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 / twitter.com/JonAlanSchmidt On Fri, Sep 5, 2025 at 2:40 PM Jack Cody <[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] <[email protected]> on > behalf of [email protected] <[email protected]> > *Sent:* Friday, September 5, 2025 4:00 PM > *To:* [email protected] <[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 }{ Turning Signs <https://gnusystems.ca/TS/> >
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