Tarski's schema T asserts that:

(T) x is true if and only if p

where x is the name of any sentence of the language in question and p is the expression which forms the translation of this sentence into the metalanguage.

A typical example is:

'snow is white is true' is true iff snow is white.

Apart from the distinction between object language and metalanguage which avoids paradoxes like the Liar, isn't this (partial) definition of truth in schema T trivial in itself?

(By trivial, I mean that the schema itself, as a sentence of the metalanguage, is an obvious theorem of the metalanguage.)

  • 1
    Define what you mean by "trivial". What Tarski does is reduce truth to satisfaction. Do you mean that reduction is trivial? There are many different theories of truth and as such many philosophers will disagree with that. Or do you mean something more like "this is a circular definition" which I've seen people have issues with as well. I really think you need to be more explicit by what you mean by "trivial" and what aspect of the definition you have the issue with.
    – Not_Here
    Sep 10 '18 at 19:01
  • Maybe... trivial as much as the "common sense" notion of truth used in everyday life and in science. The mathematical formula aseerting that the value of the Gravitational constant is approximately 6.674×10−11 N·kg–2·m2 is true iff the current method of measuring it will give the value of approximately 6.674×10−11 N·kg–2·m2. Sep 10 '18 at 19:11
  • It is the core of The Correspondence Theory of Truth dating at least to Aristotle : “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true. (Metaphysics 1011b25)” Sep 10 '18 at 19:20
  • In a sense all theorems are trivial because they can just be enumerated, so I still don't understand what you mean by trivial. Like Mauro said, maybe if you mean that it intuitively matches what we mean by the correspondence theory of truth, then yes, it is intuitive by reducing truth to satisfaction. But intuitive and trivial are very different.
    – Not_Here
    Sep 10 '18 at 19:50
  • 1
    @MauroALLEGRANZA Tarski explicitly denied any link with substantive theories of truth, like the correspondence. It is a purely formal device consistent with realism just as much as with anti-realism, coherentist and even deflationary theories of truth affirm the T schema.
    – Conifold
    Sep 11 '18 at 0:44

Tarski presented his Schema T as an adequacy condition on Truth definitions, not as a definition in itself. The idea that it should be seen as trivial is a testament to the intuitive pull of Tarski's condition - it really does seem like anything that we want to call "truth" should satisfy this condition called formal correctness, see SEP Tarski's Truth Definitions.

  • 1
    I am not quite sure what OP means by "trivial" though, so I am not sure if this answers it. There is a sense in which it is "trivial", as in "vacuous", providing no guidance towards determination of truth, so it is like "answering" a question by reformulating it.
    – Conifold
    Sep 11 '18 at 0:36
  • @Conifold "guidance towards determination" isn't a necessary criterion of a good definition, though. For example, take the definition of an Equivalence relation: en.wikipedia.org/wiki/Equivalence_relation A relation "=" is an equivalence relation if it's reflexive ("a=a"), symmetric (if "a=b" then "b=a") and transitive (if "a=b" and "b=c" then "a=c"). This definition doesn't necessarily tell you 'what makes' any two objects equivalent, but that's not the work that defining equivalence is supposed to accomplish.
    – Paul Ross
    Sep 11 '18 at 1:34
  • This is a good analogy. But on it Tarski should have relativized truth as equivalence relativizes identity, and phrased it something like "A predicate is called truthy if it satisfies the T schema". His chosen phrasing ""P" is true if and only if..." does suggest a promise it does not keep. He did it for a reason, his realist leanings and belief in "one truth" are rather transparent. The formalist reinterpretation of the T schema kind of retroactively withdraws an agenda, that Tarski did in fact have, without changing his phrasing, that was attuned to it. Hence the common puzzlement.
    – Conifold
    Sep 13 '18 at 22:15

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