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 / 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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