Re: [PEIRCE-L] Interpretants, Sign Classification, and 3ns (was Who, What, When, Where, How, and Why)

[Jon Alan Schmidt]

John, List:

JFS: We were talking about a method that a student or scholar of Peirce may
use for testing a sign to determine whether it is an instance of 1ns, 2ns,
or 3ns.


Again, according to Peirce, there are *ten different respects* by which a
sign can be classified as an instance of 1ns/2ns/3ns (or
possible/existent/necessitant). Again, none of them directly corresponds to
naming a monadic/dyadic/triadic relation.

JFS: The test is not a method of communication by means of sentences. It is
a method for determining the structure of a sign.


Here is your original claim (
https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00080.html).

JFS: And there are six kinds of reference that a sign may have to its
interpretants. Each kind corresponds to one of the six basic question words
... In short, that is the distinction between Peirce's 1ns, 2ns, and 3ns.
The monadic relations of 1ns express answers to the words Who, What, When,
or Where. The dyadic relations of 2ns express answers to the word How. And
the triadic relations of 3ns answer questions to the word Why.


This approach explicitly requires questions that start with specific words
to have answers that correspond to specific relational valencies. Setting
aside the fact that I have provided various counterexamples demonstrating
the absence of such a definitive alignment, dialogue (real or imagined) is
obviously essential to your proposed "test," although not necessarily
between two *different *people. "Moreover, signs require at least two
Quasi-minds; a *Quasi-utterer* and a *Quasi-interpreter*; and although
these two are at one (*i.e.*, are one mind) in the sign itself, they must
nevertheless be distinct. In the Sign they are, so to say, *welded*.
Accordingly, it is not merely a fact of human Psychology, but a necessity
of Logic, that every logical evolution of thought should be dialogic" (CP
4.551, 1906). "All thinking is dialogic in form. Your self of one instant
appeals to your deeper self for his assent" (CP 6.338, 1907).

As I pointed out in my initial reply, the external (dynamical or final)
interpretant of a sincere (not rhetorical) question is *not *the answer
given (actually or ideally) as another sign, but an interpreter's
*exertion *in giving that answer. Hence, the only interpretant that
*might *correspond
to the type of question being asked is the *immediate *interpretant.
However, we agree that for *who* and *what *questions, the initial word
functions as a *pronoun *denoting the blank in a rheme that the utterer is
asking the interpreter to fill. Similarly, *when*, *where*, *how*, or *why *at
the beginning of a question functions as a substitute for a *prepositional
phrase*--e.g., "on Valentine's Day," "in the eye," "by receiving it,"
"because a spark ignited it"--which Peirce likewise characterizes as
an *indexical
*sign (CP 2.290, EP 2:16, 1895). As such, the first word of a question is
always *designative *and thus belongs to its immediate *object*, not its
immediate *interpretant*.

Instead, I suggest that the logical relations represented by the syntax of
the relevant proposition as a general *type *(pure/continuous predicate),
along with the punctuation marks or voice inflections that are incorporated
into an individual *token *as qualitative *tones *to reflect the fact that
it is being posed as a question (not stated as an assertion), serve as the
immediate interpretant. After all, the intention of someone asking a
question is to obtain an answer, and "So far as the intention is betrayed
in the Sign, it belongs to the immediate Interpretant" (R 339, 1906 Apr 2).

Regards,

Jon

On Thu, Feb 15, 2024 at 9:31 PM John F Sowa  wrote:

> Jon,
>
> I completely agree with the following paragraph:
>
> JAS>  Put another way, a who or what question is often a *rheme*, such
> that the answer fills in the blank to complete the proposition. "___
> retrieved the book" becomes "My dog retrieved the book." "The man gave his
> wife ___" becomes "The man gave his wife a brooch." The key is not the word
> that begins the question, but the nature of what is missing in the mind of
> the inquirer until it is supplied by the respondent.
>
> But your paragraph is a discussion of a dialog between two two persons:
>  an inquirer and an respondent.  One of them is uttering a sentence
> (complete or partial) and the other is interpreting it.
>
> But Helmut and I were not talking about a dialog between two people.  We
> were talking about a method that a student or scholar of Peirce may use for
> testing a sign to determine whether it is an instance of 1-ness, 2-ness, or
> 3-ness.  Those are two totally different activities.  The test is not a
> method of communication by means of sentences.  It is a method for
> determining the structure of a sign.
>
> John
>
> --
> *From*: "Jon Alan Schmidt" 
> *Sent*: 2/15/24 9:47 PM
> *To*: Peirce-L 
> *Subject*: Re: [PEIRCE-L] Interpretants, Sign Classification, and 3ns
> (was Who, What, 

[PEIRCE-L] Mathematical Proof of Peirce's Reduction Thesis; and Valental Graphs

[Gary Richmond]

Jon, List,

You recently wrote:

JAS: I do not know whether anyone has posted a mathematical proof of
Peirce's reduction thesis on the Internet. Robert Burch wrote an entire
book to present his [. . .] while Sergiy Koshkin purports to demonstrate it
even more rigorously in a recent paper.

