## 1. Some groups of ITV's and their behavior



Search verbs and desire verbs manifest all three of the behaviors
listed in the prologue as "marks" or effects of
intensionality. Thus, Lois Lane may be seeking Superman. But it does
not seem to follow that she is seeking Clark, even though Superman is
Clark, and so we have an example of the first kind of anomaly
mentioned in the prologue: substitution of one name with another for
the same person leads to a change in truth-value for the embedding
sentence (here "Lois is seeking Superman"). Similarly, a
thirsty person who believes that water quenches thirst and that
H2O is a kind of rat poison may want some water but not
some H2O. [According to some, this alleged failure of
substitution to preserve truth-value is an illusion; but for reasons
of space I do not pursue this theory -- its *locus
classicus* is (Salmon 1986).]



Second, both search verbs and desire verbs create specific-unspecific
ambiguities in their containing VPs when the syntactic object of the
verb consists in a determiner followed by a nominal (this ambiguity is
also known as the relational/notional ambiguity, following Quine 1956,
where it was first studied, at least in the modern period). For
example, 'Oedipus is seeking a member of his family' could
be true because Oedipus is seeking specifically Jocasta, who is a
member of his family, though he doesn't realize it. On such an
occasion, what is true can be more carefully stated as 'there is
a member of his family such that Oedipus is seeking that
person'. The alternative, unspecific or notional reading, is
forced by adding 'but no particular one': 'Oedipus
is seeking a member of his family, but no particular one'. Here
Oedipus is implied just to have a general intention to find some
member or other of his family. Contrast the extensional
'embrace': Oedipus cannot embrace a member of his family,
but no particular one. 



Third, it is obvious that it is possible both to want, and to search
for, that which does not exist, for instance, a fountain of eternal
youth. But it isn't possible to, say, stumble across such a thing,
unless it exists.



Depiction verbs, such as 'draw', 'sculpt', and
'imagine', resist substitution in their syntactic objects,
at least if the clausal 'imagine' does: if imagining that
Superman rescues you is not the same thing as imagining that Clark
rescues you, it is hard to see why imagining Superman would be the
same thing as imagining Clark. A specific/unspecific ambiguity is also
possible, as is attested by the wall label for Guercino's *The
Aldrovandi Dog* (*ca.* 1625) in the Norton Simon Museum,
which states 'this must be the portrait of a specific
dog', thereby implicating an alternative, that 'Guercino
drew a dog' *could* be taken to mean that he drew a dog,
but no particular dog -- he just made one up. And we can clearly
draw or imagine that which does not exist (as opposed to, say,
photographing it). Braque's *Little Harbor in Normandy* (1909)
is an example, according to the curators of the Art Institute of
Chicago: 'it appears this work was painted from imagination,
since the landscape depicted cannot be identified.'



However, whether or not a notional reading of a depiction VP is
possible depends on which quantificational determiner occurs in the
noun phrase complement. If we say 'Guercino drew every
dog', 'Guercino drew most dogs', or 'Guercino
drew the dog' (non-anaphoric 'the dog'), we seem to
advert to some antecedent domain with respect to which 'drew
every/most/the dog(s)' are to be evaluated. So specific readings
are
 required.[1]
 This resistance to unspecific construal is robust across languages
and is typical of those quantificational determiners which do not
occur naturally in existential contexts such as 'there
is': contrast 'there is a dog in the garden' with
'there is every dog in the garden', 'there are most
dogs in the garden', or 'there is the dog in the
garden'. An account of what is wrong with 'there is every
dog in the garden' (see Keenan 2003) might well contain the
materials for explaining the lack of unspecific readings of depiction
VPs with determiners like 'every', 'most' and
'the'; see further (Forbes 2006:142-150).



It should be emphasized that depiction verbs are special in this
respect, for there is no problem getting unspecific readings with
'every', 'most' and 'the' using
desire verbs or search verbs. Guercino might be looking for every dog
on Aldrovandi's estate, though there are no particular dogs he is
looking for; the reader might be driving around an unfamiliar airport
rental car lot, looking for the exit, and in this case there is no
exit such that *it* is being sought. ('look' isn't
really a transitive verb, but when the following preposition is
'for', a search activity is denoted, so it is customary to
count the likes of 'looking for' as a "transitive
verb" in contexts where intensionality is under discussion.)



Mixed behavior is also manifested by evaluative verbs, for example
'respect', 'admire', 'disdain',
'worship', including emotion verbs such as 'lust
(after)' and 'fear'. Lex Luthor might fear Superman,
but not Clark, and Lois might disdain Clark, but not Superman.
However, unspecific readings of VPs with quantified complements are
harder to hear, at least when the quantifier is existential.
'Lois admires an extraterrestrial' can be heard in two
ways: there is the 'admires a particular extraterrestrial'
reading, and there is a *generic* reading, which means that
among the kinds of thing she admires are extraterrestrials in general.
Generic readings of evaluative VPs attribute dispositions, and are
not the same as unspecific or notional readings (see Cohen 1999, 2008,
and the entry on
 generics).
 There does not seem to be a sensible non-generic construal of
'Lois admires an extraterrestrial, but no particular
one'.



The verb 'need' is an interesting case. A sports team
might need a better coach, though no specific better coach, and might
need a better coach even if there are none to be had. So two out of
three marks of intensionality are present. However, 'need'
contrasts with 'want' as regards substitution: our
dehydrated subject who does not want H2O because he
believes it to be a kind of rat poison, nevertheless *needs*
H2O. It seems that co-denoting terms may be interchanged in
the complement of 'need'. But merely accidentally
co-extensive ones cannot be: Larson (2001, 232) gives the example of
Max the theater impresario, who needs more singers but not more
dancers, even though all who sing dance, and vice-versa. The property
*singer* and the property *dancer* are different
properties, so expressions for them cannot be exchanged in the
complement of 'need'. Similar restricted substitutivity is
observed with transaction verbs such as 'wager',
'owe', 'buy', 'sell',
'reserve', and perhaps the transaction resultative
'own'. One may reserve a table at a restaurant, though
there need not be a specific table one has reserved in making the
reservation, since the restaurant may be expecting a slow night. But
these verbs do allow interchange of co-referential expressions (a
purchase of water-rights is a purchase of H2O-rights)
though not (Zimmerman 1993, 151) of accidentally co-extensive ones.
For 'own' see (Zimmerman 2001, *passim*).



Indeed, it is even arguable that some marks of intensionality are
present with verbs that allow interchange of *accidentally*
co-extensive expressions. A case in point is verbs of absence, such as
'omit' and 'lack'. If it so happens that all
and only the physicists on the faculty are the faculty's Nobel prize
winners, then a faculty committee that lacks a physicist lacks a Nobel
prize winner. However, not too much weight can be put on this case,
since it may be that at some level, 'lack' should be
analyzed (possibly in a complicated way) in terms of *not
having*, in which case it would not really be an intensional verb
at all; though so far as the author knows, no convincing analysis of
this type has been formulated. See (Zimmerman 2001, 516-20) for
further discussion of relationships among the marks of
intensionality.


## 2. How many mechanisms for how many marks?



We have distinguished three "marks" or effects of
intensionality: substitution-resistance, the availability of
unspecific readings, and existence-neutrality. A natural question is
whether one and the same semantic mechanism underlies all three
effects, whether they are entirely independent, or whether two have a
common source distinct from the third's.



