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 *mis*understand 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 / twitter.com/JonAlanSchmidt On Mon, Sep 1, 2025 at 10:13 PM Jack Cody <[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]> 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]> wrote: > On Sep 1, 2025, at 11:41 AM, Jon Alan Schmidt <[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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