Is there an established distinction between semantic and syntactic predicates?

Question

My question is probing to learn whether semanticists (and syntacticians) draw a distinction between what I am calling here semantic and syntactic predicates. The question concerns the status of the NP a politician in the following examples:

a. Bill is a politician.

b. Bill, a politician, is pandering.

c. A politician (I know) is pandering. 

In (a), the predicative NP a politician is a property that is predicated of Bill. In (b), the appositive NP a politician is again a property that is also predicated of Bill. In (c) in contrast, one cannot view a politician as being predicated of another part of the sentence. What seems to be occurring, rather, is that a politican in (c) is being predicated of a discourse entity, i.e. of someone in the discourse context. The predicate-calculus-style representations for these sentences might be as follows:

 a'. is a politician (Bill)

 b'. is pandering (a politician (Bill))

 c'. is pandering (a politician)

In (a'-b'), a politician can be viewed as a predicate in every sense. In (c'), in contrast, a politician is not a predicate insofar as it is not predicated of another part of the sentence. For the sake of putting names on the distinction, a politician is both a semantic and syntactic predicate in (1a-b), but it is only a semantic predicate in (c'); it is not a syntactic predicate in (c').

The terminology I have just used is unique to my understanding. What I would like to find out is whether there is already an established terminology for this distinction. Note that the distinction in predicate types is important for predicting the distrubtion of, for instance, reflexive pronouns (e.g. Susan likes our picture of herself vs. *Susan said that we like herself) and negative polarity items (e.g. The discussion of no problem did anyone find interesting vs. *Discussing no problem did anyone find interesting). The distribution of these items is sensitive to the difference in predicate types.

Answer 1

As far as I can tell, the term 'predicate' is used rather differently in syntax and semantics.

Syntacticians speak of 'predicates' only when a 'predication' relation - 'primary' (as in Bill came home) or 'secondary' (as in Bill came home rather depressed)- is established with a syntactic 'subject', which may be the (unique) subject of the clause or another NP/DP, in certain cases of 'secondary predication' in which the 'subject' is not the subject of the clause, but an object, or the subject of a subordinate 'small clause', etc., depending on which analysis each syntactician favours (as in, e.g., I saw Bill rather depressed, I consider Bill an excellent teacher, etc.).

Hence, syntactic predicates normally or even invariably (depending on the analyses syntacticians adopt), correspond to only one type of what semanticists would call 'first-order one-place predicates', the type in which the argument that must 'saturate' the unsaturated one-place predicate to yield a 'proposition' is discharged, precisely, by the syntactic subject of the clause, but, of course, the undischarged argument of an unsaturated one-place predicate need not correspond to the subject of the clause; semantically speaking, I sent Bill__ is also a one-place first-order predicate, even though the missing argument is, syntactically, not discharged by a subject, but by a direct object (say the invitation in I sent Bill the invitation, or which in This is the invitation which I sent Bill, etc.).

In semantics, on the contrary, the term 'predicate' is used much more generally. Of course it is applied in cases of 'functional application' that do correspond to syntactic predications, but also to many other cases that do not. For one thing, semanticists, following logicians, speak of 'monadic' (= one-place), 'dyadic' (two-place), and, generally, 'n-adic' (n-place) 'predicates' (and all are 'predicates', from the semantic point of view). A transitive verb, for example, is, semantically speaking, a two-place (first-order) predicate, although, obviously, it does not by itself constitute a complete syntactic predicate, and a 'ditransitive' verb is a three-place first-order 'predicate', although it would need to be construed with two objects to constitute a complete syntactic predicate, etc. On the other hand, the 'predicates' the semanticist talks about need not be first-order, they may also be higher-order (2nd, third,... etc., depending on how rich the semanticist's ontology is), and, as a consequence, ad-nominal APs, PPs, relative clauses, etc. internal to an NP/DP, for example, are also one-place 'predicates' (2nd order, in this case, since they are predicated of a common, or modified common noun, that is itself, semantically speaking, a first-order predicate), and, correspondingly, AdvPs, PP's, etc. modifying unsaturated VPs also qualify as one-place (in this case, nth-order) predicates, since they are 'predicated' of partially constructed VPs. Actually, 'adverbials', as Ernst and Cinque, in particular, have shown, may be 'predicated' of entities that syntactically correspond to many different types of verbal or extended verbal projections, AuxPs, Modality Phrases, full predications, propositions (with polarity specified), ForcePs etc., etc., which are not first-order entities, either. So, in sum, in semantics, the extension of the predicate 'predicate' is much bigger than it is in syntax.

Answer 2

You've correctly recognized that a predicate in syntax is not what's called predicate in formal logic. As has been mentioned above, appositives can be expressed as conjunctions in formal (first-order predicate) logic.

In general, what's expressed by the logical predicate is the focus of a sentence whereas the argument is the topic. For example, "Melissa dormit" would be sleep(Melissa). But if you have "Dormit Melissa", you can't have Melissa(dormit), which is nonsense; formal logicians use lambda calculus to make Melissa a predicate: λf.f(Melissa). (I used a Latin example because it has free word order in order for both syntax trees to be identical.)

Another possibility would be to use Davidsonian semantics which is very flexible and doesn't make you use lambda calculus.