Jon, Jerry, Mike, list
JAS:You requested one example of a true proposition which represents things as
they really are. That very sentence of mine is one example of a true
proposition which represents things as they really are--you really made that
specific request. Other obvious examples include "the grass in my yard is
(mostly) green today" and "Charles Sanders Peirce died in 1914." Again, every
true proposition represents things as they really are--that is the very
definition of a true proposition. Why did you think that complying with your
request would be at all difficult, let alone "close to impossible"? As I said
before, most of our beliefs can be expressed as true propositions, because
otherwise our corresponding habits of conduct would be constantly confounded by
experience.
I asked because 5.525 demonstrates that when words migrate to predicates and
all which can be "said" of a subject is said there remains a subject, the truth
of which, cannot be what has been said of it — the subject is not what is given
in the proposition (and that's why the structural incompleteness is highly
relevant, especially if we're discussing 5.525 where such is organically
derived).
Accordingly, I find your two propositions confuse agreement on facts with truth
of the subject as it really is. Saying “Peirce died in 1914” or “the grass is
green today” is certainly valid within our practices: these statements fit
records, habits of use, and expectations. But that is not the same as
representing the subject as it really is — you are not giving the truth of
either subject — and that is what I expect cannot be done (in propositions),
following Peirce's own logic, carefully explicated, in 5.525. The bar for that
claim (this is the truth of the subject: as it "really" is) is much higher and
thus why I cannot think of a propostion which meets that truth-standard.
Why? Because what is predicated is always partial and conventional. “Green” is
one, categorically linguistic, aspect of grass, but even ignoring the
categorical linguistic (I mean categorial error/conflation...), such as it is
ignores infinitely many other aspects of what "grass" is or would be. And, even
then, qua 5.525, there would remain whatever "grass" is which could not be the
finite nor infinite descriptions/definitions of such (minimally in
propositions).
Peirce “died in 1914” is likewise: may be said to capture a historical record
about Peirce, but it is not the truth of Peirce (as subject). Only God knows
how you could go about that in a written/spoken record. Yet equivocation with
selective, functionally adequate propositions with the subject’s reality is a
categorical error. They tell us something about the subject, but they are never
identical with what the subject really is. This is obvious.
Thus, while such propositions may be “valid-true” in the pragmatic sense (our
habits are not confounded by them), they do not achieve the stronger claim:
representing the subject as it really is (which was the test one had to pass
here). That’s precisely the barrier the model-theoretic result marks out.
Anyway, you have your own distinct framework, Mike has another interesting way
of demonstrating how Peirce would respond to the result Peirce himself
anticipates, and then Jerry has made an interesting set of remarks which I have
to read more closely as I think it's highly interesting in the most technical
respect of what "interesting" conveys. So I'll spend most of the day reading
through other people's comments as I think there's lots there to consider. I
just wanted to point out that you didn't pass the test (but that I do not
understand how you could pass it, so it's not a dig or anything personal
{Peirce's logical conclusion has to be overturned for you to pass it — and it
won't be}).
Best,
Jack
________________________________
From: [email protected] <[email protected]> on behalf of
Jon Alan Schmidt <[email protected]>
Sent: Tuesday, September 2, 2025 7:03 PM
To: Peirce-L <[email protected]>
Subject: Re: [PEIRCE-L] Propositions, Truth, and Experience (was Will and
Belief)
Jerry, Jack, List:
JAS: Every proposition has at least one subject that cannot be represented
symbolically, but this does not entail that it is structurally incapable of
denoting it--only that it must do so indexically instead.
JLRC: Oh dear me, I have a symbol that can not be symbolized! Is this a variant
on the Russell paradox?
No, it is simply the logical principle that every proposition as a symbol must
involve an indexical part to denote at least one of its subjects. As Peirce
explains, "A proposition is a symbol which separately INDICATES its object, and
the representation in the proposition of that object is called the subject of
the proposition. Now to INDICATE is to represent in the manner in which an
index represents. ... Thus the subject of a proposition if not an index is a
precept prescribing the conditions under which an index is to be had" (EP
2:168, 1903). This is another way of saying that "after all that words can
convey has been thrown into the predicate, there remains a subject that is
indescribable and that can only be pointed at or otherwise indicated, unless a
way, of finding what is referred to, be prescribed" (CP 5.525, c. 1905).
JRKC: That of course is not correct. You have to ignore the mathematical paper
to come to such conclusions. It's a misunderstanding, entirely.
What I said is quite correct, and fully consistent with the actual point that
Peirce was making in CP 5.525. On the other hand, the mathematical paper is
about undecidability within formal systems, which is a different topic
altogether, irrelevant to this thread. The misunderstanding is entirely on your
part, and I recommend carefully reading EP 2:168 (the whole page) if you are
interested in correcting it.
JRKC: As I understand you above, you conflate predication, indication, and
subject. But predication is already a syllogistic indication in Peirce’s own
sense: (1) words migrate to (2) predicates, which (3) indicate subjects. That
is Peirce’s schema for how propositions work.
Like I said, you misunderstand me, as well as Peirce. Predicates do not
indicate subjects, they describe subjects. Words are symbols that in most cases
signify general concepts, although in ordinary language, some serve as indices
that denote individual objects (e.g., pronouns and proper names) or as precepts
for finding such indices (e.g., quantifiers). Predication is the attribution of
general concepts to individual objects by means of iconic syntax that embodies
their logical relations. That is Peirce's schema for how propositions work, and
it translates directly to his diagrammatic design of Beta EG--predication is
the attachment (icons of relations) of words (symbols of concepts) to lines of
identity (indices of individuals).
