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
------------------------------------------------------------------------
*From:* [email protected] <[email protected]> on
behalf of Jon Alan Schmidt <[email protected]>
*Sent:* Monday, September 1, 2025 5:41 PM
*To:* Peirce-L <[email protected]>
*Subject:* Re: [PEIRCE-L] Propositions, Truth, and Experience (was
Will and Belief)
Jack, List:
JKRC: The point I am pressing is that all propositions (as Peirce
had shown, and as I subsequently confirmed through mathematical
rigor at the meta-propositional level) necessarily have subjects
which propositions, structurally, can never account for as such
subjects exist, insofar as they exist at all.
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.
JKRC: The simplest way of putting this is that things or subjects
do exist--in themselves, or by-themselves-as-such, whatever the
habitual or conjunctive human relation--but they cannot be known
by finite or infinite inquiry.
It is impossible to /know/ that something exists that cannot be known
by /infinite /inquiry. Moreover, it violates the will to learn and the
first rule of reason to /believe /that something exists that cannot be
known by infinite inquiry. Maintaining that there is such an
incognizable thing-in-itself eventually becomes an excuse to stop
inquiring, while denying it corresponds to the habit of /always
/inquiring further.
JKRC: One might have a trillion lines in a database about a single
object and still not know what it is, as it is.
A trillion is a very large number, but it is infinitely smaller than
an infinite number. As I keep emphasizing, this is not about /actual
/knowledge, but /ideal /knowledge--what an infinite community /would
/know after infinite investigation, and thus infinite experience. It
is a methodological principle and a regulative hope, not an
epistemological or ontological dogma, that nothing real would be
excluded in that scenario.
JRKC: All experience of possible things is indeed experience of
things, but such experience is not what things are.
No one disputes this, and it is irrelevant anyway. The experience
/itself / is not what things are, but it conveys /knowledge of/ what
things are. The resulting cognition is obviously not the object
/itself/, but it is a /representation of /the object.
JRKC: My conclusion is that Peirce had something with 5.525--the
logical meta-propositional constant--but he misapplied it when
deploying it against the thing-in-itself.
On the contrary, the very reason why he stated the logical principle
in CP 5.525 that we have been discussing here was to serve as a
premiss of a simple deductive argumentation /demonstrating /that an
incognizable thing-in-itself does not exist, which I spelled out a few
weeks ago
(https://list.iu.edu/sympa/arc/peirce-l/2025-08/msg00035.html). I also
explained its meaningless in accordance with pragmaticism in my
Saturday post--there are no corresponding habits of conduct that make
any difference whatsoever in anyone's experience.
JRKC: It shows the impossibility of ever representing any subject,
not only in propositions but in the most formal sense, as such
subjects are.
This is obviously false--every /true /proposition represents things as
they /really /are. Specifically, a true proposition accurately conveys
that certain /real/ individual things (denoted by indexical signs)
conform to certain /real/ general concepts (signified by symbolic
names) in accordance with certain /real/ logical relations (embodied
by iconic syntax). I wonder again if nominalism is the underlying
obstacle here--it only affirms the reality of the individual thing,
not the general concepts nor the logical relations.
JRKC: I would like to have more from him in terms of what he was
thinking when he used that material in that way, because it's an
instance of genius, and then nonsense (by his own standards).
I will stick with recognizing that Peirce intended exactly what he
said throughout CP 5.525 vs. ascribing genius and nonsense to him in
the very same paragraph. Anyone who wants "more from him in terms of
what he was thinking when he used that material in that way" can read
his many other texts where he just as explicitly affirms the necessity
of indices in propositions to denote their subjects, and his many
other texts where he just as explicitly denies the reality of an
incognizable thing-in-itself. The mistake is thinking that these
positions are somehow inconsistent with each other.
JRKC: With the ding-an-sich one points to fallibility and a kind
of common sense (this cannot be whatever it is to me--regardless
of whatever such a thing is).
This strikes me as exactly backwards. Fallibilism /rejects /the
incognizable thing-in-itself because it denies that we ever /actually
/reach a point at which there is no more to learn about something.
