CHAPTER XII

QUANTIFICATION AND OPACITY

ALI AKHTAR KAZMI

In a 1943 paper, Quine says: "No pronoun (or variable of quantification) within an opaque context can refer back to an antecedent (or quantifier) prior to that context."1

The view articulated in these words, which I shall describe
as Quine’s Thesis, occupies a central position in many of his later papers,
and informs large parts of Chapters IV, V, and VI of *Word and Object*.

Quine’s thesis should be distinguished from his misgivings about the intelligibility of essentialism, the doctrine that, among the traits of an object some are essential and others are not, to which he thinks quantified modal logic to be committed. Likewise, Quine’s thesis should be distinguished from his more recent doubts about the intelligibility of certain epistemological doctrines to which he thinks the quantified logic of belief to be committed. Quine’s thesis is about quantification in general. It seems to be his view that quantification into opaque constructions faces a purely technical difficulty can be established on the basis of logical and semantic considerations alone. Thus, in "Quantifiers and Propositional Attitudes", after distin-guishing what he calls "the relational senses" of propositional attitudes from their corresponding "notional senses", he notes:

However, the suggested formulations of the relational sense
3/4 *viz*.,

( x) (*x* is a lion. Eanest strives that Ernest finds *x*)

( x) (*x* is a sloop. I wish that I have *x*)

( x) (Ralph believes that *x* is a spy)

( x) (Witold wishes that *x* is president)

all involve quantifying into a propositional attitude idiom from outside. This is a dubious business.2

The rest of that paper is an attempt to offer a reconstruction of the relational senses of propositional attitudes which does not involve quantifying into opaque constructions. Similarly, in "Inten-tions Revisited", after noting that quantified modal logic also involves the allegedly illicit quantifying into opaque constructions, Quine offers a reconstruction of quantified modal discourse which is free from this alleged defect.

In Section 1.1 of this paper, I present a general characteri-zation of referential opacity, and contrast it with the notion of a purely referential occurrence of a singular term. In Section 1.2 and 1.3, I examine two lines of argument in defence of Quine’s Thesis, and, argue that they fail to establish it.

**1.1**

Quine characterizes referential opacity in terms of a principle that h describes as "the principle of substitutivity". Quine formulates this principle in these words: ". . . given a true statement of identity, one of its two terms may be substituted for the other in any true statement nad the result will be true."3 Making allowarances for Quine’s use of the word "statement", this principle may be understood as the claim that:

(**A**) for all expressions and *ß*, if, relative to
an assignment ** I**, =

It should be recognized, as Quine has frequently stressed,
that (**A**) is false. For example, the propositions expressed by

(1) ‘Giorgione’ = Barbarelli, and

(2) ‘Giorgione’ contains nine letters, are true, whereas,

(3) ‘Barbarelli’ contains nine letters, expresses a false proposition. Similarly,

(4) Giorgione was so-called because of his size, expresses a true proposition, but

(5) Barbarelli was so-called because of his size,

does not expresses a true proposition. Counterexamples to (**A**)
are not confined to those cases which involve substitution within contexts of
quotation. For instance, though:

(6) 9 = the number of planets,and

(7) It is necessary that 9 is odd, both express true propositions,

(8) It is necessary that the number of planets is odd, expresses a false proposition.5

The temptation to think that (**A**) is true might arise
from a failure to distinguish (**A**) from the principle that:

(**B**) The universal closure of every instance of the
schema

(9) ( *x*) ( *y*) (*x*=*y* (F*x* F*y*))

or a notational variant of (9), expresses a true proposition.

