Ingest: The Semantic Conception of Truth and the Foundations of Semantics (Tarski 1944)

Type: types/ingest-report.md

Classification

This is a published paper by the originator of the results, from Philosophy and Phenomenological Research 4 (1944). It has citations and endnotes but no proofs. Part I gives an informal account of the 1933/1935 truth definition. Part II replies to published and spoken objections. Its claims are logical results and the author's positions; it reports no experiments. The capture is the HTML transcription hosted by John Sowa. Andrew Chrucky transcribed it and Sowa made "minor corrections". The snapshot is complete: the table of contents, all 23 sections, notes 1–35, the bibliography and the transcriber's coda are all present (683 lines, about 105k bytes). Author: Alfred Tarski, who founded model-theoretic semantics. On the internal technical points, this paper is the primary authority.

Summary

Tarski asks for a definition of "true" that is materially adequate: it implies every instance of schema (T), "X is true if, and only if, p". It must also be formally correct, which is relative to a language with an exactly specified structure. Section 6 lists what exact specification means: an unambiguous class of meaningful expressions, primitive terms and rules of definition, criteria for which expressions are sentences, and conditions of assertion. It then says the problem "obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified". For "all natural, 'spoken' languages", the problem is "more or less vague" and any solution "approximate". Sections 7–8 break the liar down into three assumptions. (I) The language is semantically closed. (II) "the ordinary laws of logic hold". (III) An empirical premise is used, and (III) can be dispensed with. Tarski keeps classical logic and therefore "decide[s] not to use any language which is semantically closed". On everyday language he explicitly declines to infer inconsistency: "the problem of consistency has no exact meaning with respect to this language". Sections 9–11 introduce the object language and the metalanguage. They show that a definition is possible exactly when the metalanguage is "essentially richer" in its logical part, and they build truth from recursively defined satisfaction. Section 12 and note 18 derive truth ≠ provability and connect the result to Gödel's incompleteness theorem. Part II argues that the conception is neutral between epistemological positions. It concedes that "no universal criterion of truth follows immediately from the definition". It also says theoretical semantics applies to natural languages "only with certain approximation".

Contribution assessment (our opinion)

The problem is central to logic and semantics: how to use "true" consistently, given the semantic antinomies. The underlying results are the 1933/1935 monograph, which this paper cites rather than reproves. This paper's own additions are three. It gives the assumptions behind the liar explicitly. It makes Convention T the stated criterion of adequacy. It replies to objections, separating the definition of truth from any criterion or warrant for asserting truths. That separation is the reason the paper still matters to philosophers. Our background knowledge, not anything in the source, says this exposition became the standard philosophical reference for the theory. Popper's adoption of the theory supports that reading. Later work also shows how far the stated assumptions bind. Kripke's 1975 fixed-point construction and paraconsistent treatments get partial semantic closure by weakening assumption (II) or full disquotation. That confirms Tarski's decomposition is the right place to aim criticism; it does not refute it. The informal claims about natural language are deliberately hedged, and they are weaker than the formal results.

Quotes

The problem of the definition of truth obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified. For other languages — thus, for all natural, "spoken" languages — the meaning of the problem is more or less vague, and its solution can have only an approximate character. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 6

(I) We have implicitly assumed that the language in which the antinomy is constructed contains, in addition to its expressions, also the names of these expressions, as well as semantic terms such as the term "true" referring to sentences of this language; we have also assumed that all sentences which determine the adequate usage of this term can be asserted in the language. A language with these properties will be called "semantically closed." --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8, assumption (I)

(II) We have assumed that in this language the ordinary laws of logic hold. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8, assumption (II)

But the assumptions (I) and (II) prove essential. Since every language which satisfies both of these assumptions is inconsistent, we must reject at least one of them; --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8

It would be superfluous to stress here the consequences of rejecting the assumption (II), that is, of changing our logic (supposing this were possible) even in its more elementary and fundamental parts. We thus consider only the possibility of rejecting the assumption (I). Accordingly, we decide not to use any language which is semantically closed in the sense given. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8, the decision

Our everyday language is certainly not one with an exactly specified structure. We do not know precisely, which expressions are sentences, and we know even to a smaller degree which sentences are to be taken as assertible. Thus the problem of consistency has no exact meaning with respect to this language. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8, everyday language

upon the fact whether the metalanguage in its logical part is "essentially richer" than the object language or not. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 10

For the condition of the "essential richness" of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth; i.e., if the metalanguage satisfies this condition, the notion of truth can be defined in it. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 10, sufficiency

