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

[Jerry LR Chandler]

List: 

Well, I will continue to search for an adequate semantic expression for my 
feelings about the meanings (plural) of a triadic relation. 
Perhaps it would be helpful to note that the meaning of “triadic” is a critical 
part of the question, but not particularly difficult or controversial (outside 
the CSP community.)
The term “relation” is highly controversial throughout the kingdom of 
mathematics. 
The word “relation” is derived from the Latin, “relates” 
(See the Wikipedia declension below) , putatively meaning to bear or to carry, 
including sense of “bearing a child”, that is, the biological sense.  That is, 
in the genetic sense.  In mathematics, it may mean to “entail”, that is, as an 
inheritance from a prior sentence or terms of a sentence. So, the implication 
of a family of relatives may be intrinsic (symbolically) to a set of triadic 
relations.

From these perspectives, I now give an examples.
When one simply states a sinsign, a single term, how is the meaning interpreted 
as a “triadic relation”.

“HEADACHE”.

Or

“ORANGE”

How does one ascribe meaning to the “triadic relation” in the sense of 
interrogatories - What, Who, When, Where, How and Why ?  (Or any other sense or 
sensory mode you are capable of exploring.)

In the cognitive (grammatical) sense, what locates the three predicates(?) 
(Or, what locates the three subjects?)  Or are the three terms of the triadic 
relations merely adjectives?

Beyond what CSP may have opined about, personal interpretations of CSP’s 
phrases are welcome. 

 (Yes, Robert, your’s in particular! As you are aware of the role of “ordered 
pairs” in set theory.)  
(Ben:  In part, this refers back to your “tetradicity” if that term is 
correctly remembered.)

Alternatively, is this a meaningful conundrum?

Cheers

Jerry 

Participle
relātus (feminine relāta , neuter 
relātum ); first 
/second-declension
  participle

Perfect passive participle of referō 
(having been) driven  or carried 
 back
(having been) returned , restored 
, repaid 

(having been) reported 
(having been) reconsidered 

> On Jan 10, 2024, at 1:28 PM, Edwina Taborsky  wrote:
> 
> List
> 
> I think the quotations provided by JAS do not change the meaning of the 
> quotations I provided to show that the categories are described by Peirce as 
> having both genuine and degenerate modes. That is, the category of Secondness 
> has both a genuine and degenerate mode; the category of Thirdness has a 
> genuine, a degenerate in the first degree, a degenerate in the third degree.
> 
> These terms of ‘genuine’ and ‘degenerate' are completely different in meaning 
> from the quotation provided by JAS 
> 
>> CSP: A sign is a Priman which is Secundan to an Object and is Tertian in 
>> determining an Interpretant into Secundanity to that Object. It has two 
>> Objects, the immediate, to which it is degenerately Secundan, the dynamic, 
>> to which it is genuinely Secundan. It has three Interpretants, the 
>> immediate, to which it is primarily Tertian, the dynamic, to which it is 
>> secundally Tertian, the rational, to which it is genuinely Tertian. (R 
>> 339:247r, 1905 Jul 7)
> 
> The above terms , with, eg, reference to the two objects, means only that the 
> Immediate Object has a ‘degenerate’ or less intact’ form of informational 
> content than the Dynamic Object. These terms, I suggest, refer to the 
> determination of the semiosic process - and have nothing to do with the 
> categories.  That is, although JAS declares:
> 
>>  In context, "primarily Tertian" clearly corresponds to doubly degenerate 
>> (1ns of 3ns) and "secundally Tertian" corresponds to degenerate (2ns of 3ns)
> 
> 
> I continue to disagree, since this is setting up the semiotic triad and 
> hexagon as having the Interpretants all in a categorical mode of Thirdness! 
> But we can see from even the list of ten classes, that there is only ONE 
> class where the Interpretant is in a mode of Thirdness - the Argument 
> Symbolic Legisign. [See 2.234-264 and also 8.341]. All the other nine classes 
> have the Interpretant in a mode of either Firstness [there are SIX of these] 
> or in a mode of Secondness [ there are three of these]. 
> 
> With regard to the following quotation
> 
> 
>> CSP: A representamen, or sign, is anything which stands, in any respect, at 
>> once in a relation of correspondence to a correlate, called its object and 
>> to another correlate, its interpretant. which is a 

RE: [PEIRCE-L] Representing sign relations in existential graphs

[John F Sowa]

Jon, List,

The following is a definition of the sign relation by Peirce that has a direct 
mapping to and from an existential graph:

“A sign is anything A, in a relation, r to something B, its object, this 
relation r consisting in fitness to determine something so as to produce 
something, C, the interpretant of the sign." (1904 MS  L107:25)

The date 1904 is significant because Peirce was actively writing his late 
Monist articles, discussing significs and semeiotic with Lady Welby, and 
working on his proof of pragmaticism.   Before, during, and after that time, he 
was also writing and lecturing about EGs, especially in his Logic Notebook.

