[PEIRCE-L] Categorizations of triadic Relationships (Was Re: Graphical Representations of the Sign by Peirce)

[Jerry LR Chandler]

Following Robert’s efforts to clarify meanings of terminology in symbolic 
logics...

> On Jan 8, 2024, at 9:45 AM, Jon Alan Schmidt  wrote:
> 
> The directionality of semiosis is such that the object determines the sign 
> while being unaffected by that sign, and the sign determines the interpretant 
> while being unaffected by that interpretant. 

Jon:

Given your background as an engineer, I would appreciate your opinion on the 
following.

In recent years, I have turned my attention to the distinctions between the 
classical philosophy of signs, originating in the medical arts and other 
simpler perspectives of communications.  Let’s call these texts as “semiology” 
texts.  In these writings, I do not find any reason not to assume that both the 
object (detected by writer) and the signs that were described by the ancients 
in scripts were naturally external to the writer.
So, the questions arises, how does one locate the origins of the “triadic 
relations”?

Then the question arises, how does one distinguish CSP’s “semiotics”.
Which semantic aspects of the “triadic relations” are external?
Which semantic aspects of the "triadic relations are internal to the describer?

In other words, Where does the syntax for triadic relation originate?
And, Where does the syntax for triadic relation reside?

And, how would such a determination fix the differentiation between the 
adjectives (…ness) and the numbers, either / or cardinal or ordinal?   ….  
neither /nor?  

Cheers

Jerry 



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Aw: [PEIRCE-L] Graphical Representations of the Sign by Peirce

[Helmut Raulien]

Edwina, list,

 

ok, I too think, that the DO does not exist without the sign, so the "sleeping" memory, in this case the knowledge, that snow can be shoveled away, is just a memory then. But in the next sign, when the person is aware of a new white, fluffy layer on the lawn and the pathway, the knowledge of new snow is part of the immediate object, because this information is transported by the sign/representamen (while the real snow is not transported, it keeps lying there, so it is the material part of the DO). And the knowledge, that snow may be handled by using a shovel, is not part of the sign, but comes from the memory. Now what is this remembered memory? Is it part of the dynamical object of "snow, actual and general", or is this memorization another representamen, that merges with the other representamen to a blended one? But anyway I am confused now, because the knowledge, that the white, fluffy layer is snow, comes from the memory too. So what is what? Or is it not one sign, but a cascade or cluster of signs with different objects, some from the memory, and others from the real snow?

 

Best, Helmut

 
 

Gesendet: Montag, 08. Januar 2024 um 17:47 Uhr
Von: "Edwina Taborsky" 
An: "Helmut Raulien" 
Cc: "Peirce-L" , "Edwina Taborsky" 
Betreff: Re: [PEIRCE-L] Graphical Representations of the Sign by Peirce


Helmut, list

I’m not quite sure if I understand your post - I don’t think that ‘habits’ [sleeping in memory?] are equivalent to Dynamicl Objects - and the Dynamical Object is always a part of the sign; ie, the DO doesn’t exist on its own outside of the semiosic interaction. 

 

With reference to the Interpretant changing the nature of the Object, I’d agree -within the understanding of the reality of evolution. That is, 

 

-  a disease, formerly reduced in its effects by an antibiotic, ….understood as O->reduction in effect, becomes, over time changed by those results [ reduction in effect] to become immune to the antibiotic.

 

- a tree, attacked by insects [ Objects]….which reduces its capacity to live [Interpretant: by the reduction of the leaves]….develops internal chemicals in the leaves  to thwart the insects [O]. But then, the insects develop new immunities to those chemicals!

 

- a word [Object] — such as the word ‘virus’…. Changes its meaning over time…

 

The point is - such changes in the nature of the functioning of the Object in the world [ disease, insects, words] can only take place if the sign vehicle [ the disease, the tree, the word] are functioning in a mode of Thirdness.  And Thirdness is vital to the nature of the universe. 

 

Again, I stress the importance of the categories in the functioning of semiosis.