In the context of a discussion of propositional attitude verbs, that
is, verbs which take clausal or clause-embedding noun-phrase
complements rather than simple noun-phrase (NP) objects, one
hypothesis which keeps explanatory apparatus to the minimum is that
all three effects of intensionality arise from the possibility of the
complement having *narrow scope* with respect to the attitude
verb. Thus we might distinguish two readings of



(1)

Lex Luthor fears that Superman is nearby,

namely



(2a)

Lex Luthor fears-true the proposition that Superman is
 nearby[2]


and



(2b)

Superman is someone such that Lex Luthor fears(-true the
proposition) that he is nearby.


In (2a) we make the clause 'that Superman is nearby' the
complement of 'proposition' to guarantee that
'Superman' is within the scope of 'fears' (the
resulting NP 'the proposition...' is a "scope
island"). And in (2b) we use a form of words that encourages an
audience to process 'Superman' ahead of
'fears'. We can associate substitution-resistance with
(2a), while allowing substitution in (2b). (2b) ascribes a complex
property to Superman, and therefore also to Clark; namely, *being
an x such that Lex fears x to be nearby*. (2a), on the other hand,
puts Lex in the fearing-true attitude relation to a certain
proposition, with essentially no implications about what other
propositions he may fear-true. So, provided the proposition that
Superman is nearby is distinct from the proposition that Clark Kent is
nearby, substitution-failure in (1) construed as (2a) is
explicable.



As for taking these two propositions to be distinct, there are many
serviceable accounts, mostly involving some variation of the original
proposal in modern philosophical semantics, found in (Frege 1892,
1970). According to Frege, every meaningful expression or phrase has
both a *customary reference* that it denotes, and a
*customary sense* that it expresses. In the case of clauses,
the customary reference would be a truth-value which is
compositionally derived from the denotations of the words of the
clause, and the customary sense would be a way of thinking of that
truth-value, compositionally derived from the senses of the words of
the clause. Therefore, provided that 'Superman' and
'Clark Kent' have different though coreferential senses
(i.e., provided they express different ways of thinking of the same
individual) we will get different propositions. (However, it's highly
non-trivial to find an adequate account of the senses of names, given
the critique of the most straightforward accounts in (Kripke
1972).)



However, on the face of it, this only has (1), intended in the (2a)
manner, *expressing a different proposition* from



(2c)
 Lex Luthor fears that Clark is nearby.


Since truth-value is on the level of reference, and the corresponding
words of (2a) and (2c) all have the same referents, the resulting
truth-values for (2a) and (2c) will be the same; but they are supposed
to be different. So Frege makes the ingenious suggestion that it is an
effect of embedding in intensional contexts (he only considered
clausal verbs) that expressions in such contexts no longer denote
their customary references, but rather their customary senses. Using
'iff' henceforth to abbreviate 'if and only
if', then (1) intended as (2a) is true iff the reference of
'Lex' stands in the fearing-true relation to
the *switched* reference of 'Superman is nearby',
namely, its customary sense. Now we have our explanation of why merely
interchanging
*customarily* co-referential expressions in (1) can produce
falsehood from a truth: the substitution does not preserve reference,
since the names are now denoting their customary senses. However, if
(1) is intended as (2b), there will be no truth-value switch, since
there is no name-reference switch: in (2b) 'Superman' is
not in the scope of 'fears', therefore it denotes its
customary reference, and interchange with any other expression
denoting that same referent must of necessity be truth-value
preserving. (Readers in search of more detailed discussion of Frege's
notion of sense might consult the section on
 Frege's philosophy of language
 in the entry on Frege. See also the entry on
 propositional attitude reports,
 and for other uses of Frege-style "switcher semantics",
Gluer and Pagin 2012.)



A view like this has the capacity to explain the other intensionality
effects. The specific-unspecific ambiguity in 'Lex fears that an
extraterrestrial is nearby' is explained in terms of scope
ambiguity, the notional or unspecific reading corresponding to



(3a)
 Lex Luthor fears-true the proposition that an extraterrestrial is
nearby


and the relational or specific reading to



(3b)
 An extraterrestrial is such that Lex Luthor fears that it is
nearby.


Existence-neutrality is also explained, since the *proposition*
that an extraterrestrial is nearby is available for its truth to be
feared, believed, doubted or denied, whether or not there are
extraterrestrials.



There are other accounts of substitution failure, but details are
incidental at this point. For there are real issues about (A) whether
a single mechanism *could* be responsible for all three
effects, and (B) whether an account of any effect in terms of a scope
mechanism is workable for transitive, as opposed to clausal,
verbs.



(A) The behaviors cited in the previous section suggest that
substitution-resistance and the availability of an unspecific reading
have different explanations. For we saw that the verb
'need' contrasts with the verb 'want' as
regards substitution-resistance, but is similar as regards the
availability of unspecific readings of embedding VPs. So it seems
that there is a mechanism that blocks substitution, perhaps the
Fregean reference-switch one, perhaps something else more compatible
with what Davidson calls "semantic innocence" (Davidson
1969, 172--a semantically innocent account of
substitution-failure is one that does not alter the semantics of the
substitution-resisting expressions themselves for the special case in
which they occur in intensional contexts). And this mechanism cannot
occur with 'need', but can with 'want'
('can' rather than 'does' because it is
optional; this is to allow for "transparent" or
substitution-permitting readings of the likes of 'Lex fears
Superman' analogous to (3b)). On the other hand, whatever
accounts for notional readings is evidently available to both verbs,
and therefore it is not the same mechanism as underlies the
substitution-resistance of 'wants'. However, this
reasoning is not conclusive, since the substitution-resistance
mechanism may be present with 'needs' (and transaction
verbs) but somehow rendered ineffective (see Parsons 1997, 370). One
would need to hear how the ineffectiveness comes about.



Evaluative verbs present the converse challenge:
substitution-resistance but apparently no unspecific readings of
embedding VPs, certainly not existential ones. It is less clear how a
defender of a 'single explanation' theory would handle
this, at least if the single explanation is a scope mechanism, since
it appears from the other cases that occurrence within the scope of
the intensional verb immediately produces an unspecific reading.



Suspension of existential commitment may group with availability of
unspecific readings for explanatory purposes. There appear to be no
cases of intensional transitives which allow notional readings of
embedded VPs, but where those VPs have the same existential
consequences as ones which differ just by the substitution of an
extensional for the intensional verb.



(B) The scope account is the only real contender for a single
explanation of the intensionality effects. But there is a major
question about whether it can be transferred at all from clausal to
transitive verbs. For the intensionality effects would all be
associated with narrow-scope occurrences of noun phrases (NPs), and
with a transitive verb such syntactic configuration is problematic
when the NP is quantified. This is because, in standard first-order
syntax, a quantifier must have a sentence within its scope (an open
sentence with a free variable the NP binds, if redundant
quantification is ruled out in the syntax). We can provide this for
relational or wide-scope readings, for example



(4)
 An extraterrestrial is such that Lois is looking for it


in which 'Lois is looking for it' is the scope of
'an extraterrestrial'. But if 'an
extraterrestrial' is supposed to be within the scope of
'looking for' there is no clause to be *its* scope;
it has to be an argument of the relation, which is not allowed in
first-order language. As Kaplan says, 'without an inner
sentential context...distinctions of scope disappear'
(Kaplan 1986, 266). (Though readers who have taught symbolic logic
will be very familiar with the student who, having symbolized
'Jack hit Bill' as '*Hjb*', then offers
something like '*Hj*([?]*x*)' as the
symbolization of 'Jack hit someone.')



