Intensional Transitive Verbs
INTENSIONAL TRANSITIVE VERBS
A verb is transitive if it takes a direct object and intensional if it exhibits one or more intensionality effects in its direct object. The three main such effects are (i) resistance to interchange of coextensive expressions, such as coreferential names or common nouns that happen to apply to exactly the same objects; (ii) lack of existence entailments even when the direct object is existentially quantified; and (iii) a relational-notional ambiguity if the direct object is quantified.
Verbs of search, desire, and expectation, exhibit all three intensionality effects. Thus, for (i), "Lois seeks Superman" and "Lois seeks Clark" might differ in truth-value even though Superman is Clark. For (ii), "Perseus seeks a gorgon" can be true even if there are no gorgons (contrast the extensional transitive found ). For (iii), "Richard III seeks a horse" is normally understood to mean that his search may be concluded successfully by finding any one of a range of horses: There need be no particular horse he must find. This is the notional reading. The relational reading is that there is some horse such that he is looking for that horse: Finding other horses will not do. Extensional transitives only allow relational readings: If Richard III rode a horse, there is a particular horse he rode. The relational/notional distinction was named and explored in Quine (1956).
Other groups of verbs exhibit various effects in various ways, providing much for an account of intensional transitives to explain. For example, depiction verbs generate a relational-notional ambiguity only with certain quantifiers in the direct object. "Guercino drew a dog" has both the relational reading—some specific dog—and the notional reading—no specific dog. But "Guercino drew every dog" seems to advert to some antecedent domain on which "every dog" is interpreted, requiring him to have drawn particular dogs (similarly with "most dogs" and "the dog"). By contrast, "Aldrovandi seeks every dog on his property" has a notional reading, according to which he simply has a general intention to find all the dogs there may be in the area. So depiction verbs are a special case.
Verbs of evaluation, such as despise, fear, respect and admire, resist interchange of coreferential expressions (for example, "Lex Luthor fears Superman but not Clark") but it is not so clear that they give rise to relational/notional ambiguities, at least with existential direct objects. The sentence "Churchill scorned a pedant" (pedantry was something up with which he was not prepared to put) can be understood in two ways: There is a relational reading, according to which there was a particular pedant who was the object of his scorn, and there is a generic reading, which attributes a ceteris paribus response-disposition to him and allows for exceptions. Generic readings are not notional ones, since they are just as common with extensional verbs—for instance, "Corporations overcompensate their CEO's" (see Ariel 1999 for more on generics). So "scorned a pedant" lacks a notional reading.
The verb need (and transaction verbs such as wager and owe ) displays the opposite behavior: notional readings are unproblematically available, but substitutions are permitted that fail with evaluation verbs and desire verbs. For example, if Richard III is dehydrated and therefore needs some water, it follows, since water is H2O, that he needs some H2O, whether or not he has such concepts as hydrogen and regardless of his other beliefs. But if he thinks H2O is a kind of rat poison, he may want some water without wanting some H2O and fear H2O without fearing water.
An obvious question is whether the three types of intensionality effect have a common ground or whether two or even three distinct mechanisms are involved. The contrast between need and scorn suggests that one mechanism is involved in substitution resistance and another in generating notional readings: The former is not available to needs, the latter not to scorn. And since one may need more flu vaccine even if there is no more left, existence neutrality apparently goes with the availability of notional readings.
It might be objected that we get existence neutrality with evaluation verbs as well: The Ancient Greeks worshipped Zeus even though there is no such entity. However, serious use of names for fictional or mythical items requires an ontology of abstract fictional or mythical entities that exist contingently (they would not have existed if the corresponding fictions or myths had not been created; see Salmon ). We should also note that worship is peculiar among evaluative verbs as regards notional readings. For instance, if a priest sacrifices with the words "To whichever god is out there," this is, arguably, a case of worshipping a god, but no particular one.
The next step is to describe the mechanisms accounting for the intensionality effects. One possibility is that in all three cases, the problems with intensional transitive verbs simply duplicate those encountered with propositional attitude verbs. This position seems quite plausible for substitution-resistance. If we have a good account of why substitution fails in "Lex Luthor fears that Superman is nearby" we would surely expect it to transfer straightforwardly to "Lex Luthor fears Superman"—unless, that is, the account for propositional attitude verbs depends on the presence of a clausal complement, as appears to be the case with Davidson's "paratactic" analysis of propositional attitude ascriptions (Davidson 1969). However, other accounts of substitution-failure in propositional attitude ascriptions transfer more smoothly—for instance, any account on which a name is associated with a way of thinking of the referent and that way of thinking somehow enters into the truth conditions of the ascription. (See, for example, the "hidden indexical" mechanisms explored in Crimmins  and Forbes ).
There is also the view that substitution resistance is an illusion (locus classicus Salmon ), which, if correct for propositional attitude verbs, should be equally correct for intensional transitives. On this view a name contributes only its referent to the meaning of a sentence, so no semantic distinction is to be drawn between "Lex fears Superman" and "Lex fears Clark."