There are certain general conditions under which the structure of a language is regarded as exactly specified. Thus, to specify the structure of a language, we must characterize unambiguously the class of those words and expressions which are to be considered meaningful. In particular, we must indicate all words which we decide to use without defining them, and which are called "undefined (or primitive) terms"; and we must give the so-called rules of definition for introducing new or defined terms. Furthermore, we must set up criteria for distinguishing within the class of expressions those which we call "sentences." Finally, we must formulate the conditions under which a sentence of the language can be asserted. In particular, we must indicate all axioms (or primitive sentences), i.e., those sentences which we decide to assert without proof; and we must give the so-called rules of inference (or rules of proof) by means of which we can deduce new asserted sentences from other sentences which have been previously asserted. Axioms, as well as sentences deduced from them by means of rules of inference, are referred to as "theorems" or "provable sentences." --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 6, specification conditions

We may at best only risk the guess that a language whose structure has been exactly specified and which resembles our everyday language as closely as possible would be inconsistent. --- kb/sources/.snapshots/tarski-semantic-conception-of-truth.md @ sha256:3efc7f9394fa51e3a5e43dcdca1c462e9a3f0d26f26fc99e40412b33bd953a5e — section 8, explicitly hedged conjecture

Connections Found

The source's role in this KB is a limiting primary source for one library appeal, and a classical anchor for codification's view of formal semantics.

The appeal was in Prompting changes failure diagnosis with the semantic reference. That note said a complete executable semantics for natural language "as a whole" is "not attainable even in principle" because of "Tarski/Gödel/halting-style impossibility results". Since rewritten: the note, now titled by the link, no longer contains the impossibility paragraph and states that it needs no impossibility claim about formalizing English. The source bears on that claim directly (is-evidence-for), but mostly to narrow it, as the Extractable Value audit sets out. Traditional software can bracket executor conformance inherits the same "no attainable formal semantics" wording from that note. A revision of the hub note therefore carries over to it.

The source supports Codification in two places (is-evidence-for). First, the definition takes formal semantics as its intuition and holds that the clerk-passing fragment of English is "a programming language in the making". Tarski's approximation procedure is the classical form of that move: replace a natural language "(or a portion of it in which we are interested)" by an exactly specified language that diverges "as little as possible". Second, Tarski allows languages with an exactly specified structure that are not formalized, where assertability may depend on "non-linguistic factors". That precedent fits codification's choice of a criterion weaker than written formal semantics. It also fits the "assigned consequences" axis of Representational form (compares-with, on what makes an artifact's consequences fixed).

Natural-language meaning is coordination among learned approximations is the main rival account (compares-with, on whether natural language has a precise semantics that formalization recovers). Tarski agrees that natural-language semantics can only be approximated. He locates the gap in unspecified structure, though: we do not know which expressions are sentences or which are assertible. He says nothing about learned competence or coordination, so he neither supports nor refutes what the hypothesis adds.

On the source side, the Church–Turing thesis ingest gives the procedural precondition for rigour (exact instructions, no insight). This source gives the semantic precondition, exactly specified structure (compares-with). The Plotkin SOS ingest shows a different way to fix meaning: syntax-directed transition rules rather than truth defined in a richer metalanguage (compares-with). This contrast matters below, because the library appeal moves from truth to execution.

Extractable Value

1. Audit of the four occasion points against the 1944 wording. [quick-win] (1) Exactly specified structure (section 6) means four things: meaningful expressions are characterized unambiguously, primitive terms and rules of definition are listed, criteria for sentencehood are given, and conditions of assertion are given (axioms, rules of inference). "Formalized" is the narrower case where the specification refers "exclusively to the form of the expressions". Exact specification without formalization is only hoped for: "It would be interesting and important actually to construct a language of this type". At the time, "the only languages with a specified structure are the formalized languages". For natural, spoken languages the truth problem is "more or less vague" and its solution "approximate". (2) Semantically closed (section 8) has three components. The language contains names of its own expressions. It contains semantic terms such as "true" that refer to its own sentences. And "all sentences which determine the adequate usage of this term can be asserted in the language", which means every T-instance for its own sentences. Not using closed languages is a decision, taken because the alternative is giving up assumption (II), "changing our logic (supposing this were possible)", which he does not discuss further. He adds that the restriction does not harm science, and that only those who believe in one "genuine" language would find it unacceptable. (3) Universality: the words "universality" and "colloquial" do not occur in this paper. That framing comes from the 1933/1935 monograph and cannot be grounded here. The 1944 counterparts are three. Everyday language "at first blush" seems to meet (I) and (II). It "is certainly not one with an exactly specified structure". And the "one 'genuine' language" remark. (4) Essentially richer metalanguage: the condition is stated in section 10, not section 9. Section 9 sets out the object language and metalanguage and their relativity, a hierarchy of languages. It requires the metalanguage to contain or translate the object language, to name every sentence of it, and to introduce semantic terms "only by definition". Section 10 says "essential richness" (in the logical part) is "not only necessary, but also sufficient". Tarski admits it "is not easy to give a general and precise definition" of it. He gives a precise version only for type-theoretic languages (higher-type variables), and note 16 adds the alternatives of admitting recursive definitions or stronger set existence. Without richness, truth can still be taken as an undefined primitive axiomatized in the metalanguage, and "there is nothing essentially wrong in such an axiomatic procedure".

