a 1906 quote was the earliest that I could
>> find (I happened to find it at Commens.org I think), and Joe came up with a
>> quote that prefigured Peirce's shift, from 1905 or 1904, I wish I could
>> remember (and I tried years ago without success to find Joe's message about
>> it), but I don't want send anybody on a wild goose chase.
>>
>> Folks, here, by the way, is a link to Robert's "76 DEFINITIONS OF THE
>> SIGN BY C.S. PEIRCE"
>> http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm
>>
>> It includes added quotes absent from the Arisbe version.
>>
>> Robert, you wrote below that "*O → S → I*" reads:
>>
>> "*O determines S, which determines I*."
>>
>> I haven't tried to learn any 

Re: [PEIRCE-L] How do we formalize the triadic sign?

[robert marty]

Ben, List

You are confronted with the mathematical notion of the composition of
morphisms. This notion appears as an axiom in the definition of a category.
Category theory is the study of mathematical structures and their
relationships. It's a unifying notion that began with the observation that
many properties of formalized systems can be unified and simplified by
point-and-arrow diagrams. Their formal definition is not gratuitous; it
aims to capture these observations in exact, well-defined terms.
Admittedly, they first concerned mathematical objects, but points and
arrows are commonly used in all fields of knowledge. I don't think I'll be
denied on this list.

We only need to see the definition of a category to be convinced that it
will give us the means to think of these unifications with exactitude (this
is Peirce's "exact thinking" at the source of an "exact philosophy"):

*The doctrine of exact philosophy, as I understand that phrase, is, that
all danger of error in philosophy will be reduced to a minimum by treating
the problems as mathematically as possible,** that is, by construction some
sort of a diagram representing that which is supposed to be open to the
observation of every scientific intelligence, and thereupon
mathematically,--that is, intuitionally,--deducing the consequences of that
hypothesis. *(NEM IV:12, unidentified fragment)



*But in order completely to exhibit the analogue of the conditions of the
argument under examination, it will be necessary to use signs or symbols
repeated in different places and in different juxtapositions, these signs
being subject to certain "rules," that is, certain general relations
associated with them by the mind. Such a method of forming a diagram is
called algebra. All speech is but such an algebra, the repeated signs being
the words, which have relations by virtue of the meanings associated with
them. What is commonly called logical algebra differs from other formal
logic only in using the same formal method with greater freedom. I may
mention that unpublished studies have shown me that a far more powerful
method of diagrammatisation than algebra is possible, being an extension at
once of algebra and of Clifford's method of graphs; but I am not in a
situation to draw up a statement of my researches*. (CP: 3.418). [emphasize
mine]

NB: Clifford's algebras remain in current scientific research (see
https://en.wikipedia.org/wiki/Clifford_algebra).

These quotations are self-explanatory regarding the adequacy of category
theory to realize Peirce's program. I am aware, of course, that he tried to
realize it himself with his existential graphs. But this should not block
the path of research since mathematicians, after Peirce, have forged potent
tools suitable for achieving the same goal.

I'm now giving the most "literary" definition of a category possible; it
requires only a common mathematical habitus to be apprehended.

A category is defined by three kinds of entities: objects, relations
between these objects (called morphisms or arrows), and an operation of
composition of these morphisms noted "o" thus defined: for three objects X,
Y, and Z, for any morphism f between X and Y and any morphism g between Y
and Z, there exists a morphism between X and Z noted g ∘ f which is the
compound of f and g. There are other axioms, in particular that of
associativity, of which everyone can take note

Let me come back to g ∘ f. This notion appears in the last year of the high
school science sections. To understand it better, I place myself in set
theory; sets are made up of elements; these will be the objects of the
category, and relations will be the applications of one set in another. To
verify that sets do indeed constitute a category, the operation "o" y needs
to be well defined: for each x of X, we have f (x)= y in Y, and for each y
of Y, we have g(y)=z in Z.  To compose the two is to apply g to the result
of f (x)=y by f, hence the new application (g ∘ f ) of X in Z well defined
by :

(g ∘ f )(x)= g(f(x)) = g(y) = z.

I now answer your question by literally reversing your doubt into belief (I
hope!): not only does   "O → S → I" not break down into the dyads "O → S"
and "S → I," but it is the composite of the two dyads that constitute the
triad in any mind. As a result, it gives I the power to represent O and
thus to be a First (i.e., a First correlate of a new triad - otherwise,
it's the third correlate that becomes a First as soon as it's present in
mind since it's the one that attention is now focused on, thus initiating
semiosis by simple iteration). Such a thing is only possible if the mind
has previously internalized the relationship between O and S through
previous "collateral" experience in the external world.

All this Peirce writes here :

*I define a Sign as anything which on the one hand is so determined by an
Object and on the other hand so determines an idea in a person's mind, that
this latter determination, which I term the Interpretant of 

Re: [PEIRCE-L] How do we formalize the triadic sign?

