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The answer to this is a philosophy of logic question would seem to unify the notion of analytic truth across all formal and natural languages. This subject of this question seems to refer to the analytic subset of Truthmaker theory.

A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context. https://en.wikipedia.org/wiki/Stipulative_definition

Within the scope of the question {analytic truth} is stipulated to mean any expression of (formal or natural) language that can be completely verified as true entirely on the basis of its meaning. It is closely related to self-evident truth.

Analytic propositions are true or not true solely by virtue of their meaning... https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. https://en.wikipedia.org/wiki/Truth-conditional_semantics

Thus analytic meaning is defined as:
Every truth that can be expressed using language and verified as completely true entirely on the basis of other expressions of language is a truth verified as true entirely on the basis of its meaning.

In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof. https://en.wikipedia.org/wiki/Self-evidence

Thought experiment: Try and provide any example of an expression of language that is known to be true entirely on the basis of its meaning that cannot be proved to be true entirely on the basis of its meaning.

By what generic method do we correctly determine that an analytical expression of language is true?

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  • The generic method is thinking about what things mean. Jan 29 at 6:14
  • Which language? Even for a formal language with precise rules describing which expressions are synonymous, such an algorithm may not exist. Something as simple and precise as the word problem for groups is undecidable in general, for example. In natural languages, this is further complicated by loose grammar, vague, ambiguous and incoherent "meanings", etc., so you can forget about any "generic method".
    – Conifold
    Jan 29 at 9:47
  • @Conifold Undecidable does not count as true. My question only refers to the subset of expressions of language that are correctly determined to be true. en.wikipedia.org/wiki/CycL Formalizes natural language quite well. Rudolf Carnap meaning postulates also work for simple expressions. For example when the new term Bachelor is defined on the basis of existing terms {Married, Adult, Male} we only need a negation operator to complete its definition: Bachelor(x) ≡ (Adult(x) ∧ Male(x) ∧ ¬Married(x)) thus the term Bachelor is defined in terms of its constituents.
    – polcott
    Jan 29 at 17:50
  • @DavidGudeman "The generic method is thinking about what things mean." Yes that seems correct. (a) What steps are involved? (b) How could these steps be specified as an algorithm?
    – polcott
    Jan 29 at 19:34
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    A question attempts to solicit answers and does not have any other goals. Your very introduction makes me think that this is another one of your hopeless attempts of promoting your views.
    – Philip Klöcking
    Jan 29 at 22:55

2 Answers 2

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Willard Van Orman Quine's famous paper Two Dogmas of Empiricism (1951) showed that the notion of an analytic truth can be defined in reference to the notion of synonymy or meaning, but there is no clear criterion for either notion and the usual explanations ("true by definition" - which definition? etc.) fail to be precise. Carnap, Grice and Stawson famously argued against it in Meaning and Truth in Natural Languages (Carnap) and In Defense of a Dogma (Grice and Strawson). Quine's response to both articles and other polemics - the book Word and Object - also contained a rough definition of analycity based on the notion of stimulus meaning (outlined in the second chapter, which is the heart of the book). Nowadays the debate is considered generally settled, with logical empiricism long dead, but there have been some proposals since. Notably, by Chalmers (Revisability and Conceptual Change in "Two Dogmas of Empiricism" and also Constructing the World) and David Lewis (Convention).

I think Chalmers' proposal is interesting, although it doesn't provide a notion analycity strong enough to challenge Quine's contribution. It's also not at all complex, if you know basic Bayesianism. The definition goes:

[Chalmers' definition:] sentence S is analytic if and only if cr(S) is high and, for every piece of possible evidence E, cr(S | E) is also high

In other words, sentence S is analytic if no evidence will cause one to significantly lower one's credence in it.

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  • Maybe this addresses the issues that you raised: Every truth that can be expressed using language and verified as completely true entirely on the basis of other expressions of language <is> a truth verified as true entirely on the basis of its meaning.
    – polcott
    Jan 29 at 22:05
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    @polcott That is not what either of these men meant. Evidence is never purely semantical since without practical implications, language is hollow, thin, nothing but smoke and mirrors. Meaning is holistic, yes, but it is also malleable as our practical relations to one another and the world change.
    – Philip Klöcking
    Jan 29 at 22:50
  • @PhilipKlöcking Evidence is on the other side of the analytic/synthetic divide, I am referring to tautologies. Tautology, in logic, a statement so framed that it cannot be denied without inconsistency. britannica.com/topic/tautology This is deductive rather than inductive inference, thus the coherence rather than correspondence theory of truth applies.
    – polcott
    Jan 29 at 23:22
  • @polcott Indeed, but tautologies (like A = A) are distinct from full-blown analytic statements (like "All bachelors are unmarried").
    – user71009
    Jan 30 at 3:43
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    @polcott I don't think so. I don't believe in any suitable criterion of analyticity.
    – user71009
    Jan 30 at 6:03
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The overview of the framework of a possible solution
Analyticity is most unequivocally defined as any expression of formal or natural language that is proven to be true entirely on the basis of its relation to other expressions of language that are known to be true.

The most general way to express the notion of a formal axiomatic system seems to be anchored in finite string transformation rules. Systems such as Montague Grammar and the CycL language of the Cyc project encode natural language semantics directly in finite strings. These systems had Rudolf Carnap Meaning postulates as their predecessor. https://en.wikipedia.org/wiki/CycL
https://en.wikipedia.org/wiki/Montague_grammar
https://en.wikipedia.org/wiki/Meaning_postulate

Within systems such as these the term Bachelor(x) can be defined as (Male(x) ∧ Adult(x) ∧ ¬Married(x)) thus within this axiomatic system we can see that Bachelor(x) semantically entails ¬Married(x) (and two other things).

When-so-ever one expression X is semantically entailed by other expressions defined to be true, (through a sequence of finite string transformation rules that process semantic entailment) then X is proved to be true.

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