2. What Tarski does not claim. [quick-win] He does not assert that everyday language is inconsistent. He says the consistency question "has no exact meaning" for it. He offers only a "guess" that an exactly specified language resembling it "as closely as possible would be inconsistent". He nowhere says natural language cannot have a consistent semantics. He says theoretical semantics applies to it "only with certain approximation", which he compares to applying "laws of logic to arguments in everyday life". The antinomy is conditional on two essential assumptions: closure, which includes asserting every T-instance (full disquotation for the language's own sentences), and classical logic, which he holds fixed without arguing that it cannot be changed. The paper never mentions computation, Turing machines or halting. Gödel enters only through truth ≠ provability for "formalized languages of a certain very comprehensive class of mathematical disciplines" (section 12, note 18).

3. What the library appeal can and cannot draw from Tarski (our opinion). [deep-dive] It can draw: (a) under classical logic, no exactly specified language that names its own sentences can assert all T-instances for its own truth predicate; (b) a truth definition for such a language therefore lives in an essentially richer metalanguage, which gives a hierarchy rather than one self-contained semantics; (c) for natural language, Tarski's own position is that only approximation by specified fragments is available; (d) a definition of truth is not a decision procedure ("no universal criterion of truth follows"), and section 19 adds that this "in a certain sense can even be proved". It cannot draw: (a) a theorem about natural language "as a whole". The results apply only to exactly specified languages, and Tarski says the consistency question is not exactly meaningful for everyday language. (b) An "in principle" impossibility that does not depend on assumptions. The result binds only together with classical logic and full disquotation, and the post-1944 literature relaxes exactly those (background knowledge, not from the source). (c) Anything about executable semantics. Tarski's barrier concerns defining truth within the same language. An operational semantics fixes execution, not truth. Self-interpreting programming languages and universal machines run programs of a language rich enough to talk about computation. Halting-style results forbid deciding properties, not executing (our inference). (d) A contrast between natural and programming languages. Undefinability and the lack of a truth criterion hit formalized arithmetic just as much, so they cannot be what separates natural language from programming languages. The defensible core is narrower: a natural language used as its own complete metalanguage cannot also be exactly specified, classical and fully disquotational. In addition, a specified fragment (Tarski's approximation) is what any codification fixes.

4. Definition versus criterion as a reusable distinction. [just-a-reference] Section 18 says the definition "implies nothing regarding the conditions under which" a sentence can be asserted. Section 19 concedes that no universal criterion of truth follows from it. This supports separating semantic definition from a total executable interpretation or decision procedure. It is general logic, not new to the KB, so it is a reference point and not a candidate note.

5. Tarski's rule for ambiguous terms. [just-a-reference] Section 14 recommends making each concept "as clear as possible", using "different terms for different concepts", and accepting a renamed "frue". This matches the KB's one-term-per-concept rule and its vocabulary collision ledger. It is historical precedent only.

Limitations (our opinion)

The paper gives no proofs. Every formal claim, including necessity and sufficiency of essential richness and the reconstruction of the liar without the empirical premise (note 11, which Tarski admits is unclear in "in what sense"), rests on the 1933/1935 work. "Essential richness" is defined precisely only for type-theoretic languages, so its general scope is asserted, not shown. Statements about natural language are informal and hedged, and none is a theorem. Anyone citing the paper for a natural-language impossibility result cites the hedges, not the theorems. The 1944 framing is dated in a way that affects reuse. Assumption (II) is held fixed by decision. Kripke-style partial truth predicates and paraconsistent semantics later showed that relaxing (II) or full disquotation yields languages that contain their own truth predicate in a restricted sense. Our knowledge of those developments is background, not in this source. The "universality of colloquial language" argument is in the 1933 monograph and not here, so this ingest cannot ground it. The transcription has visible errors, for example "on tile left side", the satisfaction example rendered as "2 is white", a bibliography date of "1911" for Fundamenta XVII, and a table-of-contents heading for section 8 ending in "?" that the body heading lacks. Liar-sentence page references ("p. 347, l. 31") point to the original journal pagination. For exact wording at a contested point, check against the printed paper.

Recommended Next Action

Since rewritten: the paragraph was removed rather than narrowed, so this recommendation is closed. Rewrite the impossibility paragraph of Prompting changes failure diagnosis with the semantic reference using the narrower claim in Extractable Value item 3. State the classical-logic and full-disquotation assumptions, preserve the hedge about everyday-language consistency, and separate truth definition from executable interpretation or decision procedures.