[Jerry LR Chandler]

> On Jan 7, 2024, at 9:10 AM, robert marty  wrote:
> 
> It's clear, then, that the composition of the two determinations gives rise 
> to the triadic relation for Peirce. That's why I've underlined "therefore." 
> Consequently, the formalization is simplified considerably, without any loss 
> of information, by : 
> 
> O  à S à I
> 
> The arrows represent determinations, and this diagram reads:
> 
> O determines S, which determines I
> 
> Referring to the Peircean conception of a determination:
> 
> We thus learn that the Object determines (i.e. renders definitely to be such 
> as it will be) the Sign in a particular manner. (CP 8.361, 1908)
> 
> We can see that O determines I by transitivity. Peirce verified this in MS 
> 611 (Nov. 1908).
> 
> This diagram has the considerable advantage of being equivalent to the 
> mathematical object below:
> 
> Schematic representation of a category with objects X, Y, Z and morphisms f, 
> g, g ∘ f. 
> 
>   (click)
> 
> It's an algebraic category, the simplest there is (non-trivial). This one is 
> the archetypal example of a category on the 
> 

Robert: 
 
You may want to check your mathematical conclusions.

While I understand that the following details are highly technical in nature, 
it is important that mathematics NOT be treated as merely a symbolic metaphor 
when an inquiry into the meaning of symbols is under the microscope.

The sequence O—> S —> I. as three alphabets symbols and two arrows.

The schematic diagram referenced by the “click," (which is, by the way, only a 
partial representation of a mathematical category,) has three arrows and 
repeats the function labels and even composes the two functions.  

In addition, the identity arrows necessary to define a mathematical category 
are missing. These notational constraints are essential for the additional 
property of closure, which is far beyond the simple property of transitivity 
illustrated by the simple sequence of three alphabetic symbols and two arrows.


Cheers
Jerry 




_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] How do we formalize the triadic sign?

[Jon Alan Schmidt]

Ben, List:

I share your concern about describing the *genuine *triadic relation of
mediating (or representing) with its three correlates (sign, object,
interpretant) as if it were reducible to dyadic relations of determining,
which could only be true if it were a *degenerate *triadic relation. It is
not *false *to say, "the object determines the sign, which determines the
interpretant," but it could be misleading because it omits the *mediation *of
the sign by which the object *also *determines the interpretant. Indeed, it
is more accurate to say, "the object determines the sign to determine the
interpretant." Peirce expresses this even more precisely as follows, in
what I consider to be one of his very best definitions of a sign.

CSP: I will say that a sign is anything, of whatsoever mode of being, which
mediates between an object and an interpretant; since it is both determined
by the object *relatively to the interpretant*, and determines the
interpretant *in reference to the object*, in such wise as to cause the
interpretant to be determined by the object through the mediation of this
"sign." (EP 2:410, 1907)


That is why I call the relation "mediating" in my Existential Graph (EG)
that I posted on Friday, rather than "representing," although the latter
could be substituted with some loss of generality. Here is that EG again.

[image: image.png]

Peirce himself apparently never scribed this EG, but he did scribe the one
for the genuine triadic relation of *giving *with its three correlates
(giver, gift, recipient). As one would expect for *any *genuine triadic
relation, it is isomorphic with the EG above, except that instead of three
heavy lines of identity with the correlate names attached, the relation
name has three dots (also called "hooks" or "pegs" in other writings) to
which Peirce assigned those names in the subsequent text. Here is an image
of that handwritten sentence in R 670 (1911).

[image: image.png]

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt

On Sun, Jan 7, 2024 at 11:54 AM Ben Udell  wrote:

