# What's so special about Tarski's T-Schema?

It seems fairly obvious. Even a five year old could probably come up with it. Its obvious that if something is the case, it is true (literally synonyms).

So, am I missing something? Is there a gulf between something being the case and it being true? What is the difference between "p" and "p is true". It seems trivially the same thing. Appending "is true" doesn't make any difference???

• One problem (see the SEP entry on deflationism for this) occurs when we take the left-hand side of an instance of the schema for a sentence. "Vixens are foxes," is true iff vixens are foxes, sure, except if, "Vixens are foxes," is a sentence rather than an abstract proposition, then the "iff" makes the existence of a fully interpreted sentence equivalent to the right-hand fact, but it could be a fact that vixens are foxes even if there were no fully interpreted sentence using those words. Generally, one can find reasons to question the T-scheme throughout the SEP. Aug 15 at 1:30
• Isn't this exactly the same question as your earlier one?
– g s
Aug 15 at 3:53
• T-schema is motivated by the correspondence theory of truth, the idea of truth as a "match" to reality. This is what makes it "obvious". However, the correspondence theory, despite its intuitive appeal, has a lot of problems. And the T-schema itself is not logically innocent. Adding it to a formal theory allows to derive statements that are not derivable without it, even those that do not mention truth. The contradiction in the Liar paradox is the most famous example. So it is not as "obvious" as it looks. The 'correct' theory of truth may be such where the T-schema is not universally valid. Aug 15 at 9:10
• @Conifold What is the fundamental difference between "Snow is white" and "Snow is white is true"? Are they not synonymous? How can one possible accept "Snow is white" and reject "Snow is white is true" and vice versa? Aug 15 at 9:40
• Well, common sense has limited uses and won't be of much help here, so you should get some rest and then parse the gibberish. The only alternative is to keep running in circles, as you've been doing so far. I already gave you examples, one can look at the snow and assert "snow is white", but not claim it true until others agree and verify it with a spectrometer. Or ever. Aug 15 at 11:13

To explain it further requires some jargon. There is a difference between an object language - a language we use to make statements - and a metalanguage - a language we use to talk about statements in the object language.

Tarski's T-schema are perhaps easier to see as being non-trivial if we use a different language for the object language. For example,

``````"La neige est blanche" is true in French if and only if snow is white.
``````

Note that the left part is in quotes and the right part is not. The quoted part is a sentence in the object language; the rest is a sentence in the metalanguage. The sentence as a whole is stating (in English) under what conditions "La neige est blanche" is true (in French).

But even if we use English in the object language, it is not trivial.

``````"Snow is white" is true in English if and only if snow is white.
``````

This sentence is stating in the metalanguage under what conditons "snow is white" is true.

``````Snow is white
``````

``````"Snow is white" is true
``````True(⌜φ⌝) ↔ φ