The description of the problem suggests two forms of solution. One is
to preserve first-order syntax by uncovering hidden material to be the
scope of a quantified NP even when the latter is within the scope of
the intensional verb. The other is to drop first-order syntax in favor
of a formalism which permits the meanings of quantified NPs to be
arguments of intensional relations such as fearing and seeking. We
consider these options in turn in the following two sections.


## 3. Propositionalism



The idea of uncovering hidden material to provide NPs in notional
readings of intensional VPs with sentential scope was prominently
endorsed in (Quine 1956), where the proposal is to paraphrase search
verbs with 'endeavor to find'. So for (5a) we would have
(5b):



(5a)
 Lois is looking for an extraterrestrial

(5b)
 Lois is endeavoring to find an extraterrestrial


Partee (1974, 97) objects that this cannot be the whole story, since
search verbs are not all synonyms ('groping for' doesn't
mean exactly the same as 'rummaging about for'), but den
Dikken, Larson, & Ludlow (1996) and Parsons (1997, 381) suggest
that the search verb itself be used in place of
'endeavor'. So we get



(6a)
 Lois is looking to find an extraterrestrial


or in somewhat non-Quinean lingo,



(6b)
 Lois is looking in order to make true the proposition that an
extraterrestrial is such that she herself finds
 it.[3]


Here 'an extraterrestrial' is within the scope of
'looking' but has the open sentence 'she herself
finds it' as its own scope.



It may or may not be meaning-preserving to replace (5a)'s
prepositional phrase with (6a)'s purpose clause, but even if it
is meaning-preserving, that is insufficient to show that (6a) or (6b)
articulates the semantics of (5a); it may merely be a synonym.
However, with 'need' and desire verbs, evidence for the
presence of a hidden clause is strong. For example, in



(7)
 Physics needs some new computers soon


it makes little sense to construe 'soon' as modifying
'needs'; it seems rather to modify a hidden
'get' or 'have', as is explicit in
'Physics needs to get some new computers soon', i.e.,
'Physics needs it to be the case that, for some new computers,
it gets them soon'. (For 'have' versus
'get', see (Harley 2004).)



Secondly, there is the phenomenon of propositional anaphor (den
Dikken, Larson, & Ludlow 2018, 52-3), illustrated in



(8)
 Physics needs some new computers, but its budget won't allow it.


What is not allowed is the truth of the proposition that Physics gets
some new computers.



Third, attachment ambiguities suggest there is more than one verb
present for modifiers to attach to (Dikken, Larson, & Ludlow 1996,
332):



(9)
 Physics will need some new computers next year


could mean that a need for new computers will arise in the department
next year, but could also mean that next year is when Physics should
*get* new computers, if its need (which may arise later this
year) is to be met.



Finally, ellipsis generates similar ambiguities:



(10)
 Physics will need some new computers before Chemistry


could mean that the need will arise in Physics before it does in
Chemistry, but could also mean that Physics will need to get some new
computers before Chemistry gets any.



However, the strength of the case for a hidden 'get' with
'need' or 'want' contrasts with the case for
propositionalism about search verbs. As observed by Partee (1974, 99),
for the latter there are no attachment ambiguities like those in (9).
For example,



(11)
 Physics will shop for some new computers next year


can only mean that the shopping will occur next year. There is no
second reading, corresponding to the other reading of (9), in which
'next year' attaches to a hidden 'find/buy'.
The phenomena in (8) and (10) also lack parallels with search verbs;
for example, 'Physics will shop for some new computers before
Chemistry' lacks a reading that has Physics shopping with the
following goal: to find/buy new computers before Chemistry finds/buys
any. And although the propositionalist might offer something like



(12)
 Physics will seek more office space by noon


as an analog of (7), it is not easy to decide if (12) genuinely has a
reading of the 'seek to find more office space by noon'
sort, or whether the hint of such a reading is just an echo of
(7).



Other groups of intensional transitives, such as depiction verbs and
evaluative verbs, raise the problem that there is no evident
propositional paraphrase in the first place. For psychological
depiction verbs such as 'fantasize' and
'imagine', Parsons (1997, 376) proposes what he calls
"Hamlet ellipsis": for 'Mary imagined a
unicorn' we would have the clausal 'Mary imagined a
unicorn to be'. Larson (2001, 233) suggests that the complement
is a "small" or "verbless" clause, and for
'Max visualizes a unicorn' proposes 'Max visualizes
a unicorn in front of him'. This is too specific, for we can
understand 'Max visualizes a unicorn' without knowing
whether he visualizes it in front of him, above him or below him, but
even if we change the paraphrase to 'Max visualizes a unicorn
spatially related to him', this proposal, as well as Parsons',
have problems with negation: 'Mary didn't imagine a
unicorn' is not synonymous with either 'Mary didn't
imagine a unicorn to be' or with 'Mary didn't imagine a
unicorn spatially related to her', since the first of these
allows for her to imagine a unicorn but not imagine it to be, the
second, for her to imagine a unicorn but not as spatially related to
her. There may be philosophical arguments that exclude these
 options,[4]
 but the very fact that a philosophical argument is needed makes the
proposals unsatisfactory as semantics.



Clausal paraphrases for verbs like 'fear' are even less
likely, since the extra material in the paraphrase can be read as the
focus of the fear, making the paraphrase insufficient. For example,
fearing *x* is not the same as fearing encountering *x*,
since it may be the encounter that is feared, say if *x* is an
unfearsome individual with a dangerous communicable disease. In the
same vein, fearing *x* is not the same as fearing that
*x* will hurt you; for instance, you may fear that your
accident-prone dentist will hurt you, without fearing the dentist.



We conclude that if any single approach to intensional transitives is
to cover all the ground, it will have to be non-propositionalist. But
it is also possible, perhaps likely, that intensional transitives are
not a unitary class, and that propositionalism is correct for some of
these verbs but not for others (see further Schwarz 2006, Montague
2007).


## 4. Montague's semantics



The main non-propositionalist approaches to ITVs begin from the work
of Richard Montague, especially his paper "The Proper Treatment
of Quantification in Ordinary English" (Montague 1973), usually
referred to as PTQ in the literature (Montague's condition (9) (1974,
264) defines 'seek' as 'try to find', but this
is optional). Montague developed a systematic semantics of natural
language based on *higher-order intensional type-theory*. We
explain this term right-to-left.



Type theory embodies a specific model of semantic compositionality in
terms of *functional application*. According to this model, if
two expressions *x* and *y* can concatenate into a
meaningful expression *xy*, then (i), the meaning of one of
these expressions is taken to be a function, (ii) the meaning of the
other is taken to be an item of the kind that the function in question
is defined for, and (iii) the meaning of *xy* is the output of
the function when applied to the input. The type-theoretic
representation of this meaning is written **x(y)** or
**y(x)**, depending on which expression is taken to be
the function and which the input or argument. A functional application
such as **x(y)** is said to be *well-typed* iff
the input that **y** denotes is the type of input for
which the function **x** is defined.