> Hi, Robert, all,
>
> I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that
> you quote in your message,
>
> *The conceptions of a First, improperly called an "object," and of a
> Second should be carefully distinguished from those of Firstness or
> Secondness, both of which are involved in the conceptions of First and
> Second. A First is something to which (or, more accurately, to some
> substitute for which, thus introducing Thirdness) attention may be
> directed. It thus involves Secondness as well as Firstness; while a Second
> is a First considered as (here comes Thirdness) a subject of a Secondness.
> An object in the proper sense is a Second.* (EP 2: 271)
>
> We had some long arguments many years ago at peirce-l about what Peirce
> meant by "First" etc., when he wasn't explicitly tying those adjectives to
> the categories.  Joe Ransdell, Gary Richmond, I, and probably others,
> argued that, yes, Peirce was alluding to his categories.
>
> I also remember a whole lot of discussion about Peirce's shift to viewing
> the sign as not only determining the interpretant but also being determined
> by the object.  At the time, a 1906 quote was the earliest that I could
> find (I happened to find it at Commens.org I think), and Joe came up with a
> quote that prefigured Peirce's shift, from 1905 or 1904, I wish I could
> remember (and I tried years ago without success to find Joe's message about
> it), but I don't want send anybody on a wild goose chase.
>
> Folks, here, by the way, is a link to Robert's "76 DEFINITIONS OF THE SIGN
> BY C.S. PEIRCE"
> http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm
>
> It includes added quotes absent from the Arisbe version.
>
> Robert, you wrote below that "*O → S → I*" reads:
>
> "*O determines S, which determines I*."
>
> I haven't tried to learn any category theory, since I got intimidated by
> its being reputedly based in very high or abstract algebra.
>
> Generally I recall people saying that —
>
> an object determines a sign to determine an interpretant
>
> — rather than that —
>
> an object determines a sign, which determines an interpretant
>
> — a phrasing which makes the sign's determination of an interpretant seem
> possibly coincidental to the sign's being determined by an object, like
> dominoes toppling, each one the next, though the earlier dominoes are not
> finally-caused to topple the later ones (except if they are literal
> dominoes that some person set up to fall that way).  I remember (though not
> in detail) a whole lot of discussion of this at peirce-l.  Does the
> category-theoretical understanding of "O determines S, which determines I"
> avoid that seeming problem?  To put it another way, how does "*O → S → I*"
> keep from breaking down into dyads "*O → S*" and "*S → 

Re: [PEIRCE-L] How do we formalize the triadic sign?

[Edwina Taborsky]

Ben, list

I remember discussions on this list about that paragraph with follows the p. 
271 warning in this text 

“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 aObject” EP: 272-3

 -  and being chastised and even sneered at, when I suggested that the terms of 
First, Second and Third, referred to ordinal numbers and not to the modal 
categories. The list members, several who still post here, insisted in very 
authoritative terms, that those words referred to the categories!

But a small bit of thought would have shown that it makes no logical sense for 
a Representamen to be in a mode of Firstness - for it would then have been 
unable to interact with an Object or Interpretant unless they also were in a 
mode of Firstness!.   However, the list wasn’t willing to take this ’small bit 
of thought’. 

I think the whole point of the semiosic process is its generative capacity; ie, 
that a semiotic triad is capable of developing and creating new knowledge and 
therefore, new forms. The reason it can do this is because the object and 
interpretant are separated from each other by the mediative function of the 
representamen. So- rather than mitosis, or mimetic clones where x produces 
another x, [ which has its functionality]  you get the more complex meiosis 
where x produces y - ie, a unique cell.

With the triad, its this ‘insertion’ of a mediating force, the representamen, 
that gathers information from other interactions over time, develops habits or 
knowledge of ‘how to deal with the external world’ and thus enables both 
anticipation and yes, adaptation, for Thirdness isn’t only ‘pure’ or genuine, 
but can connect indexically with the outside world [Thirdness-as-Secondness] , 
and thus, inform itself of those external properties and come up with adaptive 
Interpretants. 

Edwina




> On Jan 7, 2024, at 12:53 PM, Ben Udell  wrote:
> 
> Hi, Robert, all,
> 
> I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that you 
> quote in your message,
> 
> The conceptions of a First, improperly called an "object," and of a Second 
> should be carefully distinguished from those of Firstness or Secondness, both 
> of which are involved in the conceptions of First and Second. A First is 
> something to which (or, more accurately, to some substitute for which, thus 
> introducing Thirdness) attention may be directed. It thus involves Secondness 
> as well as Firstness; while a Second is a First considered as (here comes 
> Thirdness) a subject of a Secondness. An object in the proper sense is a 
> Second. (EP 2: 271)
> 
> We had some long arguments many years ago at peirce-l about what Peirce meant 
> by "First" etc., when he wasn't explicitly tying those adjectives to the 
> categories.  Joe Ransdell, Gary Richmond, I, and probably others, argued 
> that, yes, Peirce was alluding to his categories.
> 
> I also remember a whole lot of discussion about Peirce's shift to viewing the 
> sign as not only determining the interpretant but also being determined by 
> the object.  At the time, a 1906 quote was the earliest that I could find (I 
> happened to find it at Commens.org I think), and Joe came up with a quote 
> that prefigured Peirce's shift, from 1905 or 1904, I wish I could remember 
> (and I tried years ago without success to find Joe's message about it), but I 
> don't want send anybody on a wild goose chase.
> 
> Folks, here, by the way, is a link to Robert's "76 DEFINITIONS OF THE SIGN BY 
> C.S. PEIRCE" 
> http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm
> 
> It includes added quotes absent from the Arisbe version.
> 
> Robert, you wrote below that "O → S → I" reads:
> 
> "O determines S, which determines I."
> 
> I haven't tried to learn any category theory, since I got intimidated by its 
> being reputedly based in very high or abstract algebra.
> 
> Generally I recall people saying that —
> 
> an object determines a sign to determine an interpretant
> 
> — rather than that —
> 
> an object determines a sign, which determines an interpretant
> 
> — a phrasing which makes the sign's determination of an interpretant seem 
> possibly coincidental to the sign's being determined by an object, like 
> dominoes toppling, each one the next, though the earlier dominoes are not 
> finally-caused to topple the later ones (except if they are literal dominoes 
> that some person set up to fall that way).  I remember (though not in detail) 
> a whole lot of discussion of this at peirce-l.  Does the category-theoretical 
> understanding of "O determines S, which determines I" avoid that seeming 
> problem?  To put it another way, how does "O → S → I" keep from breaking down 
> into dyads "O → S" and "S → I"?  I'm not trying to be argumentative, I'm 
> actually 

