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:
1.
Tuco's View:
*
He sees Blondie as B′.
*
He sees Angel Eyes as AE′.
2.
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).
3.
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]>
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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