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Paulo asked:

Please Professor, explain me a way to teach Tarski's theory of truth for students who don't have a
logical foundation.

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Tarski's theory of truth without the logic? That's a tough proposition! In his famous paper, 'On the
Concept of Truth in Formalized Languages', Tarski describes a potentially infinite hierarchy of
'meta-languages' each one of which is able to talk about the truth or falsity of sentences in the level
just below it. The aim is to solve paradoxes like the following: You take a piece of paper and write,
'The statement on the other side of this paper is true'. Then on the other side, you write, 'The
statement on the other side of this paper is false'. (See Answers 2, answer to Susan.)

I have never found this self-referential paradox particularly gripping, so I am not persuaded that
Tarski's clunky contraption is really needed. However, the solution to the paradoxes about truth is not
the philosophically most important part of Tarski's paper.

Tarski gives a deceptively simple testwhich you can apply to any proposed theory of truth to see if
that theory is adequate.

First, we need to see that there are lots of things you can say about a sentence in a language. You
can say that it is grammatical, or that it is poetic, or that it contains exactly eleven words, or that it is
found in the King James Bible. But there is just one thing you can say about a sentence which has
the remarkable effect of producing a result which is equivalentto the original sentence. And that is
when you say that the sentence is true.

Let's forget about truth for the moment. We don't know what that is. Instead, Tarski says, let's just use
the the letter 'T'. Suppose that someone produced a definition of a predicate, 'T', which applies to
sentences of a language. And suppose that as a consequence of this definition, the following rule
(Convention T) holds:

'Snow is white' is T if and only if snow is white
'Grass is green' is T if and only if grass is green
'Giraffes live on Mars' is T if and only if Giraffes live on Mars
'Freddie Starr eats hamsters' is T if and only if Freddie Starr eats hamsters...

...and so on for every sentence in the language.

Then we would be justified in saying that 'is T' is the same as 'is true'. In fact, we can say more than
this. Convention T is all one could require of a theory of truth. It tells us what truth is, in the sense of
distinguishing the predicate 'is true' from every other predicate that can be applied to sentences, like
'is grammatical', 'is poetic', 'contains exactly eleven words', 'is found in the King James Bible' and so
on.

Just to see this working in practice, consider what is admittedly a pretty poor candidate for a theory of
truth, the Biblical theory:

Biblical theory of truth: sentence x is true if and only if x occurs in the King James Bible

Does the Biblical theory satisfy Convention T? No. Consider, for example:

'Tony Blair is Prime Minister' is found in the King James Bible if, and only if Tony Blair is
Prime Minister

But that is false. Nowhere in the King James Bible does there occur the sentence, 'Tony Blair is Prime
Minister'. So the statement on the left hand side of 'if, and only if' is false. But Tony Blair isPrime
Minister. So the statement on the right hand side of 'if and only if' is true. And the result of that is a
false statement. It follows that the Biblical theory of truth does not satisfy Convention T.

Armed with Convention T, we can dispose in a similar way with the pragmatist, coherence and
'verification under ideal conditions' theories of truth. You might try it as an exercise.

Tarski, however, makes a stronger claim. He claims that Convention T is, in effect, a correspondence
theoryof truth. Why is that? Because in each of the examples given above, 'Snow is white', 'grass is
green' etc. the left hand side talks about wordsand the right hand side talks about the world.If I say
that 'Snow is white' is true I am talking about words. If I say that snow is white then I am talking about
the world. Here we can literally seethe 'correspondence' required between words and the world in
order for there to be such a thing as truth.

I actually think that this is a logical mirage. No serious correspondence theorist would be satisfied
with such a thin account of 'correspondence'. The real import of Tarski's Convention T is to
undermine the possibility of ever giving an informativetheory of truth. The proper conclusion to draw
is the one that Tarski's predecessor Frege drew, and before Frege, Kant: truth is indefinable. —
However, that is another story.

Geoffrey Klempner