Note that the EG implied by that quotation has a relation r in with three 
correlates A, B, and C.  That has the same sshape as your EG with the sign as A 
and 'mediating' as the relation.  It also has the same shape as the EG I drew 
below in a note to Cécile.

The most important distinction, however, is one that Noeth implied and that 
Cécile had noticed when she used the word 'sign-object'.   That word is 
synonymous with the word 'sign-mark' that I had adopted after reading Noeth's 
remark.  Both of them are passive, but perceptible objects, things, or marks 
that people interpret as sign-objects or sign-marks.  But the sign itself,  as 
Peirce repeatedly said is triadic.

In Peirce's quotation above, the "anything A" is a passive sign object or mark 
that serves as first correlate.  The relation r is the active triadic sign 
relation.  In Noeth's quotation, he wrote that "sign, representamen, or 
representation were synonymously used as the names referring to the first 
correlate of the triadic relation of semiosis."

But sign as representation or representamen is active, not passive.  I believe 
that in the quotation that has a direct translation to an EG, the first 
correlate A is the passive sign object or mark.  And the relation r is the verb 
form that is a synonym for the active verb 'represents'.

The text below is a combination of two notes that I sent to Cécile on January 6 
and 7.

John

PS:My drawings of EGs below line up very nicely in the type font I'm using 
for writing this note.  But readers may view it with a different font that does 
not line up correctly.  If so, you can make the diagrams line up by adding or 
deleing spaces to make the characters / and \ link correctly to the words above 
and below those lines.


From: "John F Sowa" 

Cécile,

After reading this thread, I found a quotation by Peirce that shows how to draw 
an existential graph that follows  Peirce's words quite closely.  It's also 
consistent with the quotation by Noeth:  "Peirce did consider the sign to be a 
triadic relation, but only in 1868. However, from 1873 onwards, sign, 
representamen, or representation were synonymously used as the names referring 
to the first correlate of the triadic relation of semiosis" (p. 455).

The key to the analysis is the recognition that every sign has a physically 
perceptible mark.  That mark is only a sign when somebody interprets it as a 
sign.  Therefore, we should distinguish the physical sign-mark or sign-object 
from its action as a representamen or representation.

Since nobody has found an EG drawn by Peirce to represent the sign relation, 
the best we can do is to find a quotation by Peirce that has a simple 
translation to an EG.  The following quotation is a good candidate:
“A sign is anything A, in a relation, r to something B, its object, this 
relation r consisting in fitness to determine something so as to produce 
something, C, the interpretant of the sign." (1904 MS  L107:25)

Since Peirce had drawn many EGs before and after 1904, he probably had a direct 
translation to an EG in mind.  He might have drawn an example on his 
blackboard.  Note that this quotation mentions four items:  A, B, C, and a 
triadic relation r.

As an example, let's consider the word "cat' as a sign-object A in a relation 
of representation r to a concept of a cat B to determine a fuzzy animal C as 
the interpretation of the sign.  Following is an EG that represents the 
sentence: "The word "cat" represents a concept CAT to determine a particular 
animal named Felix."

Represents
/|\
"cat"   CAT   Felix

Shorter sentence:   The word 'cat' represents a cat named Felix.

This example follows L107;25 quite directly.  I won't claim that it is exactly 
what Peirce would have drawn, but it follows his words closely.  Since Peirce 
often represented EG relations by verbs, the verb 'represents' may be used as 
the verb from which 'representamen' and 'representation' were derived.

John

---

After sending my previous note, I thought of more examples for representing 
sign relations in EGs -- including EGs that link together whatever graphs are 
necessary to express anything.

I want to emphasize that I was inspired by some of Peirce's writings, but 

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

[Edwina Taborsky]

List

I think the quotations provided by JAS do not change the meaning of the 
quotations I provided to show that the categories are described by Peirce as 
having both genuine and degenerate modes. That is, the category of Secondness 
has both a genuine and degenerate mode; the category of Thirdness has a 
genuine, a degenerate in the first degree, a degenerate in the third degree.

