Question: is the T-schema generally regarded among philosophers as the same as Convention-T?

My understanding of Convention-T (and material adequacy) is as follows.

Consider the sentence ‘Schnee ist weiß’. Our intuition tells us that this sentence is true iff snow really is white. Material adequacy requires the definition (of what it takes for this sentence to be true) to conform to this intuition, and Tarski’s way to satisfy this is with Convention-T, an instance would be like this: ‘Schnee ist weiß’ is true iff snow is white. Clearly, there are infinitely many true sentences in L, thus this convention has infinitely many instances and take the general form: True(s) iff p, where s is the name of a sentence in L formed by adding quotation marks around it (e.g. ‘Schnee ist weiß’), p is a translation of s in M (e.g. snow is white), and True() is the truth predicate.

And I understand the T-schema to be an inductive definition of truth.

If P: Schnee ist weiß, then snow is white iff 'Schnee ist weiß' is true, i.e. P ⟷ True("P").

Inductively we can go onto define truth for more complicated sentences, e.g. P∧Q⟷ True("P") and True("Q").

But then it would seem that the T-schema just is Convention-T.

In the SEP, T-schema and Convention-T are regarded as the same:

Tarski gives a number of conditions that, as he puts it, any adequate definition of truth must satisfy. The central of these conditions is what is now most often referred to as Schema T (or the T-schema or Convention T or the Tarski biconditionals) - https://plato.stanford.edu/entries/self-reference/#ConSemPar

But at the same time, it seems that Putnam disagrees:

In his paper "Naturalism, Realism, and Normativity" published recently in the Journal of the American Philosophical Association, the late Hilary Putnam does an admirable job of disentangling Tarski's Convention-T from Tarski's T-Schema. For too long, orthodox interpretations of Tarski's theory of truth have accepted that Convention-T and the material adequacy condition are the same, indistinguishable from one another. Putnam seems to suggest an alternative to the orthodox interpretation that captures the distinction between the formal semantic theory of truth that Tarski went to great lengths to uncover in his work and the ordinary non-technical notion of truth he left aside because it was too ambiguous for us to make any headway. - https://www.josephulatowski.net/post/2018/01/06/convention-t-and-the-t-schema

So it would seem that there are those who think that the T-schema and Convention-T are not the same. But is this a general consensus among philosophers?

  • 2
    On your own description (which is conventional), they are two different things. T-schema gives an actual definition of truth (assuming that all sentences are inductively constructed, connectives are truth functional, and so on). Convention T gives a requirement on any theory of truth, whatever its definition of truth predicate might be. Of course, if the truth predicate is defined according to the T-schema then it satisfies Convention T. The converse is false. Holistic languages, where the truth of sentences is not determined by the truth of their parts, may still satisfy Convention T.
    – Conifold
    May 16 at 7:52
  • @Conifold Thank you, that's a very concise and clear explanation May 16 at 9:33
  • @Conifold What would an example of a holistic language be? Would a language that has a non-truth functional connective be such an example? e.g. A language that has the connective 'cause' and can make a sentence like 'Gravity causes the apple to fall from the tree' - because in this case this sentence is true iff gravity makes apples fall (thus satisfying Convention-T), but 'cause' is not truth functional? May 16 at 12:02
  • 1
    In intuitionistic or relevance logics even the usual connectives are non-truth functional. Deflationists endorse Convention T, but deny that any definition of truth exists at all (or is needed). Natural languages have idiomatic expressions whose truth is not determined by breaking them into parts. Inferentialism is a general approach to modeling entire languages non-compositionally. It fits well with coherence theories of truth, as opposed to correspondence theories that motivated Tarski.
    – Conifold
    May 17 at 3:52

Taski's Convention-T (material adequacy condition) is a general requirement of any semantic theory of truth for formal languages only, while his T-schema is a specific such theory satisfying the general Convention-T according to reference here:

Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"): "P" is true if, and only if, P....It is important to note that as Tarski originally formulated it, this theory applies only to formal languages. He gave a number of reasons for not extending his theory to natural languages, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is closed

Tarski developed the theory to give an inductive definition of truth as follows. (See T-schema)...By using the schema one can give an inductive definition for the truth of compound sentences. Atomic sentences are assigned truth values disquotationally. For example, the sentence "'Snow is white' is true" becomes materially equivalent with the sentence "snow is white", i.e. 'snow is white' is true if and only if snow is white... Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in the context of truth. Therefore it would be circular to use one of them in the definition of truth itself.

From your quoted content of Putnam, it seems it's about further distinction of Convention-T from material adequacy condition which is much more subtle and technically specialized and involved, but it's not about confusion with the inductive T-schema.

As for your further concern of holistic language and non-truth functional connective, the same reference mentioned Kripke's semantic theory of truth:

Kripke's theory of truth (Saul Kripke 1975) is based on partial logic (a logic of partially defined truth predicates instead of Tarski's logic of totally defined truth predicates) with the strong Kleene evaluation scheme.

So you may further refer to kleene's three-valued logic for non-truth functional connective or employ either strict conditional or C3 conditional for natural language leveraging modal logic to express "cause" connective in addition to the classic non-causal material connective. For holistic language you can refer to semantic holism:

In the 1950s, the agreement that seemed to have been reached regarding the primacy of sentences in semantic questions began to unravel with the collapse of the movement of logical positivism and the powerful influence exercised by the later Ludwig Wittgenstein. Wittgenstein wrote in the Philosophical Investigations that "comprehending a proposition means comprehending a language". About the same time or shortly after, W. V. O. Quine wrote that "the unit of measure of empirical meaning is all of science in its globality"; and Donald Davidson, in 1967, put it even more sharply by saying that "a sentence (and therefore a word) has meaning only in the context of a (whole) language"

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