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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.

  • I'm a bit confused about why you think that polar questions can't have a positive/negative polarity. It's possible to have both positive and negative polar questions, and the interpretation of negative polar questions is actually quite well-studied: (i) "Did you go to the shops yesterday?" (ii) "Didn't you go to the shops yesterday". As an aside, the traditional approach to the semantics of questions in the Montagovian tradition is to treat them not as expressing propositions, but rather a set of propositions corresponding to their possible answers (or true answers, under some variants). – P Elliott Jan 28 '15 at 14:23
  • Here's some lecture notes of Irene Heim's from 2001 which lay out how to compositionally derive the semantic value of a question from the kinds of syntactic structures assumed in generative syntax: sfs.uni-tuebingen.de/~astechow/Lehre/Wien/WienSS06/Heim/… – P Elliott Jan 28 '15 at 14:34
  • Your 1st remark does not address the real issues my question raises. I myself admit that c) might contain default polarity, so you needed not take issue with that. As to Heim's 2001 notes, what she shows how to 'interpret' is only the clause structures (CP-IP-VP) Chomsky assumed in BARRIERS! That, of course, is no problem. The clause structures that do raise problems are current Cinque-style ones, with MANY OTHER categories whose semantic import (e.g., whether, above VP, they are propositional or not) has never been properly clarified. – Sibutlasi Jan 30 '15 at 8:27
  • Ah, well in that case I suppose it depends how seriously you take the proliferation of functional heads in the cartographic tradition. This recent paper by Ramchand and Svenonius might be of interest to you, which gives a more fine-grained compositional semantics for a more articulated phrase structure: sciencedirect.com/science/article/pii/S0388000114000540. It seems to me like many of the functional heads posited in the cartographic tradition have no evident semantic import. Of course you have the option of just treating them as semantically vacuous, i.e. identity functions. – P Elliott Jan 30 '15 at 17:17
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I think the discussion in McCawley's The Syntactic Phenomena of English is good, where he gives an orderly way of discussing such questions of what category a phrase is in. I can't locate my copy of the book right now, so I'll be rather vague. He follows the proposal of Ross's paper "NP: Endstation Hauptwort" (exact title?) that category membership is a matter of degree. He distinguishes (at least) (1) internal composition, (2) external privileges of occurrence, (3) correspondence to logical form.

(1), for sentence (I'll use that term instead of your "proposition") would be something like: is there a subject? Is there a verb and is it finite? Are there parenthetical expressions of the sort we find in "root sentences"?

(2) would be something like: can it act as antecedent for "so" in such constructions as "but I don't think so".

(3) would be the correspondence to the sentences (or "propositions") of sentence logic in a translation into a logical form (as you mention in the beginning of your question).

(I'm not sure how much the jargon associated with Chomsky's current theories is understood far from MIT, but certainly I didn't understand much of the terminology in your question.)

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  • I do have and long ago read McCawley's textbook. I have not consulted it for a long time, though (since late 1988, probably), and I would not have expected it to help much in this respect, but I will check. Maybe his logic textbook 'All You Wanted to Know about Logic but Didn't Dare Ask' (if I remember correctly) did contain relevant info, too. I will check both, just in case. – Sibutlasi Jan 27 '15 at 13:00
  • The 1998 second edition of McCawley's grammar is excellent on this subject. And, in particular, in the original question, sentence (c) is not a proposition. Questions are neither true nor false; like orders, prayers, greetings, and other speech acts, they may have felicity conditions, but they don't have truth conditions. As to negation, McCawley also gives quite a lot of evidence in his logic book that in natural language, negation is not truth-functional. After all, logic is just a stick-figure model of actual language, not its source. – jlawler Apr 27 '15 at 21:21
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The exact answer depends on the approach to natural language semantics you use. I've used Jerry Hobbs' "Ontological Promiscuity" (it's an approach to pragmatics and the title of a paper) where a semantic representation is predicative (one could say "has propositional status" because all formulae in the framework are closed) whenever an eventuality is marked as existing or nonexistig (Hobbs' Rexist predicate).

In a simple affirmative sentence it would be the VP but note that typically there are more predications in a sentence that depend on the discourse context (information structure). The topic implies existence (Rexist) so in a sentence like "The king of France is bald" there are two predications (the other is that fact that France has a king, i.e. a king of France exists; the sentence has no meaning if uttered today). Hobbs uses a version of HPSG, his "The syntax of English in a abductive framework" implicitly describes the relationship between syntactic structures and their logical representaiton.

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  • As regards "The king of France is bald", I suppose you mean that, there being no individual satisfying that description at present, the (subject of that) sentence has no 'referent', and the sentence cannot be true, but, as Frege showed long ago, it, and all its constituents, have perfectly coherent 'senses', we know what the truth-conditions of that sentence would be, and, therefore, "The king of France is bald" is just as meaningful as "The king of Spain is bald". 'Sense' and 'reference' cannot be confused, as any semanticist or philosopher of language will tell you. – Sibutlasi Jan 28 '15 at 9:02
  • Your reference to the two predications in your sentence reminds me of Wundt's analysis (1900) and, later, Davidson's (Parsons', etc.). Under such views, the LF of a sentence resolves into a conjunction of PredLogic 'clauses' (with quantifiers to bind the 'state' and individual variables of which 'bald' and 'king of France' are predicated) but Davidsonian PredLogic clauses are NOT propositions, but propositional functions (x is not referential), and they have nothing to do with discourse or information structure. I do not see how your answer can be relevant to my question, with all due respect. – Sibutlasi Jan 28 '15 at 9:26
  • @Sibutlasi You asked about "propositional status" which doesn't mean anything but you probably meant predication, which implies you meant extensional meaning. The sentence I gave has intensional meaning regardless of whether there is a referent or not, but it's not relevant to the question (and answer). If uttered today, the sentence has a logical representation that leads to a contradiction. – Atamiri Jan 28 '15 at 19:35
  • They are propositions. And as for information structure, just read Hobbs (but be warned it's dozens of papers). If you don't see how the answer is relevant and don't feel like reading the papers, I can explain it to you, but not in comments here (we would be told not to do so soon). – Atamiri Jan 28 '15 at 19:40
  • P.S. It's probably a good idea to explain the terminology used in formal logic: A proposition is something that can be evaluated for truth or falsity in a modality (predicate logic has only one modality by definition). Davidson uses conjunctions of laterals (why would you call them clauses, there are no disjunctions?) that represent reified events (=eventualities). Whenever an eventuality can be evaluated for truth or falsity (i.e. can be assigned a truth value) it has "propositional status" (i.e. it is a proposition in an equivalent set of grounded propositional formulae). – Atamiri Jan 28 '15 at 20:09

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