 

Edwina

 

On Jan 8, 2024, at 10:19 AM, Helmut Raulien  wrote:
 




Edwina, yes, I agree. Only the model I used is different: While you say, that the representamen grows, I talk about old and new sign. Like the snow situation is a continuous thing in reality, in the mind of the interpreter it serves as a new sign again and again. If you say, the snow situation is the representamen, ok, then it grows, but for me the appearance of the snow situation in the interpreter´s mind is the representamen in either case of noticing it. What grows in the interpreter´s mind, is the object of snow. Whether that is the immediate or the dynamical object, is hard to decide for me: At times of no sign, it still is in the interpreter´s memory: How to handle the snow. But while this knowledge is sleeping in the memory, it is not a part of any sign, so it is dynamical object, i would say. Anyway, it is hard for me to distinguish between immediate and dynamical/real object: An object part may be dynamical in the intentional or effectual interpretant, but immediate in the cominterpretant, and sometimes it may be hard to know the size of the commens, because, especially in the internet, nobody knows who is taking part in a discourse. I know, that the flow of determination can categorally not go upwards. The object determines the sign, the sign the interpretant, and the interpretant changes the object, which is some sort of determination too. And then I guess, as the interpretant serves as a new sign, this sign is, besides by the old interpretant, also determined by the now having changed object. This looks like a redundancy of course, but if the object is changed in a larger context/commens, this change too determines the sign of a smaller (sub-) commens, and in this case, this determination part is not redundant with the information/determination carried by the interpretant in the narrower commens. Like this, i think we might better see the complexity of all this, and how signs interact via object change, if we construct or tell more examples. In signs including physical action, there is an energetic interpretant, and the object change is material as well. The material part of the dynamical object then is easy to identify, as it is spatially defined, it can be marked. But the 

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] Graphical Representations of the Sign by Peirce

[Edwina Taborsky]

Helmut, list
I’m not quite sure if I understand your post - I don’t think that ‘habits’ 
[sleeping in memory?] are equivalent to Dynamicl Objects - and the Dynamical 
Object is always a part of the sign; ie, the DO doesn’t exist on its own 
outside of the semiosic interaction. 

With reference to the Interpretant changing the nature of the Object, I’d agree 
-within the understanding of the reality of evolution. That is, 

-  a disease, formerly reduced in its effects by an antibiotic, ….understood as 
O->reduction in effect, becomes, over time changed by those results [ reduction 
in effect] to become immune to the antibiotic.

- a tree, attacked by insects [ Objects]….which reduces its capacity to live 
[Interpretant: by the reduction of the leaves]….develops internal chemicals in 
the leaves  to thwart the insects [O]. But then, the insects develop new 
immunities to those chemicals!

- a word [Object] — such as the word ‘virus’…. Changes its meaning over time…

The point is - such changes in the nature of the functioning of the Object in 
the world [ disease, insects, words] can only take place if the sign vehicle [ 
the disease, the tree, the word] are functioning in a mode of Thirdness.  And 
Thirdness is vital to the nature of the universe. 

Again, I stress the importance of the categories in the functioning of semiosis.

Edwina

> On Jan 8, 2024, at 10:19 AM, Helmut Raulien  wrote:
> 
> Edwina, yes, I agree. Only the model I used is different: While you say, that 
> the representamen grows, I talk about old and new sign. Like the snow 
> situation is a continuous thing in reality, in the mind of the interpreter it 
> serves as a new sign again and again. If you say, the snow situation is the 
> representamen, ok, then it grows, but for me the appearance of the snow 
> situation in the interpreter´s mind is the representamen in either case of 
> noticing it. What grows in the interpreter´s mind, is the object of snow. 
> Whether that is the immediate or the dynamical object, is hard to decide for 
> me: At times of no sign, it still is in the interpreter´s memory: How to 
> handle the snow. But while this knowledge is sleeping in the memory, it is 
> not a part of any sign, so it is dynamical object, i would say. Anyway, it is 
> hard for me to distinguish between immediate and dynamical/real object: An 
> object part may be dynamical in the intentional or effectual interpretant, 
> but immediate in the cominterpretant, and sometimes it may be hard to know 
> the size of the commens, because, especially in the internet, nobody knows 
> who is taking part in a discourse. I know, that the flow of determination can 
> categorally not go upwards. The object determines the sign, the sign the 
> interpretant, and the interpretant changes the object, which is some sort of 
> determination too. And then I guess, as the interpretant serves as a new 
> sign, this sign is, besides by the old interpretant, also determined by the 
> now having changed object. This looks like a redundancy of course, but if the 
> object is changed in a larger context/commens, this change too determines the 
> sign of a smaller (sub-) commens, and in this case, this determination part 
> is not redundant with the information/determination carried by the 
> interpretant in the narrower commens. Like this, i think we might better see 
> the complexity of all this, and how signs interact via object change, if we 
> construct or tell more examples. In signs including physical action, there is 
> an energetic interpretant, and the object change is material as well. The 
> material part of the dynamical object then is easy to identify, as it is 
> spatially defined, it can be marked. But the conceptual part of the dynamical 
> object can not, that is why it is not always easy to exactly tell it from the 
> immediate object, i guess.
>  
> Best, Helmut
>  
>  
> Gesendet: Sonntag, 07. Januar 2024 um 19:28 Uhr
> Von: "Edwina Taborsky" 
> An: "Helmut Raulien" 
> Cc: "Peirce-L" , "Edwina Taborsky" 
> 
> Betreff: Re: [PEIRCE-L] Graphical Representations of the Sign by Peirce
> Helmut -  I think one has to be clear about terms.  Do you mean that the 
> Interpretant [ which is a relation not a thing-in-itself] becomes a new triad 
> or only a new Representamen?
>  
> My own view is that the Interpretant, which ‘holds and moulds’ information, 
> contributes to the formation of both a new triad [as, for example, when 
> nutrients from the food-as-object,  contribute to the formation of the 
> cell-as a triadic Sign] ; when information about the weather [as object] 
> contributes  to my Interpretant decision to shovel the snow…and I then, 
> remember in the future what to do when snow arrives..
>  
> That is, this interpretant would also enhance the knowledge content of the 
> Representamen if it were operating in its mode of Thirdness. That is, 
> Representamens in a mode of Thirdness grow in informational content. 
>  
> And that’s another 

