I am interested in the definitions and roles of the Object . Peirce’s 5.525
outlines the definition of the External Object - [ see also 8.314] which is NOT
the same as the Dynamic Object or Immediate Object - and the Ding an sich. [
which is a non-object!] The three {EO, DO, IO} are all different and refer, I
think, to the diverse nature of semiosic functions of interaction and
interpretation [ which means sign-production] related to matter and mind in the
Phaneron.
As for mathematics - there’s a recommended book ‘ Philosophy of Mathematics:
Selected Writings by C.S.Peirce. Matthew Moore. Ed. Indiana U Press…which
apparently has notes and commentary.
Edwina
> On Aug 20, 2025, at 7:24 PM, Jack Cody <[email protected]> wrote:
>
> Hi Jon,
>
> That publication is a placeholder. It has absolutely zero value beyond the
> general concept — thus you can see how messy it is but the kernel compoments
> exist there. I.e., if it is cited in twenty years, I can demonstrate proof of
> concept (though I have internal publishings which can do that also).
>
> I would direct your attention to Tarski's general threoem and then ask you to
> study Godel's and try to understand, within that context, why Peirce's 5.525
> is highly relevant. It can be understood far more broadly than even Tarski
> understands and there are problems with Tarski's own logic (in terms of
> realizing the full solution). He doesn't understand the "meta" aspect even as
> he invokes it, for instance. I will be more than clear, anyway, about all
> these things in due time.
>
> Briefly? All representational systems, and all possible, as I can eventually
> show, are incomplete (no matter how one wishes to define it or describe it —
> as Tarski or Godel, wisely of course, set minimal limits — but then miss
> entirely, though Tarski comes closer, to the general fact that all
> representational systems are incomplete).
>
> By the time I'm ready to respond to you, it will be very clear with much more
> minimal assumptions and so forth. I have no idea how you came across that
> (google?) because it's not something I put out there for any reason other
> than to "placehold". Like registering a website name I want to use ten years
> down line if you catch my drift. I wouldn't cite it in that formal
> presentation ever — genuinely. The only work it does is link some key
> concepts which within the context of an actual long-essay makes more than
> perfect sense.
>
> Yes, I appreciate your thoughts on Peirce. I think we've been over that. More
> on me than you to re-contextualize that and see where it goes. I don't
> disregard your opinions/thoughts — in fact, they work well as that
> against/with which I myself formalize certain responses. But readiness is not
> there.
>
>
> https://zenodo.org/records/14777823
>
> That's the only other use I ever made of that website. Again, a place-holder
> (not a final product). But not even relevant to this discussion — I just post
> it here so you might understand that "proof" (if I even used that term — I
> cannot recall) is used loosely in that publication. It's an archetypal
> logical outline which, there, is ironcially very much incomplete. Not to be
> really taken as anything other than the placeholder it is. I suppose the
> original post to this thread is similar.
>
> By the time the full-length essay is done I'm certain you'll understand what
> I mean when I link 5.525 directly to incompleteness theorems (though if you
> play around with the internal logic and look more to Tarski than Godel — his
> logical statements — you might understand some of it already).
>
> Best,
> Jack
> From: [email protected] <[email protected]> on behalf
> of Jon Alan Schmidt <[email protected]>
> Sent: Wednesday, August 20, 2025 10:56 PM
> To: Peirce-L <[email protected]>
> Subject: Re: [PEIRCE-L] Peirce and Incompleteness -- Why the Parsimony of
> "Credit"?
>
> Jack, List:
>
> What is your exact definition of "incompleteness" in this context? In the
> linked paper, Tarksi defines the decision problem as "whether there exists a
> mechanical means of deciding whether any given statement of a formal system
> is a theorem," and (more precisely) "whether the set of provable statements
> of a formal system is general recursive" (p. 24). He also states that "by
> completeness we mean simply that, given any formula [without free variables],
> either that formula or its negation is a theorem" (ibid.). He goes on to say,
> as quoted below, that the result "is negative ... for the general case of the
> predicate calculus" (p. 25), i.e., the predicate calculus is incomplete in
> the defined sense. As I understand it, Gödel's incompleteness theorem
> demonstrates that number theory is likewise incomplete in this sense.
