Jon, Gary, List, Jon, there's a good bit there. Yes, predication is indexical-symbolic (has to be). Consider that example of a true proposition which you gave to me — "you really did ask for that" (a proposition which is almost entirely indexical: that is, you indexed my previous statement, as per recursion/embedding, as if to point to it (through obvious use of deictic signifiers qua predication).
Your proposition doesn't meet the criteria I stipulated for a "true proposition" wherein the subject proposed/represented would be precisely, within the propositional structure, what said subject, if extant, in any respect, is beyond that structure. I.e., it is not a test that can be passed —it refers to the ontic reality rather than the agreed-upon meaning such as "grass is green" —yes, I can understand you, and it will not "confound experience", but such is not the truth of "grass" or "green". The threshold for the "test" is set by an interpretation, valid, my analysis shows, of Peirce's own conclusion in 5.525. At any rate, your position was later clarified as facts of the propositional kind, though you note the same or similar nuance, though differently, as being the only kind of truth there is (or at least the only kind within that category). We don't agree there but that clearly demarcates why you think you've passed and why I disagree. We are arguing at two different categorical levels — which is fine. Anyway, leaving the above aside, for I am working on it within a new (more nuanced) proof-structure (with more Peircean references), I'd like to share the below abstract with respect to LLM/AI: Abstract: Charles S. Peirce was interested on logical machines developed in the late 19th century and discussed whether they could develop the authentic semiotic processes indispensable for deductive reasoning. Is it possible for machines to have a genuine capacity to carry out inferences? In this paper, Peirce's arguments are analyzed, who argued that deduction, in general, cannot be reduced to mechanical factors. To this end, reference will be made to the idea of theorematic reasoning, which is fundamental for mathematical proofs and goes beyond mechanical procedures. The idea of semiosis in Peirce will also be explored, which seems to extend to the organic realm, but not to the artificial inorganic world of machines. Finally, some conclusions will be drawn about Artificial Intelligence from Peirce’s semiotic perspective. https://www.academia.edu/oa/4403458984 Artificial Intelligence Through Peirce's Lens In short, I agree. That which is functional artifice, algorithmic/transform, is not intelligence. Nor do I think it ever will be. Not merely for the reasons you cite but for kinds of reasons and the Peircean lens offers but a few. Best, Jack Academia.edu | Log In<https://www.academia.edu/oa/4403458984> Academia.edu is the platform to share, find, and explore 50 Million research papers. Join us to accelerate your research needs & academic interests. www.academia.edu ________________________________ From: [email protected] <[email protected]> on behalf of Jon Alan Schmidt <[email protected]> Sent: Saturday, September 6, 2025 3:17 PM To: Peirce-L <[email protected]> Subject: Re: [PEIRCE-L] Propositions, Truth, and Experience (was Will and Belief) Gary F., Jack, List: I agree with Gary F. that his linked excerpt from Turning Signs is quite pertinent to the thread discussion. As he says there, "the element of 2ns or surdity must be involved in any honest attempt to understand, speak or hear the truth," such that "dicible facts, no matter how well known, always carry a residue of unspeakable or inexplicable surdity." That is why every proposition involves at least one index or precept for finding an index to denote its dynamical object, not just words describing that object. "But an index is a representamen which is such by virtue of standing in a genuine reaction with its object ... Consequently, though the subject need not be individual, the object to which the subject of a proposition applies must be the object of a possible index and as such it must be such as it is independently of any representamen or other Third. That is to say it must be real" (EP 2:168, 1903). This gets at one reason why I maintain that "artificial intelligence" is a misnomer for large language models (LLMs). One of Peirce's definitions of "logic as semiotic" is the science that ascertains "what must be the characters of all signs used by a 'scientific' intelligence, that is to say, by an intelligence capable of learning by experience" (CP 2.227, c. 1897). LLMs do not qualify because they do not have that capability--they have no beliefs with corresponding habits of conduct that can be corroborated or confounded by the "outward clash" with reality itself. Just like formal systems of deductive logic, LLMs cannot establish truth, only preserve it once they have been "trained" by being fed a vast quantity of information; the principle of "garbage in, garbage out" still applies. LLMs cannot even verify the truth of any given sentence apart from comparing it with other sentences, so it is no wonder that they sometimes suffer from "hallucinations" that produce false or misleading responses to prompts. As for Jack's reply, I have already said above and throughout this thread that every proposition must include at least one index (or precept) as its subject that denotes its object; and unless it merely affirms the existence of that object, it also must include at least one symbol in its predicate that signifies its interpretant. In that sense, I obviously agree that predication is both indexical and symbolic, and I will add (again) that it is also iconic by virtue of a proposition's syntax that embodies the logical relations between the individual objects that it indicates and the general concepts that it attributes to them. However, as I pointed out a few weeks ago when I took exception to Michael Silverstein's discussion of "indexical meaning," an index by itself has no meaning at all--it predicates nothing, because it conveys no information about its object. On the other hand, I agree that recognizing the context of a proposition is essential for properly understanding it, and so does Peirce. "Every proposition whatever has the Universe of Discourse for one of its subjects and all propositions have one Subject in common which we call the Truth" (EP 2:173, 1903). "No object can be denoted unless it be put into relation to the object of the commens," which "consists of all that is, and must be, well understood between utterer and interpreter, at the outset, in order that the sign in question should fulfill its function" (SS 197, EP 2:478, 1906 Mar 9). Is it a true proposition that Hamlet was the Prince of Denmark? If the universe of discourse is the actual world, then no; but if it is the imagined world of Shakespeare's play, then yes--it is a real fact that Hamlet was the Prince of Denmark in that fictional world. 