I vividly recall, although it was over a decade ago, a young
scholar (either Joachim Hereth or Reinhard Poschel) whom I'd previously not
met  coming up to me at an outdoor party during an ICCS conference,
excitedly announcing that he and another scholar had completed a
mathematical proof of Peirce's Reduction Thesis that went beyond Robert
Burch's PAL. This is described in the Abstract of the paper below.

Peircean Algebraic Logic and Peirce's Reduction Thesis


   - Joachim Hereth and Reinhard Pöschel

*Abstract*

Robert Burch describes *Peircean Algebraic Logic (PAL)* as a language to
express Peirce's “unitary logical vision” (1991: 3), which Peirce tried to
formulate using different logical systems. A “correct” formulation of
Peirce's vision then should allow a mathematical proof of Peirce's
Reduction Thesis, that all relations can be generated from the ensemble of
unary, binary, and ternary relations, but that at least some ternary
relations cannot be reduced to relations of lower arity.

Based on Burch's algebraization, the authors further simplify the
mathematical structure of PAL and remove a restriction imposed by Burch,
making the resulting system in its expressiveness more similar to Peirce's
system of existential graphs. The drawback, however, is that the proof of
the Reduction Thesis from Burch (A Peircean reduction thesis: The
foundations of topological logic, Texas Tech University Press, 1991) no
longer holds. A new proof was introduced in Hereth Correia, and Pöschel
(The teridentity" and Peircean algebraic logic: 230–247, Springer, 2006)
and was published in full detail in Hereth (Relation graphs and contextual
logic: Towards mathematical foundations of concept-oriented databases,
Technische Universität Dresden dissertation, 2008).

In this paper, we provide proof of Peirce's Reduction Thesis using a graph
notation similar to Peirce's existential graphs.
Keywords:: Peirce

; Existential Graphs

; Burch

; Peircean Algebraic Logic

; Relational Graphs

Published Online: 2011-08-08
*Peircean Algebraic Logic and Peirce’s Reduction Thesis*
https://wwwpub.zih.tu-dresden.de/~poesch-r/poePUBLICATIONSpdf/2011_Hereth_Poe.pdf
Published in Print: 2011-August

I must admit that the complexities of the math involved in their paper as
well as Koshkin's (which I only recently became aware of) has precluded my
reading much of either of them. But then, I tend to strongly agree with you
in this comment of yours.

JAS: I find Peirce's own diagrammatic demonstration to be simple and
persuasive enough--relations of any adicity can be built up of triads, but
triads cannot be built up of monads or dyads despite involving them (EP
2:364, 1905).

In *A Thief of Peirce *Kenneth Ketner calls these diagrams "valental
graphs" and discusses them in one or two of the appendices of that book (I
remember buying the book for just those appendices even though it seemed a
small fortune at the time).
[image: image.png]

Best,

Gary
_ _ _ _ _ _ _ _ _ _
ARISBE: THE PEIRCE GATEWAY is now at 
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https://www.cspeirce.com .  It'll take a while to repair / update all the links!
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[PEIRCE-L] Commens

[Gary Richmond]

List,

A couple of List members have noted that *Commens *is back up and running.
http://www.commens.org

We have Ben Udell to thank for noodling within the site when it went down,
then alerting Mats Bergman -- who manages and, along with Sami Paavola and João
Queiroz, developed that very useful site -- that the cause was likely
database corruption (which it was). Mats managed to repair it, but he's not
certain that it will remain stable. The good news, though, is that he's
been developing a new site to replace the current one.

Thank you both, but I worry that the solution may be temporary. The
database is now running in a fault-tolerant mode, which is not recommended,
but which should work as long as no new content is added. The new version
(which I have been developing offline) needs to be uploaded sooner rather
than later ‒ fingers crossed that the old site stays up and running until I
get it all done.


Please alert Ben if you encounter any errors on Commens.