These terms of ‘genuine’ and ‘degenerate' are completely different in meaning 
from the quotation provided by JAS 

> CSP: A sign is a Priman which is Secundan to an Object and is Tertian in 
> determining an Interpretant into Secundanity to that Object. It has two 
> Objects, the immediate, to which it is degenerately Secundan, the dynamic, to 
> which it is genuinely Secundan. It has three Interpretants, the immediate, to 
> which it is primarily Tertian, the dynamic, to which it is secundally 
> Tertian, the rational, to which it is genuinely Tertian. (R 339:247r, 1905 
> Jul 7)

The above terms , with, eg, reference to the two objects, means only that the 
Immediate Object has a ‘degenerate’ or less intact’ form of informational 
content than the Dynamic Object. These terms, I suggest, refer to the 
determination of the semiosic process - and have nothing to do with the 
categories.  That is, although JAS declares:

>  In context, "primarily Tertian" clearly corresponds to doubly degenerate 
> (1ns of 3ns) and "secundally Tertian" corresponds to degenerate (2ns of 3ns)


I continue to disagree, since this is setting up the semiotic triad and hexagon 
as having the Interpretants all in a categorical mode of Thirdness! But we can 
see from even the list of ten classes, that there is only ONE class where the 
Interpretant is in a mode of Thirdness - the Argument Symbolic Legisign. [See 
2.234-264 and also 8.341]. All the other nine classes have the Interpretant in 
a mode of either Firstness [there are SIX of these] or in a mode of Secondness 
[ there are three of these]. 

With regard to the following quotation


> CSP: A representamen, or sign, is anything which stands, in any respect, at 
> once in a relation of correspondence to a correlate, called its object and to 
> another correlate, its interpretant. which is a possible representamen 
> determined by the first and referring to the same object. (R 1147, c. 1901-2)

I consider that the triad is made up of three correlates or relations, and is 
irreducible. My reading of the above is that the mediate Representamen/Sign 
does not stand in - which suggests some kind of passive existence - but 
actually functions, in that it acts; it transforms the information of the 
Object into a meaning, an Interpretant, according to the knowledge base 
/habits, held within the Sign/Representamen in itself. 

I see no evidence in the many quotations provided that "  the 
representamen/sign stands in or has that relation to its object and 
interpretant, it is not that relation itself.”

I consider that the Sign/Representamen is a mediate node in the triadl;  it is 
an active relation and its function is to do just that - mediate between the 
Object and Interpretant. Therefore - I agree that the Sign/Representamen can be 
defined as

> "anything, of whatsoever mode of being, which mediates between an object and 
> an interpretant" (EP 2:410, 1907).

And note - that Peirce says ‘of whosoever mode of being’ - which means that 
this Sign/Representamen can function in any of the modal categories - and we 
can see in the ten classes, that it is in the mode of Firstness only once, in 
the mode of Thirdness six times, and in the mode of Secondness, three times.

Edwina



> On Jan 10, 2024, at 1:51 PM, Jon Alan Schmidt  
> wrote:
> 
> List:
> 
> For the record, Peirce describes the first, second, and third correlates of a 
> triadic relation as "simplest," "of middling complexity," and "most complex" 
> right before explicitly identifying the representamen/sign, object, and 
> interpretant as the three correlates of one such relation (CP 2.235-242, EP 
> 2:290, 1903); and he later outlines the two objects and three interpretants 
> in terms of genuine and degenerate in his Logic Notebook, as follows.
> 
> CSP: A sign is a Priman which is Secundan to an Object and is Tertian in 
> determining an Interpretant into Secundanity to that Object. It has two 
> Objects, the immediate, to which it is degenerately Secundan, the dynamic, to 
> which it is genuinely Secundan. It has three Interpretants, the immediate, to 
> which it is primarily Tertian, the dynamic, to which it is secundally 
> Tertian, the rational, to which it is genuinely Tertian. (R 339:247r, 1905 
> Jul 7)
> 
> CSP: The Interpretant is Threefold. The Normal Interpretant is the Genuine 
> Interpretant, embracing all that the Sign could reveal concerning the Object 
> to a sufficiently penetrating mind, being more than any mind, however 
> penetrating, could conclude from it, since there is no end to the distinct 
> conclusions that 

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

[Jon Alan Schmidt]

List:

For the record, Peirce describes the first, second, and third correlates of
a triadic relation as "simplest," "of middling complexity," and "most
complex" right before explicitly identifying the representamen/sign,
object, and interpretant as the three correlates of one such relation (CP
2.235-242, EP 2:290, 1903); and he later outlines the two objects and three
interpretants in terms of genuine and degenerate in his Logic Notebook, as
follows.

