I have some worries related to Stephen’s thesis according to which the asymmetry involved in TM can be accounted for with no appeal to the asymmetry between truth and being pointed out by truth-conditional theorists. As must be remembered, Stephen claims that in order to make room for the asymmetry it is enough to take into account that
(i) the truth-predicate can be taken to be introduced in the language by means of an introduction rule similar to the ones that govern the use of the logical connectives
(ii) this introduction rule licenses an inference from <S> to <S> is true (but not the other way around) that provides us with an account of the priority of <S> over <S> is true that is captured by TM.
Now, this explanation of the asymmetry rests on an analogy between the truth-predicate and certain logical terms. The analogy in question urges us to assimilate the semantic functioning of the truth-predicate to the semantic functioning of the logical connectives. Since it is taken for granted that the semantic functioning of the latter can be given in terms of rules, the same should be assumed concerning the semantic functioning of the former, namely, the truth-predicate. My first point of concern is that Stephen cannot be proposing a complete assimilation of the semantic functioning of the truth-predicate to what a use theory of meaning has to say about the logical connectives. If that were the case, there would be no difference between expressivism and inferentialism about truth –which does not seem to be one of Stephen’s purposes.
I will then assume that Stephen is taking the analogy to illuminate just a partial aspect of the semantic functioning of the truth-predicate. But, now, I do not see any reason to put all the emphasis on introduction rules, while setting elimination rules aside: according to an inferentialist or use theory of meaning, the meaning of a logical connective is given by the set of introduction and elimination rules that governs its use. The same should then be said regarding the truth-predicate: there is no priority of one kind of rules over the other kind. But then the analogy in question should enable us to go both ways: from <S> to <S> is true as well as from <S> is true to <S>, with the consequence that the desired asymmetry would not be preserved.
Eduardo Barrio has suggested to me that Stephen might be thinking of an asymmetry among uses according to which there are certain uses of the language (simple sentences about the world with no metalinguistic predicates) that are more basic than others (sentences containing metalinguistic predicates such as the truth-predicate). The sense of baseness in question seems to be related to a chronological priority in the process of acquisition of the language. I think that this might be descriptively adequate, but it is certainly no part of what is established by the proposed analogy with the logical connectives.