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 



_ _ _ _ _ _ _ _ _ _
ARISBE: THE PEIRCE GATEWAY is now at 
https://cspeirce.com  and, just as well, at 
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Re: [PEIRCE-L] Graphical Representations of the Sign by Peirce

[Jon Alan Schmidt]

Helmut, List:

HR: The object determines the sign, the sign the interpretant, and *the
interpretant changes the object*, which is some sort of determination too.


According to Peirce, the bolded part is incorrect.

CSP: As a *medium*, the Sign is essentially in a triadic relation, to its
Object which determines it, and to its Interpretant which it determines. In
its relation to the Object, the Sign is *passive*; that is to say, its
correspondence to the Object is brought about by an effect upon the Sign,
the Object remaining unaffected. On the other hand, in its relation to the
Interpretant the Sign is *active*, determining the Interpretant without
being itself thereby affected. (EP 2:544n22, 1906)


The directionality of semiosis is such that the object determines the sign
while being unaffected by that sign, and the sign determines the
interpretant while being unaffected by that interpretant. Hence, the object
determines the interpretant through the mediation of the sign while being
unaffected by that interpretant.

Regards,

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

On Mon, Jan 8, 2024 at 9:20 AM Helmut Raulien  wrote:

> Edwina, yes, I agree. Only the model I used is different: While you say,
> that the representamen grows, I talk about old and new sign. Like the snow
> situation is a continuous thing in reality, in the mind of the interpreter
> it serves as a new sign again and again. If you say, the snow situation is
> the representamen, ok, then it grows, but for me the appearance of the snow
> situation in the interpreter´s mind is the representamen in either case of
> noticing it. What grows in the interpreter´s mind, is the object of snow.
> Whether that is the immediate or the dynamical object, is hard to decide
> for me: At times of no sign, it still is in the interpreter´s memory: How
> to handle the snow. But while this knowledge is sleeping in the memory, it
> is not a part of any sign, so it is dynamical object, i would say. Anyway,
> it is hard for me to distinguish between immediate and dynamical/real
> object: An object part may be dynamical in the intentional or effectual
> interpretant, but immediate in the cominterpretant, and sometimes it may be
> hard to know the size of the commens, because, especially in the internet,
> nobody knows who is taking part in a discourse. I know, that the flow of
> determination can categorally not go upwards. The object determines the
> sign, the sign the interpretant, and the interpretant changes the object,
> which is some sort of determination too. And then I guess, as the
> interpretant serves as a new sign, this sign is, besides by the old
> interpretant, also determined by the now having changed object. This looks
> like a redundancy of course, but if the object is changed in a larger
> context/commens, this change too determines the sign of a smaller (sub-)
> commens, and in this case, this determination part is not redundant with
> the information/determination carried by the interpretant in the narrower
> commens. Like this, i think we might better see the complexity of all this,
> and how signs interact via object change, if we construct or tell more
> examples. In signs including physical action, there is an energetic
> interpretant, and the object change is material as well. The material part
> of the dynamical object then is easy to identify, as it is spatially
> defined, it can be marked. But the conceptual part of the dynamical object
> can not, that is why it is not always easy to exactly tell it from the
> immediate object, i guess.
>
> Best, Helmut
>
_ _ _ _ _ _ _ _ _ _
ARISBE: THE PEIRCE GATEWAY is now at 
https://cspeirce.com  and, just as well, at 
https://www.cspeirce.com .  It'll take a while to repair / update all the links!
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
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co-managed by him and Ben Udell.