For example, in *the simple theory of types*, a common noun
such as 'sweater' is assigned a meaning of the following
type: a function from individuals to truth-values (a function of type
*ib*, for short; *b* for 'boolean'). For
'sweater' the function in question is the one which maps
all sweaters to the truth-value TRUE, and all other individuals to the
truth-value FALSE. On the other hand, an ("intersective")
adjective such as 'woollen' would be assigned a meaning of
the following type: a function from (functions from individuals to
truth-values) to (functions from individuals to truth-values), or a
function of type (*ib*)(*ib*) for short. Thus the
meaning of 'woollen' can take the meaning of
'sweater' (an *ib*) as input and produce the
meaning of 'woollen sweater' (another *ib*) as
output; this is why the meaning of 'woollen' has the type
(*ib*)(*ib*). **woollen(sweater)** is the
specific function of type *ib* that maps sweaters made of wool
to TRUE, and all other individuals to FALSE.



In this framework, a quantified NP such as 'every sweater'
has a meaning which can take the meaning of an intransitive verb
(e.g., 'unravelled'), or more generally, a Verb Phrase
(VP), as input and produce the meaning (truth-value) of a sentence
(e.g. 'every sweater unravelled') as output. Intransitive
verbs and VPs are like common nouns in being of type *ib*. For
example, the VP **quickly(unravelled)** is of type
*ib*, mapping all and only individuals that unravelled quickly
to TRUE. So a quantified NP is a function from inputs of type
*ib* to outputs of type *b*, and is thus of type
(*ib*)*b*. 'Every sweater unravelled
quickly' would be represented as
**(every(sweater))(quickly(unravelled))**, and would
denote the truth-value that is the result of applying a meaning of
type (*ib*)*b*, that of **every(sweater)**,
to a meaning of type *ib*, that of
**quickly(unravelled)** (the adverb
**quickly** itself is of type (*ib*)(*ib*),
like the adjective **woollen**). Rules specific to
**every** guarantee that **every(sweater)**
maps **quickly(unravelled)** to TRUE iff
**quickly(unravelled)** maps to TRUE everything that
**sweater** maps to TRUE.



So far, the apparatus is extensional, which, besides providing only
two possible sentence-meanings, TRUE and FALSE, imposes severe
limitations on the range of concepts we can express. Suppose that the
Scottish clothing company Pringle has a monopoly on the manufacture of
woollen sweaters, and makes sweaters of no other material. Then a
garment is a woollen sweater iff it is a Pringle sweater, meaning that
**woollen(sweater)** and
**pringle(sweater)** are the same function of type
*ib*, and these two terms for that function are everywhere
interchangeable in the type-theoretic language. Then modal operators
such as 'it is contingent that' cannot be in the language,
since interchanging **woollen(sweater)** and
**pringle(sweater)** within their scope should sometimes
lead to change of truth-value, but cannot if the two expressions
receive the same meaning in the semantics. For example, 'it is
contingent that every Pringle sweater is woollen' is true, but
'it is contingent that every woollen sweater is woollen'
is false. Therefore the concept of contingency has no adequate
representation in the type-theoretic (boldface) language.



Shifting to *intensional* type theory deals with this
difficulty. The intension of any expression X is a function from
possible worlds to an extension of the type which that expression has
in the extensional theory just sketched, if it has such an extension,
otherwise to something appropriate for intensional vocabulary such as
'it is contingent that'. An intension which is a function
from possible worlds to items of type ***t*** is
said to be of type *s**t***.
**sweater**, for instance, will have as its intension a
function from possible worlds to functions of type *ib*,
providing for each possible world a function that specifies the
individuals which are sweaters at that world; so
**sweater**'s intension is of type
*s*(*ib*). However, a modal sentential operator such as
'it is contingent that' will have as its intension a
function that, for each possible world, produces the very same
function, which takes as input functions of type *sb* and
produces truth-values as output. So the extension of 'it is
contingent that' at each world is the same function, of type
(*sb*)*b*. (The operator is said to be
*intensional* because its *ex*tension at each world is a
function taking intensions, such as functions of type *sb*, as
input.)



A function of type *sb* is sometimes called a
*possible-worlds proposition*, since it traces the truth-value
of a sentence across worlds. For example, with appropriate assignments
to the constituents,



(13)

**(every(woollen(sweater)))(woollen)**


should be true, that is, refer to TRUE, at every
 world.[5]
 So the intension of (13) is the function ***f***
of type *sb* such that for every world w,
***f***(w) = TRUE. This is a *constant*
intension. On the other hand,



(14)

**(every(pringle(sweater)))(woollen)**


is true at some worlds but false at others, those where Pringle makes
non-woollen sweaters; so its intension is non-constant.



We define the intension of **contingent** to be the
function which, for each world *w* as input, produces as output the
function ***c*** of type (*sb*)*b*
such that for any function ***p*** of type
*sb*, ***c***(***p***)
is true at w iff there are worlds *u* and *v* such that
***p***(*u*) = TRUE and
***p***(*v*) = FALSE (this is the meaning of
'contingent that' in the sense 'contingent
whether'). So the intension of 'contingent' is also
constant, since the same function ***c*** is the
output at every world.



Since **contingent** expects an input of type
*sb*, we cannot write



(15)

**contingent((every(woollen(sweater)))(woollen))**

since in evaluating this formula at a world *w* we would find ourselves
trying to apply the reference of **contingent** at w,
namely, the function ***c*** just defined, to the
reference of **(every(woollen(sweater)))(woollen)** at w,
namely, the truth-value TRUE. But ***c*** requires
an input of type *sb*, not *b*. So we introduce a new
operator, written **^**, such that if X is an expression
and ***t*** is the type of X's reference at each
w, then at each w, the reference of **^**X is of type
*s**t***. **^**X may be read as
'the intension of X', since the rule for
**^** is that at each world, **^**X refers
to that function which for each world w, outputs the reference of X at
w.



If we now evaluate



(16)

**contingent^((every(woollen(sweater)))(woollen))**


at a world w, the result will be FALSE. This is because the function
***p*** of type *sb* that is the reference
of **^((every(woollen(sweater)))(woollen))** at every
world, maps every world to TRUE. So there is no *u* such that
***p***(*u*) = FALSE. But there is such a *u* for
**^((every(pringle(sweater)))(woollen))**, and so



(17)

**contingent^((every(pringle(sweater)))(woollen))**

is TRUE at w. Note that choice of *w* doesn't matter, since the
intension of **contingent** produces the same function
***c*** at every world, and the reference of,
e.g., **^((every(pringle(sweater)))(woollen))**, is the
same function of type *sb* at every world.



Finally, our type-theory, intensional or extensional, is
*higher-order*, because the semantics makes available
higher-order domains of quantification and reference.
**sweater** refers to a property of individuals, a
*first-order* property. **(every(sweater))**
refers to a property of properties of individuals, a second-order
property. For just as **sweater(my favorite garment)**
attributes the property of being a sweater to a certain individual, so
we can think of **(every(sweater))(woollen)** as
attributing a property to the property of being woollen. Which
property is attributed to being woollen? The rules governing
**every** ensure that **(every(F))** is
truly predicated of **G** iff **G** is a
property of every *F*. In that case, **G** has the
property of being a property of every *F*. So
**(every(F))** stands for the property of being a
property of every *F*.