But, notice that whereas the proposition that (1) and (4)
express true propositions, and (5) fails to expresses a true proposition
falsifies (**A**), it does not falsify (**B**); and, therefore, (**B**)
does not entail (**A**).6

Quine argues in defense of (**B**) as follows:

(**B**) does have the air of a law; one feels that any
interpretation of "F*x*" violating (**B**) would be simply a
distortion of the manifest intent of `F*x*’. Anyway I hope one feels
this, for there is good reason to. Since there is no quantifying into an opaque
construction, the position of `*x*’ and `*y*’ in `F*x*’ and
`F*y*’ must be referential if `*x*’ and `*y*’ in those
positions are to be bound by the initial `( *x*)’ and `( *y*)’ of
(9) at all. Since the notation of (9) manifestly intends the quantifiers to bind
`*x*’ and `*y*’ in all four shown places, any interpretation of `F*x*’
violating (**B**) would be a distortion.7

Now, even if one were to disagree with the details of Quine’s
argument, his conclusion that nay interpretation of ‘F*x*’ violating (**B**)
would be a distortion seems indisputable. One is inclined to say that (**B**)
is false, only if there is a sequence and an expression **F**, such that
there is an assignment under which the element of the sequence assigned to the
free occurrences of *x* and *y* in F*x* and
F*y* respectively are
identical; the sequence satisfies F*y* but
fails to satisfy F*x* . But, if
there is an assignment under which a sequence satisfies F*x*
, then, the element of this sequence assigned to the free
occurrences of *x* in F*y* ,
call it ‘*a*’, is in the extension of **F** under that assignment.
And, if, under that assignment, the element of the sequence assigned to the free
occurrences of *y* in F*y* ,
call it ‘*a’*’, is identical with *a*, *a’* is in the
extension of **F** under that assignment; and, therefore, under that
assignment, the sequence satisfies F*y* .
Though one is inclined to say this, it is unlikely that this would satisfy
critics of (**B**). For in the claim that if *a* is identical with *a’*,
then, if *a* is in the extension of **F** under an assignment, the *a’*
is in the extension of **F** under that assignment, a critic of (**B**)
will see yet another appeal to (**B**).

Some critics of (**B**), on the other hand, are likely to
argue that (**B**) is false, because, for example, (i)

(10) ( *x*) ( *y*) (*x*=*y* (it is
necessary that *x* is odd it is necessary that *y* is odd))

is an instance of (9), and, (ii) the proposition expressed by (10) is falsified by the proposition expressed by

(9)=the number of planets. It is necessary that 9 is odd. (It is necessary that the number of planets is odd)).

An advocate of (**B**), then, must reject either (i) or
(ii). Consider, for instance:

(11) ( *x*) ( *y*) (*x*=*y* (‘*x*’
is the 24th letter of the alphabet ‘*y*’ is the 24th letter of the
alphabet)).

There is, presumably, a way of understanding (11) according to which it exereses a false proposition, a proposition which is also expressed by, for instance:

(12) ( *w*) ( *z*) (*w*=*z* (‘*x*’
is the 24th letter of the alphabet ‘*y*’ is the 24th letter of the
alphabet)).

But it is unlikely that it would be thought that the
proposition that (11) expresses a false proposition falsifies (**B**).
Instead, one is inclined to say that (11) is not really an instance of (9), that
given the interpretation of:

‘*x*’ is the 24th letter of the alphabet,

which is required for (11) to express a false proposition,

‘*x*’ is the 24th letter of the alphabet,

is not an open sentence. Now, some advocates of (**B**)
would be inclined to assimilate the case of (10) to that of (11). They would be
inclined to say that (10) is not really an instance of (9) either, because,

It is necessary that *x* is odd,

is not an intelligible open sentence. However, the apparent intelligibility of such sentences as:

There is something such that it is necessary that is odd,

and

The number of planets is such that it is necessary that it is odd, suggests, on the contrary, that

It is necessary that *x* is odd,

is an intelligible open sentence, and that, therefore, (10)
is an instance of (9). But, if (10) is indeed an instance of (9), then, (**B**)
is true only is (ii) is false.

