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I have another question on Tarski's definition of truth.

In his book "Theories of Truth. A Critical Introduction", Kirkham (p. 145) gives the following example of the definition of truth for a language which consists of only five sentences (here, I only mention two of them for simplicity):

"The table is round.

The carpet is purple.

.../...

One theory (...) is the conjunction of all the T-sentences. (...) By a "logical conjunction", Tarski means something equivalent to the conjunction of the T-sentences. The following is just such a logical conjunction:

(s)[s is true :=: either (s = 'The table is round' and the table is round) or (s = 'The carpet is purple' and the carpet is purple)]."

I don't get this. To me the above definition is rather a disjunction (not a conjunction). What do I misunderstand?

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  • i don't think Tarski gave a definition of truth. the T-schema is a criterion of adequacy, if i'm not mistaken. it is not a definition of truth.
    – user20153
    May 18, 2017 at 20:18
  • ps. you might want to pick up a copy of books.google.com/books/about/… which has lots of great essays by lots of highly-regarded contemporary philosophers.
    – user20153
    May 18, 2017 at 20:21
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    Tarski most definitely did give a definition of truth, a recursive definition to be more precise, which of course can be turned into an explicit definition which was important to Tarski.
    – Johannes
    May 21, 2017 at 19:24
  • Tarski gave a criterion that definitions of truth need to have and then went on to give multiple definitions of truth for different systems of logic. So yes schema T is a criterion but he also, explicitly, gave multiple actual definitions for specific theories.
    – Not_Here
    May 22, 2017 at 1:46

1 Answer 1

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No; there is no error.

With only two sentences, it is quite easy to verify the general schema.

From one side, we have the "natural" condition:

"The table is round" is true iff the table is round.

The general schema, instead, is:

For every sentence x (in the language L), x is true iff (either the table is round, and x is identical to "The table is round", or the carpet is purple, and x is identical to "The carpet is purple").

Consider now one (of the only two possible) instantiation of the schema; what we get is:

"The table is round" is true iff (either the table is round, and "The table is round" is identical to "The table is round", or the carpet is purple, and "The table is round" is identical to "The carpet is purple").

Clearly, the disjunct: the carpet is purple and "The table is round" is identical to "The carpet is purple", is false and we can discrad it.

What we get is:

"The table is round" is true iff (the table is round and "The table is round" is identical to "The table is round").

But P ∧ t=t is equivalent to P and finally we get:

"The table is round" is true iff the table is round.

Presumably, the term conjunction comes from the consideration that in a finite universe, an universal quantification is equivalent to a conjunction:

∀xPx is equivalent to Px1∧...∧Pxn.

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    Thanks for the reply, but I still don't see why the list-like scheme has to be called "conjunction or logical product". Isn't it because the list-like scheme is in fact not a definition, but the 'extension' of the concept of a true sentence, the definition of truth being therefore the conjunction of all instance of the T-sentences in the list-like scheme?. This poses no problem of interpretation, and also fulfils the condition that the definition of truth (as the conjunction of all T-sentences in the list-like scheme) implies each and every instance of the T-biconditional.
    – user13738
    May 19, 2017 at 10:37

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