>
> I still do not see what these decidability results for sufficiently powerful
> formal systems have to do with the general logical principle stated by Peirce
> in CP 5.525--every proposition has a subject that must be indicated or found,
> because it cannot be described in words. This corresponds to the line of
> identity in the Beta part of Existential Graphs, which implements a version
> of the predicate calculus without free variables, as well as the indefinite
> pronoun "something" in ordinary English. Can you make the alleged connection
> explicit for me? I just came across the "proof" that you recently published
> on Zenodo (https://zenodo.org/records/16681952), which purports to
> demonstrate that for every symbolic system, there is some truth-value or
> independently existing object that it cannot express. However, Peirce's whole
> point is that symbols alone are indeed insufficient for formulating
> propositions--indices are also required.
>
> Again, nobody is disputing that one individual person's actual representation
> of something is never identical to another individual person'sactual
> representation of the same thing--a sign token always produces at least
> slightly different dynamical interpretants in different interpreters, because
> their minds have been determined by different previous signs, such that they
> have different habits of interpretation. The question is whether it would be
> possible, as an ideal limit in the infinite future, for an infinite community
> to have identical representations of everything realafter infinite
> investigation and thus infinite experience--the final interpretant of every
> sign. Peirce, of course, says yes--not as a demonstrable fact, but as a
> methodological principle and regulative hope of inquiry.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt
> <http://www.linkedin.com/in/JonAlanSchmidt> / twitter.com/JonAlanSchmidt
> <http://twitter.com/JonAlanSchmidt>
> On Wed, Aug 20, 2025 at 3:58 AM Jack Cody <[email protected]
> <mailto:[email protected]>> wrote:
> On a more "fun" tangent, I have been experimenting with classical semiotic
> ideas of experience and representation which no doubt can be read in
> semeiotic qua object/interpretant/determination and so forth (in
> classification). I've used the famous sequence in The Good, The Bad, and The
> Ugly to make the point:
> P(O)P Truth Table — Tuco (T), Blondie (B), Angel Eyes (AE)
>
> | Subject | Object | Prime (representation) | Non-identity to base |
> Cross-prime inequality |
> |---------|--------|-------------------------------|----------------------|--------------------------------|
> | T | B | B' (Blondie-as-to-Tuco) | B' != B |
> B' != B'' |
> | T | AE | AE' (AngelEyes-as-to-Tuco) | AE' != AE |
> AE' != AE'' |
> | B | T | T' (Tuco-as-to-Blondie) | T' != T |
> T' != T'' |
> | B | AE | AE'' (AngelEyes-as-to-Blondie)| AE'' != AE |
> AE'' != AE' |
> | AE | T | T'' (Tuco-as-to-AngelEyes) | T'' != T |
> T'' != T' |
> | AE | B | B'' (Blondie-as-to-AngelEyes)| B'' != B |
> B'' != B' |
>
> Minimal consequences (also copy/pasteable):
>
> Incompleteness (prime != base):
> T' != T, T'' != T, B' != B, B'' != B, AE' != AE, AE'' != AE
>
> Unique experience (cross-prime, same base):
> T' != T'', B' != B'', AE' != AE''
> The table illustrates a core concept in social cognition and philosophy of
> mind: an individual is not a single, fixed object but is constituted
> differently in relation to others. Each person (the subject) has their own
> unique representation (or model) of another person (the object).
> Subject: The person who is doing the perceiving.
> Object: The person who is being perceived.
> Prime (representation): This is the Subject's internal representation or
> mental model of the Object. The prime symbol ( ′ ) denotes that this is a
> version for or as seen by the Subject.
> B′ is "Blondie as seen by Tuco."
> T′′ is "Tuco as seen by Angel Eyes."
> Non-identity to base: This column states a fundamental rule: a person's
> representation of another (Prime) is never identical to that other person's
> base identity or their representation of themselves. B′ ≠ B means "Tuco's
> version of Blondie is not the same as Blondie's version of himself (or
> Blondie's 'true' self, if such a thing exists)."
> Cross-prime (same object, different subject): This column states another
> fundamental rule: two different subjects will have different representations
> of the same object. Tuco's version of Angel Eyes (AE′) is not the same as
> Blondie's version of Angel Eyes (AE′′).
> Summary of the Relations Shown:
> Tuco's View:
> He sees Blondie as B′.
> He sees Angel Eyes as AE′.
> Blondie's View:
> He sees Tuco as T′ (which is different from Tuco's view of himself and Angel
> Eyes' view of Tuco).
> He sees Angel Eyes as AE′′ (which is different from Angel Eyes' view of
> himself and Tuco's view of him).
> Angel Eyes' View:
> He sees Tuco as T′′.
> He sees Blondie as B′′.