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 Fri, Sep 5, 2025 at 2:40 PM Jack Cody <[email protected]<mailto:[email protected]>> wrote: Gary, List, A quick note synthesizing why predication in propositions is inherently indexical — and, in Peirce’s vocabulary, at least minimally indexical–symbolic. * Model-theoretic core (Tarski; Hodges): Predication P(x) is only truth-evaluable relative to an interpretation/model M and a variable assignment s. An open formula is satisfied by a sequence only relative to M and s; a sentence is true in M if satisfied by all sequences in M. Without the index (M, s), predication lacks a determinate extension. See Tarski, The Concept of Truth in Formalized Languages (1935/1956); On the Concept of Logical Consequence (1936). For a modern treatment, see Hodges, Model Theory (1993). * Context and domain restriction (Stanley & Szabó; Bach; von Fintel): Ordinary predicates tacitly depend on a contextually supplied domain/standard/comparison class. The extension of tall, local quantifiers, and many gradable predicates is fixed only after a contextually restricted domain is provided. See Stanley & Szabó, On Quantifier Domain Restriction (1999); Bach, The Myth of Semantic Representations (2001); von Fintel, Restrictions on Quantifier Domains (1994 ms). * Indexicals and parameters (Kaplan; Lewis; Montague; Kratzer): Even non-overtly indexical predicates are evaluated relative to indices: worlds, times, speakers, standards. Kaplan (Demonstratives, 1989) makes explicit the role of contexts and characters; Lewis (Index, Context, and Content, 1980) formalizes multi-dimensional indices; Montague Universal Grammar (1970) and Kratzer’s modal/conditionals work show world–time (and more) parameters as constitutive of predicate interpretation. * Information states and dynamics (Heim; Kamp): Predication updates an anaphorically and situationally constrained information state; felicity and truth conditions are state-indexed. See Heim, The Semantics of Definite and Indefinite Noun Phrases (1982); Kamp & Reyle, From Discourse to Logic (1993). * Proof-theoretic and type-theoretic context (Martin-Löf; Dummett): Judgments (and so predicate application-as-typing) are meaningful only in a context Γ. The well-formedness and applicability of A(x) are Γ-indexed. See Martin-Löf, Intuitionistic Type Theory (1984); Dummett, The Logical Basis of Metaphysics (1991). * Categorical/topos-theoretic truth (Lawvere; Mac Lane & Moerdijk): Predicates are arrows into Ω in a given topos, often evaluated at “stages.” Truth and subobject classifiers are internal to, and hence indexed by, the ambient categorical structure. See Lawvere, ETCS (1964) and hyperdoctrines (1969); Mac Lane & Moerdijk, Sheaves in Geometry and Logic (1992). * Structuralism in mathematics (Benacerraf; Shapiro; Resnik): Properties are defined relative to structures; predication is structure-indexed rather than absolute set-membership. See Benacerraf, What Numbers Could Not Be (1965); Shapiro, Philosophy of Mathematics: Structure and Ontology (1997); Resnik, Mathematics as a Science of Patterns (1997). Putting this together: across semantics, logic, and foundations, predication’s extension is fixed only relative to indices — models and assignments, worlds/times, domains/standards, discourse states, proof contexts, categorical stages, or mathematical structures. That is precisely what “indexicality” amounts to. In Peirce’s terms, because the symbol’s interpretant and object are fixed via such context-anchoring parameters, predication is at least minimally indexical–symbolic: symbolic in its rule-governed form, but irreducibly indexed to a context that determines its application. Cited from Julius because apparently the burden of proof is on the one who claims what is logically necessary (that predication is minimally indexical-symbolic). Anyway, to suggest that predication is not "indexical" (it's not really relevant how much you want to quote Peirce, here, because the logical function of predicates demands it — as can be seen above — is a tiny irritation but one I want to resolve with this post). I consider it resolved - regardless of replies (that is, I know that such has to be secondness in thirdness? — indexical-symbolic, or some-such hybrid, which is only to say that it functions indexically). Plenty agree and those who do, are, as far as I can tell, entirely correct. Best Jack ________________________________ From: [email protected]<mailto:[email protected]> <[email protected]<mailto:[email protected]>> on behalf of [email protected]<mailto:[email protected]> <[email protected]<mailto:[email protected]>> Sent: Friday, September 5, 2025 4:00 PM To: [email protected]<mailto:[email protected]> <[email protected]<mailto:[email protected]>> Subject: RE: [PEIRCE-L] Propositions, Truth, and Experience (was Will and Belief) Perhaps I should apologize for the link I am about to post here, since it may be interpreted by some as a comment on the dialogue between the two main participants in this thread. It was written several years ago, so it is definitely not a response to what has been said in this thread. It does, however, throw some light on the relationship between reality and language, which I take to be an underlying subject of it. https://gnusystems.ca/TS/snc.htm#srd Love, gary Coming from the ancestral lands of the Anishinaabeg } What's good for the gorse is a goad for the garden. [Finnegans Wake, 450] { substack.com/@gnox<https://substack.com/@gnox> }{ Turning Signs<https://gnusystems.ca/TS/>
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