Best,

Gary Richmond (writing as co-manager of Arisbe with Ben Udell)
_ _ _ _ _ _ _ _ _ _
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!
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PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
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Aw: [PEIRCE-L] Interpretants, Sign Classification, and 3ns (was Who, What, When, Where, How, and Why)

[Helmut Raulien]

Jon, John, List,

 

The answer "A brooch" looks like a rheme, but as an answer it is a proposition, as "he gives her" is just omitted for the reason, that both know this opening. A triadic proposition, I think, if not already is an argument, at least involves a "because". For example if you say; "He gives her a brooch" involves, that he is able of giving something, because he has a brooch. "Egbert has a cat and a dog" involves, that the "and" can be said, because "a cat" has already been mentioned, so "a dog" can be added.


 

Best, Helmut

 

16. Februar 2024 um 03:47 Uhr
Von: "Jon Alan Schmidt" 
 



John, List:
 

At the risk of belaboring the point, I will take one more stab at showing why I think that Peirce would not have agreed with distinguishing 1ns, 2ns, and 3ns by aligning them with the answers to who/what/when/where, how, and why questions as (allegedly) monadic, dyadic, and triadic.

 

If I ask, "Who retrieved the book?" and you reply, "My dog," then from a logical standpoint, you are not merely uttering the name of a monadic relation, you are asserting the dyadic proposition that your dog retrieved the book. If I ask, "What did the man give his wife?" and you reply, "A brooch," then from a logical standpoint, you are not merely uttering the name of a monadic relation, you are asserting the triadic proposition that the man gave his wife a brooch.

 

Put another way, a who or what question is often a rheme, such that the answer fills in the blank to complete the proposition. "___ retrieved the book" becomes "My dog retrieved the book." "The man gave his wife ___" becomes "The man gave his wife a brooch." The key is not the word that begins the question, but the nature of what is missing in the mind of the inquirer until it is supplied by the respondent.

 

In fact, sometimes the answer to a what question is the name of a dyadic or triadic relation. "What did your dog do with the book?" "My dog retrieved the book." "What did the man do with the brooch?" "He gave it to his wife."

 

A when or where question is even less straightforward. If I ask, "When did the man give his wife the brooch?" and you reply, "On Valentine's Day," this is only informative if I already know that Valentine's Day is February 14 and what today's date is--there is an unavoidably indexical aspect here. If I ask, "Where did the datestone hit the Jinnee?" and you reply, "In the eye," this just changes the relevant proposition from "The datestone hit the Jinnee" to "The datestone hit the Jinnee's eye."

 

Again, a how question need not have a dyadic answer. If I ask, "How are you?" and you reply, "I am cold" (after shoveling snow), then you are obviously asserting a monadic proposition. If I ask, "How did the man celebrate Valentine's Day?" and you reply, "He gave his wife a brooch," then you are obviously asserting a triadic proposition.

 

Likewise, a why question need not have a triadic answer. If I ask, "Why are you shivering?" and you reply, "I am cold," then you are obviously asserting a monadic proposition. If I ask, "Why did the man give his wife a brooch?" and you reply, "He was celebrating Valentine's Day," then you are obviously asserting a dyadic proposition.

 


These examples illustrate the imprecision and resulting flexibility of natural languages. The fact that information can be added to or subtracted from someone's answer to a question in ordinary conversation reflects the context-dependency of both utterances, as well as the dialogic nature of human semiosis. Consequently, it is better to stick with Peirce's own paradigmatic conceptions for distinguishing 1ns/2ns/3ns as discovered in phaneroscopy, namely, quality/reaction/mediation.


 

Regards,

 





Jon Alan Schmidt - Olathe, Kansas, USA

Structural Engineer, Synechist Philosopher, Lutheran Christian

www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt







 


On Thu, Feb 15, 2024 at 3:32 PM John F Sowa  wrote:



I have to shovel snow right now, but I'll briefly explain the two sentences.

 

JAS> 

        JAS: How did the woman obtain the brooch? Her husband gave it to her. 



JFS: The verb 'give' is triadic. It implies a dyadic physical transfer (answer to How) plus the reason why: a gift includes the reason why the transfer was made.




 

The question begins with the word "How," not "Why"; and by your own admission, the answer is triadic, thus a genuine example of 3ns by your criterion. "Why did the woman's husband give her the brooch?" is a completely different question that would require a completely different answer.

 

By including the verb 'give' in the answer, her husband gave a triadic answer to a dyadic question.  That includes more information than was requested.  In the other question, with the word 'why', the answer stated less information, and the person who asked would typically ask a follow-on question to get the reason why.

 

The possibility that the answer might not contain exactly