Re: [PEIRCE-L] How do we formalize the triadic sign?

[Ben Udell]

Hi, Robert, all,

I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that you 
quote in your message,

   /The conceptions of a First, improperly called an "object," and of a Second 
should be carefully distinguished from those of Firstness or Secondness, both of which 
are involved in the conceptions of First and Second*. A First is something to which* (or, 
more accurately, to some substitute for which, thus introducing Thirdness) *attention may 
be directed*. It thus involves Secondness as well as Firstness; *while a Second is a 
First considered as (here comes Thirdness) a subject of a Secondness.* An object in the 
proper sense is a *Second*./ (EP 2: 271)

We had some long arguments many years ago at peirce-l about what Peirce meant by 
"First" etc., when he wasn't explicitly tying those adjectives to the 
categories.  Joe Ransdell, Gary Richmond, I, and probably others, argued that, yes, 
Peirce was alluding to his categories.

I also remember a whole lot of discussion about Peirce's shift to viewing the 
sign as not only determining the interpretant but also being determined by the 
object.  At the time, a 1906 quote was the earliest that I could find (I 
happened to find it at Commens.org I think), and Joe came up with a quote that 
prefigured Peirce's shift, from 1905 or 1904, I wish I could remember (and I 
tried years ago without success to find Joe's message about it), but I don't 
want send anybody on a wild goose chase.

Folks, here, by the way, is a link to Robert's "76 DEFINITIONS OF THE SIGN BY C.S. 
PEIRCE"
http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm

It includes added quotes absent from the Arisbe version.

Robert, you wrote below that "*O → S → I*" reads:

"*O determines S, which determines I*."

I haven't tried to learn any category theory, since I got intimidated by its 
being reputedly based in very high or abstract algebra.

Generally I recall people saying that —

   an object determines a sign to determine an interpretant

— rather than that —

   an object determines a sign, which determines an interpretant

— a phrasing which makes the sign's determination of an interpretant seem possibly coincidental to the sign's being 
determined by an object, like dominoes toppling, each one the next, though the earlier dominoes are not finally-caused 
to topple the later ones (except if they are literal dominoes that some person set up to fall that way).  I remember 
(though not in detail) a whole lot of discussion of this at peirce-l.  Does the category-theoretical understanding of 
"O determines S, which determines I" avoid that seeming problem?  To put it another way, how does "*O → 
S → I*" keep from breaking down into dyads "*O → S*" and "*S → I*"?  I'm not trying to be 
argumentative, I'm actually wondering.

Best, Ben

On 1/7/2024 10:10 AM, robert marty wrote:

Cécile, List

I present here, in the most condensed form possible, the merits of a purely 
algebraic formalization of Peirce's semiotics, entirely indexed to the history 
of its development.

*/How do we distinguish the correlates of a triadic sign?
How do we formalize the triadic sign?/*

This question arises because the definition of a triad, strictly speaking, implies no a priori 
distinction between the elements it links together. If you represent them by letters, you're 
surreptitiously introducing lexicographical order and by numbers, the order of natural integers. 
This is why I draw attention to an important warning Peirce gives about "First" and 
"Second" in a footnote to the Syllabus in Part III (EP 2, selection 20):

   */The conceptions of a First, improperly called an "object," and of a Second 
should be carefully distinguished from those of Firstness or Secondness, both of which 
are involved in the conceptions of First and Second*. A First is something to which* (or, 
more accurately, to some substitute for which, thus introducing Thirdness) *attention may 
be directed*. It thus involves Secondness as well as Firstness; *while a Second is a 
First considered as (here comes Thirdness) a subject of a Secondness.* An object in the 
proper sense is a *Second*./ (EP 2: 271)

This warning should shed light on the following definition of the Sign (which, 
in my opinion, is far from the best) on page 272:

   /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*./ (EP 
2: 272)

On the other hand, the definition given in the fifth version of the Syllabus 
(EP 2, selection 21), which is much more precise, will avoid confusion:

   /*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,* by which triadic relation the