Conditions of Material Adequacy

A definition of truth ought to be such that it defines all that is truth and nothing that falls under it which is not truth. Not only this but it should also capture the intuitive notion of truth. The material adequacy condition aims at securing all these. The material adequacy condition is given in terms of 'convention T' which states that the definition of truth for a language L is correct iff we are able to deduce a sentence (T-sentence) from the schema called T-schema available for every sentence of that language which is: "X is true iff P". Here 'X' is replaced by a structural descriptive name of a sentence say 'S', and P is replaced by a correct translation of S into the meta-language (i.e., the language of the truth theory). For Example, "'Snow is white' is true iff snow is white". This asserts that his theory confines within the boundary of reference and truth conditions.

Davidson does not restrict himself to the Tarskian model of truth theory because he aims at establishing the theory of meaning which can be applicable to all languages including natural language. To do so, he states that when we derive the meaning of a sentence the T-sentences of it are meant to match the sentence of the object language with a sentence in the meta-language in a way that the latter is a correct translation of the former. Therefore, the sentence in the meta-language gives us the meaning of the sentence of the object language. It is so because being a correct translation of the sentence of the object language it retains the same meaning. Hence, the T-sentences give us the specification of meanings. Moreover, we have to note that the manner in which we arrive at T-sentences by deriving them from the definition does not involve the concept of meaning and still the definition along with the derivational system ensures the matching of sentences of the object language with sentences of the meta-language which have the same meaning. One may say that the concept of meaning via the concept of translation has been used in laying down the condition of material adequacy. But this does not lead to any kind of circularity as the condition of material adequacy is neither part of the definition of truth nor of any such derivational system is associated with it. It is simply an external check to ensure the correctness of the definition of truth.

In this regard, Davidson states that mastery of a theory of meaning is same as the mastery of a language for which the theory is formulated. A theory, on his view, lays down a systematic way of determining the meaning of all the significant expressions of a language. Hence, a theory of meaning is supposed to lay down the most general conditions to be considered as a satisfactory theory. A satisfactory theory of meaning gives an account of how meanings of sentences depend upon the meanings of words. A legible theory for a semantic determination of truth conditions of all statements provides the conditions under which a sentence will be treated as true or false. Thus, a theory of truth for a language L must be such that:

1. For each sentence S of L a T-sentence should be provable.
2. Each of such provable T-sentence should be true.

These two basic principles together explain the material adequacy of truth that explains the underlying conditions under which a sentence will be judged as either true or false. For example, "'Snow is white' is true if and only if snow is white".

Proceeding further, Davidson says that Tarski's T-schema has its own limitations because it is applicable to only logically perfect language or formal language. It cannot be applicable to all other languages. Hence, there might be a question regarding how to determine the truth-value of a T-sentence of ordinary language. But we could not also claim that sentences of ordinary language are irrelevant because of not capable of determining their truth-value and, therefore we must omit them from the language system. To overcome this lacuna, Davidson gives an alternative solution of finding a truth theory which will be a stronger and valid one for determining the meaning of a proposition.