Treating quantified NPs as terms for properties of properties means
they can occur as arguments to any expression defined for properties
of properties. We can even rescue the uncomprehending student's
attempt at 'Jack hit someone', for provided
'hit' is of the right type -- which is easily
arranged -- we can have **(hit(someone))(jack)**.
Here **hit** accepts the property of being a property of
at least one person, and produces the first-order property of hitting
someone, which is then attributed to Jack. In extensional type-theory,
**hit** has the type
((*ib*)*b*)(*ib*) if
**(hit(someone))(jack)** is well-typed and
**jack** is of type
 *i*.[6]



The significance of this for the semantics of intensional transitives
is that we now have a way of representing a reading of, say,



(18)
 Jack wants a woollen sweater


in which the quantified NP is within the semantic scope of the verb
without having scope over a hidden subsentence with a free variable
for the NP to bind: the quantified NP 'a woollen sweater'
can just be the argument to the verb. To allow for the intensionality
of the transitive verb, Montague adopts the rule that if *x*
and *y* can concatenate into a meaningful expression
*xy*, the reference of the functional expression is a function
which operates on the *intension* of the argument expression.
Suppressing some irrelevant detail, this means that if
'wants' syntactically combines with 'a woollen
sweater' to produce the VP 'wants a woollen
sweater', then in its semantics, **want** applies
to the intension of **(a(woollen (sweater)))**, resulting
in the following semantics for (18):



(19)

**want(^(a(woollen(sweater))))(jack)**.[7]


In (19), **a(woollen((sweater))** is within the scope of
**want**. So if we take (19) to represent the notional
reading of (18), the idea that notional readings are readings in which
the quantified NP has narrow scope with respect to the intensional
verb is sustained.


## 5. Revisions and refinements



How does Montague's account of intensional transitives fare
*vis* *a* *vis* the three marks of
intensionality? The existence-neutrality of existential NPs is
clearly supported by (19), for there is nothing to prevent the
application at a world *w* of **want** to
**^(a(woollen(sweater)))** from producing a function
mapping Jack to TRUE even if, at the same w,
**(woollen(sweater))** maps every individual to FALSE
(woollen sweaters don't exist).



Substitution-failure is supported for contingently coextensive
expressions. For instance, (19) does not entail
**want(^(a(pringle(sweater))))(jack)** even if there are
worlds where all and only woollen sweaters are Pringle sweaters, so
long as there are other worlds where this is not so. Let *u* be a world
of the latter sort. Then **a(pringle(sweater))** at *u* and
**a(woollen(sweater))** at *u* are different functions of
type (*ib*)*b*, making
**^(a(pringle(sweater)))** and
**^(a(woollen(sweater)))** different at every world.
Therefore **want(^(a(pringle(sweater))))** may map Jack
to FALSE at worlds where **want(^(a(woollen(sweater))))**
maps Jack to TRUE: since **want** is applied to different
inputs here, the outputs may also be different.



But this result depends on the fact that
**(pringle(sweater))** and
**(woollen(sweater))** are merely contingently
coextensive. If 'water' and 'H2O'
are *necessarily* co-extensive, then wanting a glass of water
and wanting a glass of H2O will be indistinguishable in
higher-order intensional type theory. This failure to make a
distinction, however, traces to the intensionality of the semantics
-- to its being (merely) a possible-worlds semantics -- not
to its being higher-order or type-theoretic. So possible solutions
include (i) augmenting higher-order intensional type theory with extra
apparatus, or (ii) employing a different kind of higher-order type
theory. In both cases the aim is to mark distinctions like that
between wanting a glass of water and wanting a glass of
H2O.



A solution of the first kind, following (Carnap 1947), is proposed in
(Lewis 1972:182-6); the idea is that the meaning of a complex
expression is not its intension, but rather a tree that exhibits the
expression's syntactic construction bottom-up, with each node in the
tree decorated by an appropriate syntactic category label and semantic
intension. But as Lewis says (p. 182), for non-compound lexical
constituents, sameness of intension implies sameness of meaning. So
although his approach will handle the water/H2O problem if
we assume the term 'H2O' has structure that the
term 'water' lacks, it will not without such an
assumption. For the same reason, it cannot explain
substitution-failure involving unstructured proper names, on the usual
view (deriving from Kripke 1972) that identity of extension (at any
world) for such names implies identity of intension. So we have no
account of why admiring Cicero isn't the same thing as admiring
Tully.



A solution of the second kind, employing a different kind of
higher-order type theory, is pursued in (Thomason 1980). In Thomason's
"intentional" logic, propositions are taken as a primitive
category, instead of being analyzed as intensions of type *sb*.
In turns out that a somewhat familiar higher-order type theory can be
built on this basis, in which, roughly, the type of propositions plays
a role analogous to the type of truth-values in extensional type
theory. A property such as **orator**, for example, is a
function of type *ip* (as opposed to *ib*), where
*p* is the type of propositions: given an individual as input,
**orator** will produce the proposition that that
individual is an orator as output. Proper names, however, are not
translated as terms of type *i*, for then
**cicero** and **tully** would present the
same input to **orator**, resulting in the same
proposition as output: **orator(cicero)** =
**orator(tully)**. So there would be no believing Cicero
is an orator without believing Tully is an orator. Instead, Thomason
assigns proper names the type (*ip*)*p*, functions from
properties to propositions. And merely the fact that Cicero and Tully
are the same individual does not require us to say that
**cicero** and **tully** must produce the
same propositional output given the same property input. Instead, we
can have **cicero(orator)** and
**tully(orator)** distinct (see Muskens 2005 for further
development of Thomason's approach).



Applying this to intensional transitives is just a matter of assigning
appropriate types so that the translations of, say, 'Lucia seeks
Cicero' and 'Lucia seeks Tully', are different
propositions (potentially with different truth-values). We need to
keep the verb as function, and we already have the types of
**cicero** and **tully** set to
(*ip*)*p*. The translations of 'seeks
Cicero' and 'seeks Tully' should be functions
capable of accepting inputs of type (*ip*)*p*, such as
**lucia**, and producing propositions as output.
**seeks** therefore accepts input of type
(*ip*)*p* and produces output that accepts input of type
(*ip*)*p* and produces output of type *p*. Thus
**seeks** is of type
((*ip*)*p*)(((*ip*)*p*)*p*), and we
get substitution-failure because **seeks(cicero)** and
**seeks(tully)** can be different functions of type
((*ip*)*p*)*p* so long as **cicero**
and **tully** are different functions of type
(*ip*)*p* (as we already said they should be).
**seeks(cicero)** can therefore map
**lucia** to one proposition while
**seeks(tully)** maps it (not 'her') to
another; and these propositions can have different
 truth-values.[8]



Finally, there is the question whether (19) shows that Montague's
semantics supports notional readings. One problem is that Montague's
semantics for extensional verbs such as 'get' is exactly
the same as for intensional verbs, and it takes an extra stipulation,
or *meaning-postulate*, for 'get', to guarantee
that the extension of **get(^(a(woollen(sweater))))** at
*w* maps Jack to TRUE only if the extension of
**(woollen(sweater))** at *w* maps some individual to TRUE
(you can want a golden fleece even if there aren't any, but you can't
*get* one if there aren't any). So apparently (19)'s pattern
embodies something in common to the notional meaning of 'want a
woollen sweater' and the meaning of 'gets a woollen
sweater', something which is neutral on the existence of woollen
sweaters. This is unintuitive, but is perhaps not a serious problem,
since it can be avoided by a different treatment of extensional
transitives.