Common sense /affirms /that at least some of our representations of
things are correct, because otherwise, our corresponding habits of
conduct would /constantly /be confounded by experience. Accepting that
we can never achieve /complete /knowledge of something does not entail
that we /do not/ have genuine knowledge of it /at all/, and also does
not entail that infinite investigation by an infinite community with
infinite experience /would not/ result in complete knowledge of that
thing.
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 Sun, Aug 31, 2025 at 6:35 PM Jack Cody <[email protected]> wrote:
Jon, List,
Jon, I appreciated your long proposition form — or
semantic-statement — of 5.525. It is worth reading carefully and
critically.
The point I am pressing is that all propositions (as Peirce had
shown, and as I subsequently confirmed through mathematical rigor
at the meta-propositional level) necessarily have subjects which
propositions, structurally, can never account for as such subjects
exist, insofar as they exist at all.
What this shows is that one could know a quasi-infinite amount
about a thing through propositions, and yet structural
incompleteness still holds: the subject is never known. If you
replace “subject” with “thing” you are not far from Kant, though
Peirce himself may have preferred to resist that association.
The simplest way of putting this is that things or subjects do
exist — in themselves, or by-themselves-as-such, whatever the
habitual or conjunctive human relation — but they cannot be known
by finite or infinite inquiry. This is what the broader
incompleteness demonstrates. One might have a trillion lines in a
database about a single object and still not know what it is, as
it is. That is a condition that will never change. It is a
constant, and it holds for all propositions and all possible
representation. No amount of time makes a difference to that
incapacity.
It is therefore a broader incompleteness, ontological rather than
merely mathematical.
The thing-in-itself must exist. All experience of possible things
is indeed experience of things, but such experience is not what
things are. It is human use of things, and this says nothing about
the non-human status of those same things, which also exist both
logically and chronologically.
Peirce’s 5.525 is important, but it demands something his own
logic cannot provide. In fact, it supports the thing-in-itself
more strongly than it undermines it. My conclusion is that Peirce
had something with 5.525 — the logical meta-propositional constant
— but he misapplied it when deploying it against the
thing-in-itself. A Kantian would instead take it as confirmation.
I am not a Kantian, nor a Peircean; I am interested in what is
true in either framework, and I try to carry that forward.
*JAS:* /Also, ‘how people understand the world they live in’ has
no effect whatsoever on ‘what is reality’ because, by definition,
the latter is as it is regardless of how anyone understands./
I would emphasize here that the /ding-an-sich/ is as it is,
regardless of experience or understanding. That is the minimal
price of admission to the principle.
Finally, 5.525 gives us a subject — indeed every possible subject
— which negates “time,”*** since it holds axiomatically as a
mathematical and logical constant. It shows the impossibility of
ever representing any subject, not only in propositions but in the
most formal sense, as such subjects are. This is the constant
tension between existence and human consubstantial experience of
existence, present at the most basic logical level.
*** — Peirce is right in the logical section in 5.525 but it is
not a good proof against Kant, at all. Whatever his arguments
elsewhere, using what amounts to a much more general
incompleteness (which I have been using very much in favour of the
existence of the ding-an-sich) makes no real sense. I would like
to have more from him in terms of what he was thinking when he
used that material in that way, because it's an instance of
genius, and then nonsense (by his own standards). Dogma, rather —
maybe just an incorrect line of argumentation rather than being
too harsh.
When I say negates time, I mean it holds for all possible
propositions and so no infinite inquiry is going to overturn that
— thus, what the principle points to, so to speak, is not
positivist knowledge of things, qua subjects, which cannot be had
at all, really, (as they are in themselves), but a clear
delimitation of that idea. That's the mathematical-logical outcome
(I overdid it and I think you may have, too) of that statement.
Now I know you'll disagree with me — which is fine — but there is
so much contradication as far as I can tell that one has to
account for it. Consider the depth of Peirce's system — and now
consider that truth cannot be defined within systems — does this
give no one pause for thought regarding maximal assumptions? With
the ding-an-sich one points to fallibility and a kind of common
sense (this cannot be whatever it is to me — regardless of
whatever such a thing is). Said to be the Kantian price, yet the
buy-in is basically free. With the "real", I need dynamic objects,
and final interpretants, and so on and on and if these be subjects
of propositions one has to seriously consider their status
(especially as such is second or third order, being
linguistic-categorical).
Just some thoughts.
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