JRKC: I would ask only that you present one example of a true proposition which
represents things as they really are.
You requested one example of a true proposition which represents things as they
really are. That very sentence of mine is one example of a true proposition
which represents things as they really are--you really made that specific
request. Other obvious examples include "the grass in my yard is (mostly) green
today" and "Charles Sanders Peirce died in 1914." Again, every true proposition
represents things as they really are--that is the very definition of a true
proposition. Why did you think that complying with your request would be at all
difficult, let alone "close to impossible"? As I said before, most of our
beliefs can be expressed as true propositions, because otherwise our
corresponding habits of conduct would be constantly confounded by experience.
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 Mon, Sep 1, 2025 at 10:13 PM Jack Cody
<[email protected]<mailto:[email protected]>> wrote:
Jon, List,
Second post (this is next day for me — last night, now this morning — just for
posting restrictions but it's my post for the second subsequent to my post for
the first — of September). It's worth noting because the moderation is explicit
but is US-based so timezones are often not taken into account or forgotten
(which is OK). Anyway, it's a very short post for the day.
You write (objecting to me) that "every true proposition represents things as
they really are".
I would ask only that you present one example of a true proposition which
represents things as they really are. I think that close to an impossible task
given the way you use "really" (sometimes regardless of whatever people
experience or think at all). Even without your usage, correct or incorrect (in
terms of consistency, not in terms of citation as such), I think it close to
impossible. I cannot think of one.
Now "every true proposition represents things as they really are" leaves
Peircean metaphysical (or meta-language) wiggle room where you might insert
infinite inquiry again or defer to the real and so you have a principle but no
proof of it, as such, except the self-referential tautological statement (if
that's what you mean?).
I might be pre-empting you, here, in which case I apologize, but I'd merely ask
for one exmaple of a true proposition where things, as they really are, are
incontestably represented precisely as they are without deference to metaphyics
or technicalities (if it's true, then it must be so... — as an example of
self-referential tautology without an example required!) — again, I'm trying to
avoid that kind of thing in advance if you are able to reply. If not, it's
fine. It's not an easy task but I am trying to understand whether you think you
have any concrete propositions which are true and function as you say or are
rather saying that such must be the case because of possibility or some other
reason without concrete example.
Best wishes,
Jack
On Mon, Sep 1, 2025 at 5:48 PM Jack Cody
<[email protected]<mailto:[email protected]>> wrote:
Jon, List,
JAS:This is exactly the opposite of what Peirce demonstrates in CP 5.525 and
elsewhere. Anything that exists--in the metaphysical sense, as well as in the
logical sense of belonging to a universe of discourse--is capable of being the
subject of a proposition. Every proposition has at least one subject that
cannot be represented symbolically, but this does not entail that it is
structurally incapable of denoting it--only that it must do so indexically
instead.
That of course is not correct. You have to ignore the mathematical paper to
come to such conclusions. It's a misunderstanding, entirely.
As I understand you above, you conflate predication, indication, and subject.
But predication is already a syllogistic indication in Peirce’s own sense: (1)
words migrate to (2) predicates, which (3) indicate subjects. That is Peirce’s
schema for how propositions work. When this is carried out exhaustively, Peirce
himself acknowledges (CP 5.525) that there remains a subject that cannot be
described in words. That meta-proposition — and it is one, insofar as Peirce
holds it universally — is already a statement about the structure of all
propositions. In other words: the system is already indexical. There is no need
to “retreat to indexicality” as if it were a new solution; indexicality is the
condition Peirce presupposes in the very operation of predication. The point of
the paper is precisely that, once you formalize this structure in terms of
L-definability (Bridge Principle B1), you can show by Compactness and
Löwenheim–Skolem (Lemmas 2–3) that the residual subject — the one “indicated”
but never symbolically captured — cannot be decided within any sound,
recursively axiomatized, L-conservative theory. Thus indexicality fails in
5.525 qua predication itself: it does not solve the problem; it is the site of
the problem. That is why the “retreat” in your reply misfires — it reintroduces
at the meta-level what was already conceded at the object level, and the formal
result shows exactly why that concession entails undecidability.
This portion of your reply is, at best, tautological. There are also several
other problems I have noted, but given how much attention is required even for
a single point (as the above shows), I think the most productive way forward is
a step-by-step exchange. Taking your response point by point, over the course
of several posts, and days, would keep things clear, concise, and grounded in
the logical paper I wrote for such exchanges, which provides a decent reference
guide for the issue at hand. It would also open the door for others to
intervene with their own perspectives, rather than this turning into a wall of
me quoting you and then refuting, followed by you quoting me and doing the
same. That seems the better structure for a useful exchange.
Best,
Jack
On Mon, Sep 1, 2025 at 2:13 PM Jerry LR Chandler
<[email protected]<mailto:[email protected]>> wrote:
On Sep 1, 2025, at 11:41 AM, Jon Alan Schmidt
<[email protected]<mailto:[email protected]>> wrote:
Every proposition has at least one subject that cannot be represented
symbolically, but this does not entail that it is structurally incapable of
denoting it--only that it must do so indexically instead.
Oh dear me, I have a symbol that can not be symbolized!
Is this a variant on the Russell paradox?
Cheers
Jerry
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