A more pressing question is what justification we have for thinking
that (19) captures the notional, 'no particular one',
reading of
 (18).[9]
 On the face of it, (19) imputes to Jack the wanting attitude towards
the property of being a property of a woollen sweater. This is the
same attitude as Jack may stand in to a particular woollen sweater,
say *that* one. But it is not at all clear that we have any
grasp of what a single attitude with such diverse objects could be,
and the difficulty seems to lie mainly with the proposed semantics for
notional readings. What does it mean to have the attitude of desire
towards the property of being a property of a woollen sweater?



Two ways of dealing with this suggest themselves. First, we might
supplement the formal semantics with an elucidation of *what it
is* to stand in a common-or-garden attitude to a property of
properties. Second, we might revise the analysis to eliminate this
counterintuitive aspect of it, but without importing the
propositionalist's hidden sentential contexts.



Both (Moltmann 1997) and (Richard 2001) can be read as providing,
within Montague's general approach, an account of what it is to stand
in an attitude relation to a property of properties. Both accounts are
modal, having to do with the nature of possible situations in which
the attitude is in some sense "matched" by the situation:
an attitude-state of need or expectation is matched if the need or
expectation is met, an attitude-state of desire is matched if the
desire is satisfied, an attitude-event of seeking is met if the search
concludes successfully, and so on. According to Moltmann's account
(1997, 22-3) one stands in the attitude relation of seeking to
**^(a(woollen(sweater)))** iff, in every *minimal
situation* s in which that search concludes successfully,
you find a woollen sweater in s. Richard (2001, p. 116) offers a
more complex analysis that is designed to handle negative quantified
NPs as well ('no woollen sweater', 'few woollen
sweaters', etc.). On this account, a search p
*demands* **^(a(P))** iff for every relevant
success-story *m* = <w, s> for p, things in s with a
property entailing **P** are in the extension of
**^(a(P))** at w. Here s is the set of things that are
found when the search concludes successfully in w.



By contrast, (Zimmerman 1993) and (Forbes 2000, 2006) propose
revisions in (19) itself and its ilk. Zimmerman (161-2) replaces
the quantifier intension with a property intension, since he holds
that (i) unspecific readings are restricted to "broadly"
existential quantified NPs, and (ii) the property corresponding to
the nominal in the existential NP (e.g., 'woollen
sweater') can do duty for the NP itself. Of course, the proposed
restriction of unspecific readings to existentials is controversial
(*cf*. our earlier example, 'Guercino is looking for
every dog on Aldrovandi's estate'). It may also be wondered
whether there is any less of a need to explain what it is to stand in
the seeking relation to a property of objects than to a property of
properties (but for a response to this kind of objection, see
Grzankowski 2018, 146-9).



According to (Forbes 2000) the need for such an explanation already
threatens the univocality of a verb such as 'look for' as
it occurs in 'look for *that* woollen sweater' and
'look for some woollen sweater'. Observing that search
verbs are action verbs, Forbes applies Davidson's event semantics to
them (Davidson 1967). In this semantics, as developed in (Parsons
1990), search verbs become predicates of events, and in relational
(specific) readings, the object searched for is said to be in a
thematic relation to the event, one denoted by 'for'; thus
'some search *e* is for *that* woollen
sweater'. But in unspecific readings, no thematic relation is
invoked; rather, the quantified NP is used to *characterize*
the search. So we would have 'some search *e* is
characterized by **^(a(woollen(sweater)))**', i.e.,
*e* is an a-woollen-sweater search (Forbes 2000, 174-6;
2006, 77-84). What it is for a search to be characterized by a
quantifier, say **^(a(woollen(sweater)))**, is explained
in terms of 'outcome postulates'. For the current example,
as a first approximation, a search is characterized by
**^(a(woollen(sweater)))** iff any course of events in
which that search culminates successfully includes an event of finding
a woollen sweater whose agent is the agent of the search. Similar
postulates can be given for, e.g., the meeting of expectations and the
satisfaction of desires: a state of desire is characterized by
**^(a(woollen(sweater)))** iff any course of events in
which that desire is satisfied includes an event of getting a woollen
sweater whose recipient is the agent of the search (Forbes 2006,
94-129). 



There is therefore a range of different non-propositionalist
approaches to intensional transitives. As we already remarked, one
possibility is that propositionalism is correct for some verbs and
non-propositionalism correct for others. However, there is also the
option that non-propositionalism is correct for all. A
non-propositionalist who makes this claim will have to explain the
phenomena illustrated in (7)-(10), without introducing degrees
of freedom that make it unintelligible that these phenomena do not
arise for all intensional transitives.


## 6. Prior's Puzzle



Intensional transitive verbs are also involved in another puzzle of
substitution-resistance besides the one already discussed. In the
literature on propositional attitude reports, it's the received view
that the complement clauses in such reports refer to propositions. So,
for example, in 'Holmes believes that Moriarty has
returned', the clause 'that Moriarty has returned'
is taken to stand for the proposition that Moriarty has returned. The
whole ascription is then understood to have the form *Rab*,
which in terms of the example means that Holmes (*a*) stands in
the relation of belief (*R*) to the proposition that Moriarty
has returned (*b*). However, as well as being denoted by
*that*-clauses, it seems that propositions are also denoted by
proposition descriptions, noun phrases that explicitly use 'the
proposition', such as, in the previous sentence, 'the
proposition that Moriarty has returned'. So, if the clause and
the description co-denote, we have the following truth: 



(20)
 that Moriarty has returned is the proposition that Moriarty has
returned.


But then we should be able to substitute proposition-description for
*that*-clause, which, indeed, works well enough for
'believes': from 'Holmes believes that Moriarty has
returned' it does seem to follow that Holmes believes the
proposition that Moriarty has returned, even though a side-effect of
the substitution is to change the clausal 'believes' into
its transitive form. However, 'believes' is rather special
in this respect. Despite (20), examples (21a) and (21b) below
appear to have very different meanings:



(21a)
 Holmes {fears/suspects} that Moriarty has returned.


(21b)
 Holmes {fears/suspects} the proposition that Moriarty has
returned.


(21a) may well be true, but it is unlikely that Holmes fears a
proposition, or that some proposition is a thing of which he is
suspicious. (This phenomenon seems first to have been noted in print
by A. N. Prior (1963).) 



That the meaning of the minor premise does not survive substitution is
the rule rather than the exception: we get a similar outcome with
'announce', 'anticipate', 'ask',
'boast', 'calculate', 'caution',
'complain', 'conclude', 'crow',
'decide', 'detect', 'discover',
'dream', 'estimate', 'forget',
'guess', 'hope', 'insinuate',
'insist', 'interrogate' (literary theory),
'judge', 'know', 'love',
'mention', 'notice', 'observe',
'prefer', 'pretend',
'question','realize', 'rejoice',
'require', 'see', 'suggest',
'surmise', 'suspect', 'trust',
'understand', 'vote', 'wish', and
various cognates of these. In some cases, substitution fails because
it is meaning-altering, in others because it is meaning-dissolving (a
selection constraint is violated, or the purported transitive verb
simply doesn't exist in the language). The verbs for which
substitution is acceptable are thinner on the ground: inference verbs
such as 'conclude', 'deduce',
'entail' and 'establish', along with a few
others like 'accept','believe',
'doubt', 'state' and 'verify' (but
for 'believe' see King 2002, 359-60; Forbes 2018,
118; and Nebel 2019, 97-9). 