The idea that no new problem is presented by intensional transitives runs into trouble, however, when we consider the relational-notional distinction. With propositional attitude verbs, the difference between (a) ascribing some cognitive relation between a subject and a specific item that the attitude is about and (b) not making such an ascription is captured by a scope distinction: "Lex fears that an extraterrestrial is nearby" gets the relational meaning when the quantifier "an extraterrestrial" is moved out of the attitude-content specification so that it has scope over "fears," as in "An extraterrestrial is such that Lex fears it is nearby"; the notional reading corresponds to unambiguous restriction of the quantifier to the attitude-content specification, as in "Lex fears-true the proposition that an extraterrestrial is nearby." But when we turn to intensional transitives, we find that, at least within a first-order framework, notional readings cannot be represented as ones in which the intensional verb has scope over the quantifier. For the verb to have wide scope, the quantifier must be one of its arguments: "seeks (Lois, an extraterrestrial)." But in first-order language a quantifier cannot be an argument to a relation: it must take scope over a sentence, open or closed, hence "without an inner sentential context, distinctions of scope disappear" (Kaplan 1986, p. 266).
According to propositionalism, the inner sentential context is there but partly hidden. Quine (1956) advances this view in the thesis that search-verb sentences can be paraphrased in terms of trying to find. So "Perseus seeks a gorgon" would be paraphrased as "Perseus is trying to find a gorgon." Partee (1974, p. 97) notes that search verbs cannot all be paraphrased using "trying to find," since they are not all synonymous (cf. "hunt" and "rummage about"), but in defense of propositionalism, both Parsons (1977) and Larson (2001) suggest using the search verb itself along with "to find." So we get "Perseus seeks to find a gorgon," or, in a more explicitly propositionalist formulation, "Perseus seeks (in order) to make it true that he himself finds a gorgon."
Evidence for an implicit inner sentential context varies with different kinds of verbs. For example, "Richard III needs a horse quickly" barely makes sense if quickly is understood to modify "needs" or any other explicit material. It seems instead to modify an implicit get. Along with other evidence (see Den Dikken et al.  for more) this makes it quite plausible that desire verbs and needs are not really transitive but take infinitival to get clauses as their true complements. However, comparable evidence for search verbs is hard to find, and whether converting the direct object into a purpose clause is meaning-preserving can be doubted. Depiction verbs and evaluative verbs present even more of a challenge. For instance, to fear x is not to fear encountering x, since one may not fear x but may fear encountering x because x has a dangerous communicable disease. Nor is fearing x the same as fearing that x will hurt you, since you may fear that your accident-prone dentist will hurt you without fearing your dentist. It is therefore conceivable that intensional transitives are not a unified semantic group: for some, such as desire verbs, need, and maybe verbs of expectation, propositionalism is workable, but not for others.
The main alternative to propositionalism is developed in Montague (1973) as part of a higher-order, type-theoretic semantics for natural language. In this framework, quantifiers can be arguments to verbs, so "seeks (Lois, an extraterrestrial)" is allowed as the semantics of the notional reading of "Lois seeks an extraterrestrial." Montague's ideas are refined, revised, and developed in Zimmerman (1993), Moltmann (1997), and Richard (2001), although in all these accounts, notional readings of search-verb sentences still put the searcher into a search relation to an abstract entity, the meaning of the quantifier (in standard Montague grammar, this is something rather complicated, a function from possible worlds to sets of intensional entities; see Dowty et al.  for an accessible account). It is unclear that such a semantics is compatible with the evident univocality of seeks in "seeks an extraterrestrial, but no particular one" and "seeks a particular extraterrestrial."
The approach of Forbes (2000) avoids this problem by employing a Davidsonian event-semantics (Davidson 1967) in which verbs are treated as predicates of events and the same predicate search appears in both relational and notional readings. In relational readings, the syntactic object signals a theme of the event, but in notional readings, it simply classifies the search as being one of a certain kind, for instance, as being a search of the at-least-one-extraterrestrial kind.
Intensional transitives raise interesting logical problems. It may be argued that propositional attitude ascriptions have no logic at all: even "x believes that p and q" does not logically entail that "x believes that p": at best we may endorse a psychological principle that persons aware that they accept a conjunction will also accept each conjunct individually. But for intensional transitives, there are substantial questions about the validity of certain inference-patterns. For example, if Richard III needs a warhorse, does it follow that he needs a horse? If notional readings are glossed in terms of indifference ("any would do," as in Lewis [1972, p. 199]) it does not follow: Even if Richard III needs a warhorse, and any one will do, it does not follow that he needs a horse, and any one will do—in the mayhem of the Battle of Bosworth, a cart horse would not do. On the other hand, the standard glossing of notional readings using "no particular one" seems to leave open the logical status of the inference rather than settling it one way or the other. These and other issues about the validity of specific inference patterns are pursued in Richard (2000) and Forbes (2003).
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Graeme Forbes (2005)