An exchange centring on the validity of an assertion — the identity of the Subject, the choice and degree of polarity — may be realised by clauses consisting of the Mood only, the Residue being established at the start and then presupposed by ellipsis, or by substitution with do.
The notion of validity relates to the arguing of the case, if it is a proposition, or to the putting into effect, if it is a proposal. The Subject is that element in which the particular kind of validity (according to the mood) is being invested.
The problem only arises when predication is interpreted in terms of truth value, since proposals — commands and offers — have no truth value. This mistake arose because predication was assumed to be an experiential relation; but it is not — it is an interpersonal relation, enacting the form of exchange between speaker and listener.
(i) From below, it is that nominal element (nominal group or nominalised phrase or clause) that is picked up by the pronoun in the mood tag.
(ii) From round about, it is that which combines with the Finite (operator) to form the Mood element in the clause; it is also that which constitutes the unmarked Theme if the mood is declarative, and which switches place with the Finite if the mood is yes/no interrogative.
(iii) From above, it is that which carries the modal responsibility; that is, responsibility for the validity of what is being predicated (stated, questioned, commanded or offered) in the clause.
This last point is the basic insight that informed the original, pre-structuralist interpretation of the Subject function, that in terms of a configuration of Subject + Predicate.
This rôle [modal responsibility] is clearly recognisable in the case of offers and commands; but it is the same principle that is at work in statements and questions. Here, too, the Subject specifies the ‘responsible’ element; but in a proposition this means the one on which the validity of the information is made to rest. (It is important to express it in these terms rather than in terms of true or false. The relevant concept is that of exchangeability, setting something up so that it can be caught, returned, smashed, lobbed back, etc. Semantics has nothing to do with truth; it is concerned with consensus about validity, and consensus is negotiated in dialogue.)
The Subject supplies the rest of what it takes to form a proposition: namely, something by reference to which the proposition can be affirmed or denied. … the Subject specifies the entity in respect of which the assertion is claimed to have validity.
A clause has meaning as an exchange, a transaction between speaker and listener; the Subject is the warranty of the exchange. It is the element the speaker makes responsible for the validity of what he is saying.
In the environment of ‘mental’ projection, the contrast between statement and question is not concerned with the speech functional orientation of giving vs demanding information but rather with the status of the validity of the information. In a statement, it is fixed with respect to the polarity and the elements of transitivity (realised by an indirect declarative clause optionally introduced by that), but in a question, it is open with respect [to] the polarity (realised by an indirect yes/no interrogative clause introduced by whether or if) or one (or more) of the elements of transitivity (realised by an indirect wh- interrogative clause introduced by who, which, when, where, etc). Consequently, mental clauses representing an ‘undecided’ state of mind are used to project indirect questions. These include clauses of wondering and doubting, finding out and checking, and contemplating, which tend to be characterised by special lexical verbs such as wonder, ascertain …
Semantics has nothing to do with truth; it is concerned with consensus about validity, and consensus is negotiated in dialogue.