In standard propositional logic, both p and –p are ‘propositions’. In natural language, however, what phrases smaller than TP are ‘propositional’ is much less obvious. For example, take the simplest sentences, sentences like a), b) and c), where a) is specified for ‘default’, positive ‘polarity’, b) has ‘marked’, negative ‘polarity’, and, arguably, c) is unspecified for ‘polarity’.
a) Bach composed this concert.
b) Bach did not compose this concert.
c) Did Bach compose this concert?
According to Chomskian GB/P&P/MT assumptions, a clause like a) minimally contains a ‘saturated’ vP/VP with Bach in Spec v/V and this concert in Compl of V, and, on top of that, at least three ‘functional’ heads that respectively allow for the specification of polarity (Pol/PolP, in one widely used terminology), tense (TP, earlier IP), and illocutionary ‘force’ (ForceP, earlier CP). [Of course further heads may be involved (e.g., unmarked ‘modality’), but I will ignore them here, as they do not substantially alter the issue; let’s leave ForceP/CP aside, too, for the same reason].
As far as I can tell, the saturated vP or VP would correspond to the syntactic encoding of an ‘event’. I ignore here the question whether a VP must be tensed or not to be able to encode an event and how the sub-events that an 'accomplishment verb' like compose entails can satisfy this condition to qualify as ‘(sub)events’, although, of course, if it must, then, arguably, only TP can really correspond to en event and everything becomes even more obscure and complicated. But let’s leave that aside, too.
In at least both a) and b) it would be the respective PolarityP’s that would be ‘propositional’, but shall we say that ‘propositional’ categories start at PolarityP or at the respective X’ level (i.e., at Pol’, constituted by the Pol head, which would already contain whatever features license positive, negative or unspecified polarity, and its vP/VP complement)?
And what about c)? Under the assumptions above, in c) polarity is unspecified, and, as a consequence, its PolP, if it contains one - as I asume - cannot have a truth-value, and so cannot encode a ‘proposition’ at all. Case c), then, would illustrate a kind of ‘sentence’ (in the sense of ‘syntactic category that can be used to perform a speech act’), whose PolarityP would not be ‘propositional’. Some PolPs, then, would be ‘propositional’ and some would not, and, in cases like c), arguably neither TP nor ForceP could be ‘propositional’ either, and as a consequence yes/no questions would contain ‘propositional content’, but no propositional projections. [Of course, granted the existence of negative questions like Didn´t Bach compose this concert?, one can always argue that c) has just default positive polarity and that that value is 'questioned' at the higher illocutionary level, I know, but the alternative view should not be lightly discarded, should it?].
I once thought about this for a while, and went back to Frege, Russell, Strawson and other major early sources, but was unable to reach a really satisfying conclusion, which was an embarrassment, for at the time I always tried to convince my students of the feasibility of a well-behaved compositional semantics even for the highly articulated syntactic structures of current Chomskian theories of the clause.
Question: Could anybody here clarify this matter?
Of course I am aware that this question is only a tiny aspect of a much bigger one that has already been raised here at least once, namely, the ontological and, correspondingly, ‘semantic’ status of the extra- (or intra-!) linguistic correlates of the multiple syntactic heads and projections that figure in current ‘Chomskian’ analyses of the clause, but it seems to me that it is an important aspect and a good starting point for the investigation of that bigger, for semanticists, crucial and, to my knowledge, so far largely unanswered question.
Thank you in advance.