The puzzle doesn't depend on the credentials of (20) as an identity
sentence. Even if, for whatever reason, it isn't, it is still hard to
see how truth-value can change going from (21a) to (21b), granted
that *the proposition that Moriarty has returned* and *that
Moriarty has returned* are co-denoting. There also doesn't seem to
be a useful application of a traditional account of referential
opacity, such as Frege's (discussed in connection with (2c) above).
Substitution-failure is explained in Fregean terms by co-denoting
expressions having different senses, but it's unclear that adding or
deleting 'the proposition' is a significant enough
difference to change sense. We also expect that examples of
substitution-failure become unrealistic if the subject is attributed
explicit belief in the identity premise. However, adding that Holmes
is absolutely clear about the truth of (20) and has it at the
forefront of his consciousness doesn't make it any more likely that
(21b) is true, even though (21a) is. 



Consequently, there is some appeal to solutions of Prior's Puzzle that
discern an equivocation in the inference, or propose that the crucial
terms, *the proposition that Moriarty has returned* and
*that Moriarty has returned*, aren't really coreferential as
they occur in the inference. An approach of the first kind, in (King
2002), argues that the transitive and clausal forms of the intensional
verb are *polysemous*, that is, weakly ambiguous (the two
senses are related). This has been criticized on the basis of ellipsis
examples, such as 'Bob didn't even mention the proposition that
first-order logic is undecidable, let alone that it is provable'
(Boer 2009, 552), and 'the Soviet authorities genuinely fear a
religious revival, and that the contagion of religion will
spread' (after Nebel 2019, 77). Since these examples don't
strike one as amusingly incongruous, in the way that typical examples
of zeugma do ('All over Ireland the farmers grew potatoes,
barley, and bored'), they are in tension with a postulation of
polysemy. Consequently, Boer (2009) and Nebel (2019) propose that the
problem lies in an equivocation in the terms *the proposition that
Moriarty has returned* and *that Moriarty has returned*. On
both their accounts, it is the propositional description 'the
proposition that...' which fails to denote what one might
expect. On the other hand, as evidence in favor of polysemy, there is
the fact that some cases of ellipsis seem in some way anomalous, such
as 'John heard thunder and that a storm was rolling in'.
Here the anomaly can be explained in terms of *how*
different the two senses of 'heard' are.



Event semantics (see section 5 above) provides an alternative which
may avoid the need for any kind of equivocation. An initial proposal
is made in (Pietroski 2000) for 'explain', which behaves
like 'fear' and 'suspect', as in



(22a)
 Martin explained that the nothing itself nothings.


(22b)
 Martin explained the proposition that the nothing itself
nothings.


(22a) may well be true but (22b) is unlikely. The idea is then that
the clausal and transitive forms of 'explain' take
different thematic complements, content versus theme: with the clausal
verb of (22a), a 'that'-clause provides a content, while
with the transitive verb of (22b), a proposition description provides
a theme, the thing that *gets* explained. Since, as already
noted, a side-effect of the substitution is to change the verb from
its clausal to its transitive form, a consequent side-effect is to
change the role ascribed to the proposition from content to theme.
This account is developed in (Pietroski 2005) and also, as an
extension of the event semantics of (Forbes 2006), in (Forbes
2018).


## 7. The logic of intensional transitives



There may be no such topic as the logic of *propositional*
attitudes: it may be doubted whether 'Mary wants to meet a man
who has read Proust and a man who has read Gide'
*logically* entails 'Mary wants to meet a man who has
read Proust'. Even if standing in the wanting-to-be-true
attitude to *I meet a man who has read Proust and a man who has
read Gide* somehow necessitates standing in the wanting-to-be-true
attitude to *I meet a man who has read Proust*, the
necessitation appears to be more psychological than logical. On the
other hand, what we might call 'objectual attitudes', the
non-propositional attitudes ascribed by intensional transitives, seem
to have a logic (for a compendium of examples, see Richard 2000,
105-7): 'Mary seeks a man who has read Proust and a man
who has read Gide' does seem to entail 'Mary seeks a man
who has read Proust'.



Yet, as Richard notes (Richard 2001, 107-8), the inferential
behavior of quantified complements of intensional transitives is still
very different from the extensional case. For example (his
'Literary Example'), even if it is true that Mary seeks a
man who has read Proust and a man who has read Gide, it may be false
both that she seeks at most one man and that she seeks at least two
men; for she may be indifferent between finding a man who has read
both, versus finding two men, one a reader of Proust but not Gide, the
other of Gide but not Proust. Contrast 'saw',
'photographed', or 'met': if she met a man who
has read Proust and a man who has read Gide, it cannot be false both
that she met at most at one man and also that she met at least two
men. As Richard insists, it is a constraint on any semantics of
intensional transitives that they get this type of case right.



By contrast, in other cases, even very simple ones, it is
controversial exactly what inferences intensional transitives in
unspecific readings support. If Mary seeks a man who has read Proust,
does it follow that she seeks a man who can read? After all, it is
unlikely that a comic-book reader will satisfy her tastes in
 men.[10]
 If Perseus seeks a mortal gorgon, does it follow that he seeks a
 gorgon?[11]
 After all, if he finds an immortal gorgon, he is in trouble.
Zimmerman (1993, 173) takes it to be a requirement on accounts of
notional readings that they validate these deletion or
"weakening" inferences. But there are characterizations of
unspecific readings on which these inferences are in fact invalid, for
instance, a characterization in terms of *indifference* towards
which object of the relevant kind is found (Lewis uses such an
'any one would do' characterization in Lewis 1972, p.
199). For even if it is true that Mary seeks a man who has read
Proust, and any male Proust-reader would do, it does not follow that
Mary seeks a man who can read, and any man who can read would do. For
not every man who can read has read Proust.



Is there anything intrinsic to the indifference characterization of
unspecificity ('any one would do') that we can object to
while leaving the status of weakening inferences open? One objection
is that the characterization does not work for every verb or
quantifier: 'Guercino painted a dog, any dog would do'
makes little sense, and 'the police are looking for everyone who
was in the room, any people who were in the room would do' is
not much better. More importantly, the characterization seems to put
warranted assertibility out of reach, since the grounds which we
normally take to justify ascribing an existentially quantified
objectual attitude will rarely give reason to think that the agent has
absolutely no further preferences going beyond the characterization of
the object-kind given in the ascription (probably Mary would pass on
meeting a male psychopathic killer who has read Proust; see further
Graff Fara 2013 for analogous discussion of desire).



Still, this is not to validate weakening inferences; for that we would
need to show that the more usual gloss of the unspecific reading,
using a 'but no particular one' rider, supports the
inferences as strongly as the indifference characterization refutes
them. And it is unclear how such an argument would proceed (see
further Forbes 2006, 94-6). In addition, making a good case that
the inferences are intuitively valid is one thing, getting the
semantics to validate them is another. Both the propositionalist and
the Montagovian need to add extra principles, since there is nothing
in their bare semantics to compel these inferences. For even if Jack
stands in the wanting relation to
**^(a(woollen(sweater)))**, that by itself is silent on
whether he also stands in the wanting relation to
**^(a(sweater))**. The accounts of Moltmann and Richard
both decide the matter positively, however (e.g., if in every minimal
situation in which Jack's desire is satisfied, he gets a woollen
sweater, then in every such situation, he gets a sweater; so he wants
a sweater).