CSP: A sign is a Priman which is Secundan to an Object and is Tertian in
determining an Interpretant into Secundanity to that Object. It has two
Objects, the *immediate*, to which it is *degenerately* Secundan, the
*dynamic*, to which it is *genuinely* Secundan. It has three Interpretants,
the *immediate*, to which it is primarily Tertian, the *dynamic*, to which
it is secundally Tertian, the *rational*, to which it is genuinely Tertian.
(R 339:247r, 1905 Jul 7)

CSP: The Interpretant is Threefold. The Normal Interpretant is the Genuine
Interpretant, embracing all that the Sign could reveal concerning the
Object to a sufficiently penetrating mind, being more than any mind,
however penetrating, could conclude from it, since there is no end to the
distinct conclusions that could be drawn concerning the Object from any
Sign. ...
This triplet concerns the Dynamical, or Genuine Object. It is misleading to
call it the *real* object, since it may be unreal. It is the object that
truly determines the sign. (R 339:277r&279r, 1906 Apr 2-3)


It seems clear that the rational and normal interpretants in these passages
correspond directly to what Peirce calls the eventual and final
interpretants elsewhere, reflecting his confession "that my own conception
of this third interpretant is not yet quite free from mist" (CP 4.536,
1906). In context, "primarily Tertian" clearly corresponds to doubly
degenerate (1ns of 3ns) and "secundally Tertian" corresponds to degenerate
(2ns of 3ns). Again, these are results of phaneroscopic analysis--1ns, 2ns,
and 3ns are "the most universal categories of elements of all experience"
(CP 1.417, c. 1896), by no means limited to Peirce's various trichotomies
for sign classification.

Note also that the three divisions in his best-known taxonomy are according
to the nature of the representamen/sign *itself*, its *relation *to its
object, and its *relation *to its interpretant (CP 2.243, EP 2:291, 1903).
The representamen/sign, object, and interpretant are all *correlates*, not
relations, although they only serve as such *within *their genuine triadic
relation to each other. As Peirce states repeatedly (bold added in
quotations below), the representamen/sign *stands in *or *has *that
relation to its object and interpretant, it is not that relation *itself*.

CSP: A *representamen*, or sign, is anything which *stands, in any respect,
at once in a relation* of correspondence to a *correlate*, called its
*object* and to another *correlate*, its *interpretant*. which is a
possible representamen determined by the first and referring to the same
object. (R 1147, c. 1901-2)

CSP: 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. (CP 2.274, EP 2:272-273, 1903)

CSP: A *Representamen *is the First *Correlate of a triadic relation*, the
Second *Correlate *being termed its *Object*, and the possible Third *Correlate
*being termed its *Interpretant*, by which triadic relation the possible
Interpretant is determined to be the First Correlate of the same triadic
relation to the same Object, and for some possible Interpretant. (CP 2.242,
EP 2:290, 1903)

CSP: A sign therefore is *an object which is in relation* to its object on
the one hand and to an interpretant on the other, in such a way as to bring
the interpretant into a relation to the object, corresponding to its own
relation to the object. (CP 8.332, 1904)


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.
(EP 2:544n22, 1906)

CSP: A sign, therefore, *has a triadic relation* to its Object and to its
Interpretant. (CP 8.343, EP 2:482, 1908)


Again, although that relation can be called "representing," I prefer to
call it "mediating" because Peirce more generally defines a sign as
"anything, of whatsoever mode of being, which mediates between an object
and an interpretant" (EP 2:410, 1907).

Regards,

Jon

On Tue, Jan 9, 2024 at 5:08 PM Jon Alan Schmidt 
wrote:

> Jerry, List:
>
> I am honestly not sure exactly what all you are asking me to address here
> and how my engineering background is relevant. What do you mean by "the
> origins of the 'triadic relations'"? From what are we seeking to
> distinguish Peirce's semeiotic? What do you have in mind as *semantic*
>