> Note, three base (person(s)) generate six necessary primes and no person's
> primes (two unique for each one) can be the same as anyone else's without
> contradicting identity principles.
>
> A fun way to explore semeiotics whilst illustrating certain points which can
> be understood variously.
>
> The most important part to me, here, is that there are necessarily six prime
> "people" (as far as I can tell) from three base person(s). As each person
> "sees/experiences" two others, distinct, the mathematics is not difficult.
> The larger question is what that means in more general terms. It goes
> directly to relativity in prime representation as far as I can tell but the
> base does not seem relative to me at all. Need more explication but more a
> fun way of asking quesitons than a strict thesis.
>
> Best
> Jack
>
> From: Jack Cody
> Sent: Tuesday, August 19, 2025 8:09 AM
> To: Peirce-L <[email protected] <mailto:[email protected]>>
> Subject: Peirce and Incompleteness -- Why the Parsimony of "Credit"?
>
> Dear List,
>
> I have been studiously preparing an on-list reply to a post made by JAS a
> week or more ago. I would like to say, in advance, that I find it incredibly
> interesting that Peirce is basically writing about incompletness
> (Godel/Tarski) 50 years (1881) before Godel (1931?) renders his famous
> theorems. Now Peirce's findings are proto-incompleteness but maximal within
> that discovery period.
>
> There are a few things to note: one, Peirce establishes the truth-table
> system and also the logic of number (article) which massively influences not
> merely Tarski/Godel (more Tarski first hand and Godel second), but also Peano
> et al in their work regarding the very system Godel will later use. Tarski,
> at an address to Stanford in 1947 (where Godel and many other famous
> logicians are present) cites Peirce's work directly (he wasn't sure if it was
> Peirce or Frege — each had done something of note here but in this instance
> it was indeed Peirce whom he meant. Peirce is aware, too, of all those in
> the area of truth-tables or what would now be called "PA" and you can find
> citations to all the canonical figures within Peirce's writings (from the
> 19th through very early 20th centuries).
>
> Why is this interesting? Park the ding-an-sich for a minute. We do not all
> agree. That's the subject of my larger thesis. However, before I even arrive
> at that I have two more minor theses. One, a far more rigourously formatted
> understanding of the above which gives Peirce his credit which I believe has
> been seriously neglected over the years. I mean, I search Google Scholar and
> so forth and there are some articles which are interesting but nowhere is
> 5.525 ("It has been shown [3.417ff] that in the formal analysis of a
> proposition, after all that words can convey has been thrown into the
> predicate, there remains a subject that is indescribable...") cited as a
> necessary example of proto-incompleteness.
> That statement, logically, foreshadows so much in the semantic of Godel and
> Tarski (and this before even citing Peirces schematic work on truth-tables
> and also a kind of proto Peano Arithematic) .
> I find it odd, basically, that of all the scholarship done on Peirce no one,
> it seems, has made the obvious connection. If you take that section of 5.525
> and read Peirce's mathematical work as cited by Tarski
>
> "Now let us examine the decision problem in some elementary forms of logic.
> First, the sentential calculus: for this there is the positive result based
> on the two-valued truth-table method. I do not know who actually is the
> author of this procedure - whether it was Frege or Peirce - but what is
> important is that we do have this now classical result.20 For the monadic
> functional calculus it is well known that the result is positive.21 It is
> negative, however, for the general case of the predicate calculus."
> https://www.jstor.org/stable/421074
> it is very difficult not to understand the work Peirce was doing as essential
> to incompleteness (what it would come to be called in the next century). (I
> park the ding-an-sich to one side because there is an area, here, where
> surely there is List agreement — there are two kinds of incompleteness, to me
> at least, who has studied almost nothing but for years now: maximal and
> minimal). Peirce is maximal in his logic ("after all that words can convey
> have been thrown into [predicates of subjects] there remains [subjects which
> are indescribable and thus we have "incompleteness"]. 5.525.
>
> I have changed that wording, clearly, but it's not problematic to the overall
> logical analysis. If one runs with Tarski and Godel here, one sees
> immediately that you cannot derive, easily, anything other than
> incompleteness (protean) from that which Peirce is speaking about.
>
> Anyway, this is overly long already but I wanted to throw it open for others
> to consider as many diverse backgrounds exist here in interdisciplinary
> fields. I'm just genuinely amazed, ding-an-sich or no (a different day...),
> that such little work has been done here in terms of threading the needly
> to/through Peirce and those exponents of incompleteness theorems.
>
> Best,
> Jack
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