The intuitive validity of weakening can also be directly challenged.
For example, via weakening we can infer that if A is looking for a cat
and B is looking for a dog, then A and B are looking for the same
thing (an animal). For discussion of this kind of example, see
(Zimmerman 2006), and for the special use of 'the same
thing', (Moltmann 2008). Asher (1987, 171) proposes an even more
direct counterexample. Suppose you enter a competition whose prize is
a free ticket on the Concorde to New York. So presumably you *want
a free ticket* on the Concorde. But you don't *want a
ticket* on the Concorde, since you know that normally these are
very expensive, you are poor, and you strictly resist desiring the
unattainable. Asher is here assimilating notional uses of indefinites
to generics, which on his account involve quantification over
*normal* worlds. So if for some bizarre reason you want a
sloop, but one whose hull is riddled with holes, it will not be
literally true to say you want a sloop.



Undeniably there is a real phenomenon here, but perhaps it belongs to
pragmatics rather than semantics. If I say 'I want a sloop',
someone who offers to buy me any sloop floating in the harbor could
reasonably complain 'You should have said that' if I decline the
offer on the grounds that none of those sloops meets my unstated
requirement of having a hull riddled with holes. But my aspirational
benefactor's complaint might be justified because normality is a
*default implicature* or presupposition that a co-operative
speaker is under some obligation to let her audience know isn't in
force, when it isn't. It is still literally true, on this view, that
you want a sloop, despite the idiosyncrasy of the details of your
desire. However, this is far from the end of the story. Those with
doubts about weakening will find the discussion in (Sainsbury 2018,
129-133) congenial.



Another interesting logical problem concerns the "conjunctive
force" of disjoined quantified NPs in objectual ascriptions.
There is a large literature on the conjunctive force of disjunction in
many other contexts (e.g., Kamp 1973, Loewer 1976, Makinson 1984,
Jennings 1994, Zimmerman 2000, Simons 2005, Fox 2007), for instance as
exhibited in '*x* is larger than *y* or
*z*' and 'John can speak French or Italian to
you'. In these cases the conjunctive force is easily captured by
simple distribution: '*x* is larger than *y* and
larger than *z*', 'John can speak French to you and
can speak Italian to
 you'.[12]
 However, with intensional transitives we find the same conjunctive
force, but no distributive articulation. If we say that Jack needs a
woollen sweater or a fleece jacket, we say something to the effect
that (i) his getting a woollen sweater is one way his need could be
met, *and* (ii) his getting a fleece jacket is another way his
need could be met. But 'Jack needs a woollen sweater or a fleece
jacket' does *not* mean that Jack needs a woollen sweater
*and* needs a fleece jacket. This last conjunction ascribes two
needs, only one of which is met by getting a satisfactory woollen
sweater. But the latter acquisition by itself meets the disjunctive
need for a woollen sweater or a fleece jacket. So there is a challenge
to explain the semantics of the disjunctive ascription, while at the
same time remaining within a framework that can accommodate all cases
of conjunctive force -- comparatives, various senses of
'can', counterfactuals with disjunctive antecedents
('if Jack were to put on a woollen sweater or a fleece jacket
he'd be warmer') and so on; see further (Forbes 2006,
97-111).



A penultimate type of inference we will mention is one in which
intensional and extensional verbs both occur, and the inference seems
valid even when the intensional VPs are construed unspecifically. An
example:



(23a)
 Jack wants a woollen sweater

(23b)
 Whatever Jack wants, he gets

(23c)
 Therefore, Jack will get a woollen sweater


Obviously, (23a,b) entail (23c) when (23a) is understood specifically.
But informants judge that the inference is also valid when (23a) is
understood unspecifically, with 'but no particular one'
explicitly appended. If we seek a validation of the inference that
hews to surface form, Montague's uniform treatment of intensional and
extensional verbs has its appeal: (23b) will say that for whatever
property of properties ***P*** Jack stands in the
wanting relation to, he stands in the getting relation to. So the
inference is portrayed as the simple *modus ponens* it seems to
be. It would then be the task of other meaning-postulates to carry us
from his standing in the getting relation to
**^(a(woollen(sweater)))** to there being a woollen
sweater such that he gets it.

 The final example to be considered
here involves fictional or mythical names in the scope of intensional
transitives. An example (Zalta 1988, 128) of the puzzles these can
lead to is:


(24a)
 The ancient Greeks worshipped Zeus.

(24b)
 Zeus is a mythical character.

(24c)
 Mythical characters do not exist.

(24d)
 Therefore, the ancient Greeks worshipped something that does
(did) not exist.


Or even:



(24e)
 Therefore, there is something that doesn't exist such that the
ancient Greeks worshipped it.


One thing the example shows is that specific/unspecific is not to be
confused with real/fictional. (24a) is a true specific ascription,
just as 'the ancient Greeks worshipped Ahura Mazda' is a
false one. (24b) is also true. So the ancient Greeks, who would not
have *knowingly* worshipped a mythical character, were making a
rather large mistake, if one of a familiar sort.



(24c) is also true, if we are careful about what 'do not
exist' means in this context. It is contingent that Zeus-myths
were ever formulated, and one sense in which we might mean (24c) turns
on the assumption that fictional and mythical characters exist iff
fictions and myths about them do. In this sense, (24c) is false,
though an actual fictional character such as Zeus would not have
existed if there had been no Zeus-myths. This also explains why (24a)
and (24b) can both be true: 'Zeus' refers to the mythical
character, a contingently existing abstract object.



However, by far the more likely reading of (24c) is one on which it
means that mythical characters are not real. Zeus is not flesh and
blood, not even immaterial flesh and blood. With this in mind, (24d)
and (24e) are both true. The quantifier 'something' ranges
over a domain that includes both real and fictional or mythical
entities, and there is something in that domain, the mythical
character, which was worshipped by the ancient Greeks and which is not
in the subdomain of real items.



This gets the right truth-values for the statements in (24), but might
be thought to run into trouble with the likes of 'Zeus lives on
Mt. Olympus': if 'Zeus' refers to an abstract
object, how can Zeus live anywhere? One way of dealing with this kind
of case is to suppose, evidently plausibly, that someone who says
'Zeus lives on Mt. Olympus' and knows the facts means



(25)
 According to the myth, Zeus lives on Mt. Olympus.


On the other hand, if an ancient Greek believer says 'Zeus lives
on Mt. Olympus', he or she says something false, there being no
reason to posit a covert 'according to the myth' in this
case.



However, even the covert operator theory might be contested, on the
grounds that within its scope we are still unintelligibly predicating
'lived on Mt. Olympus' of an abstract object. Simply
prefixing 'according to the myth' to the unintelligible
cannot render it intelligible. But there is the evident fact that (25)
is both intelligible and true. So either prefixing 'according to
the myth' *can* render the unintelligible intelligible,
or what is going on in the embedded sentence is not to be construed as
standard predication. For further discussion of these matters, see,
for example, van Inwagen 1977, Parsons 1980, Zalta 1988, Thomasson
1998, and Salmon 2002.