Aw: [PEIRCE-L] Graphical Representations of the Sign by Peirce

[Helmut Raulien]

Edwina, yes, I agree. Only the model I used is different: While you say, that the representamen grows, I talk about old and new sign. Like the snow situation is a continuous thing in reality, in the mind of the interpreter it serves as a new sign again and again. If you say, the snow situation is the representamen, ok, then it grows, but for me the appearance of the snow situation in the interpreter´s mind is the representamen in either case of noticing it. What grows in the interpreter´s mind, is the object of snow. Whether that is the immediate or the dynamical object, is hard to decide for me: At times of no sign, it still is in the interpreter´s memory: How to handle the snow. But while this knowledge is sleeping in the memory, it is not a part of any sign, so it is dynamical object, i would say. Anyway, it is hard for me to distinguish between immediate and dynamical/real object: An object part may be dynamical in the intentional or effectual interpretant, but immediate in the cominterpretant, and sometimes it may be hard to know the size of the commens, because, especially in the internet, nobody knows who is taking part in a discourse. I know, that the flow of determination can categorally not go upwards. The object determines the sign, the sign the interpretant, and the interpretant changes the object, which is some sort of determination too. And then I guess, as the interpretant serves as a new sign, this sign is, besides by the old interpretant, also determined by the now having changed object. This looks like a redundancy of course, but if the object is changed in a larger context/commens, this change too determines the sign of a smaller (sub-) commens, and in this case, this determination part is not redundant with the information/determination carried by the interpretant in the narrower commens. Like this, i think we might better see the complexity of all this, and how signs interact via object change, if we construct or tell more examples. In signs including physical action, there is an energetic interpretant, and the object change is material as well. The material part of the dynamical object then is easy to identify, as it is spatially defined, it can be marked. But the conceptual part of the dynamical object can not, that is why it is not always easy to exactly tell it from the immediate object, i guess.

 

Best, Helmut

 
 

Gesendet: Sonntag, 07. Januar 2024 um 19:28 Uhr
Von: "Edwina Taborsky" 
An: "Helmut Raulien" 
Cc: "Peirce-L" , "Edwina Taborsky" 
Betreff: Re: [PEIRCE-L] Graphical Representations of the Sign by Peirce


Helmut -  I think one has to be clear about terms.  Do you mean that the Interpretant [ which is a relation not a thing-in-itself] becomes a new triad or only a new Representamen?

 

My own view is that the Interpretant, which ‘holds and moulds’ information, contributes to the formation of both a new triad [as, for example, when nutrients from the food-as-object,  contribute to the formation of the cell-as a triadic Sign] ; when information about the weather [as object] contributes  to my Interpretant decision to shovel the snow…and I then, remember in the future what to do when snow arrives..

 

That is, this interpretant would also enhance the knowledge content of the Representamen if it were operating in its mode of Thirdness. That is, Representamens in a mode of Thirdness grow in informational content. 

 

And that’s another reason why it’s difficult to create a visual diagram of the semiosic process - those modalities - which are rarely discussed on this site. 

 

But, just as we acknowledge the semiosic determinative process of 

O-R-I…..and even

DO-IO-R-II-DI-FI.     [and I’m assuming everyone knows what these letters stand for….

 

We also have to acknowledge the modal restrictions, 

It is obvious that a Possible cannot determine anything other than a Possible, and likewise a Necessitant cannot be determined by anything other than a Necessitant (letter to Lady Welby of December 23, 1908 )

 

Essentially this sets up restrictions on the development of the informational nature of the triad. That is, an Object in a mode of 2ns cannot determine/produce an Interpretant in a mode of 3ns. A Representamen in a mode of 2ns cannot produce an Interpretant in a mode of 3ns. 

 

And it gets even more complex when you Bring in the concept of the genuine and degenerate categorical modes. 

 

That is, as an example, there is only one of the ten classes where the Interpretant is in a mode of Thirdness. One has to consider - are all three Interpretants in this mode? But - are they all ‘genuine Thirdness or is there any one of the three that is in a degenerate mode [3-1 or 3-2, ie, Thirdness degenerate in the 2nd degree or first degree]? 

BUT - we have to consider that one cannot move from Firstness to Secondness to Thirdness! Even within another mode - ie, you cannot move from 3-1 to 3-2 to 3-3 without an external ‘assistance from another sign input]. 

 

So- the 

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