Quine takes the falsity of (**A**) as evidence that an
occurrence of some singular term in a sentence is not purely referential. For
instance, in ‘Reference and Modality’, he writes: ‘Failure of
substitutivity reveals merely that the occurrence to be supplanted is not purely
referential, that is, that the statement depends not only on the object, but on
the form of the name.’8 And
elsewhere in the same essay, he notes: the failure of substitutivity shows that
the occurrence of the personal name in (4) is not purely referential. These
remarks indicate that Quine would endorse the following principle"

(**C**) For any sentence ** S**, any singular
term , and any

Since, (1) and (4) express true propositions, and (5) does
not express a true proposition, if (**C**) is true, then, the occurrence of
‘Giorgione’ in (4), and, the occurrence of ‘Barbarelli’ in (5) are not
purely referential. Similarly, since (6) and (7) express true propositions, and
(8) does not express a true proposition, if (**C**) is true, then, the
occurrence of ‘9’ and ‘the number of planets’ in (7) and (8)
respectively are both not purely referential. It is worth stressing that (**C**)
is a strong principle. If (**C**) is true, it is also true that:

(**D**) For any sentences ** S** and

Though there is evidence that Quine would endorse (**C**),
there is also evidence that he does not intend (**C**) to be taken as part of
a definition of ‘a purely referential occurrence of a singular term’, then,
we are owed an account of what this expression means. Quine has, at times,
described a purely referential occurrence of a singular term in a sentence as an
occurrence of a singular term ‘used in a sentence purely to specify its object’.9
Quine’s remark that ‘failure of substitutivity reveals merely that the
occurrence to be supplanted is not purely referential, that is, that the
statement depends not only on the object but on the form of the name’, may
appear more helpful.10 Presumably,
the thought is that the only contribution a purely referential occurrence of a
singular term in a sentence makes towards determining the truth-value of that
sentence is the specification of the object it refers to. One might, then
propose to understand a purely referential occurrence of a singular term in a
sentence as follows:

(**E**’) For any sentence ** S**, any
non-vacuous singular term , and any

(**E**’) accords with some of the remarks in the
literature about the concept of a purely referential occurrence of a singular
term. If (**E**’) is true, then, the first occurrence of ‘Giorgione’ in

Giorgione was called ‘Giorgione’ because of his size, is purely referential, since, this sentence exereses a true proposition if and only if, for any variable Giorgione satisfies was called ‘Giorgione’ because of his size.

On the other hand, given (**E**’), the occurrence of ‘Giorgione’
in

(4) Giorgione was so-called because of his size,

is presumably, not purely referential. We want to say that for any variable , Giorgione does not satisfy was so-called because of his size.

For any variable ,

was so-called because of his size,

is not a kind of sentence that anything satisfies, and,
hence, Giorgione does not satisfy it; but (4) expresses a true proposition if (**E**’)
is true, the occurrence of ‘Giorgione’ in (4) is not purely referential.

However, it should be noted that an advocated of (**C**)
is in no position to endorse (**E**’). Surely we also want to say that, for
any variable , Barbarelli does not satisfy was so-called
because of his size.

For any variable , was so-called because of his size, is not a kind of sentence that anything satisfies, and, hence, Barbarelli does not satisfy it; but

(5) Barbarelli was so-called because of his size, does
not express a true proposition, and, hence, if (**E**’) is true, the
occurrence of ‘Barbarelli’ in (5) is purely referential. But, since unlike
(5), (4) and

(1) Giorgione = Barbarelli,

express true proposition, if (**C**) is true, the
occurrence of ‘Barbarelli’ in (5) is not purely referential; and, hence, if
(**E**’) is true, (**C**) is not true.

It would seem that our present difficulty arises because (**E**’)
fails to take into account the fact that, for any variable , was
so-called because of his size, is not a kind of sentence
that anything would either satisfy it or its denial. This suggests that we
should revise (**E**’) as follows:

(**E**’’) For any sentence ** S**, any
non-vacuous singular term , and any

Unlike (**E**’), (**E**’’) is not in conflict
with (**C**). It is not true that if (5) does not express a true proposition,
and, for any variable a, Barbarelli does not satisfy was
so-called because of his size, then, (**E**’’) is
true only if the occurrence of ‘Barbarelli’ in (5) is purely referential. A
further condition needs to he met in order for the occurrence of ‘Barbarelli’
in (5) to be purely referential, i.e. that for any variable , was
so-called because of his size, is an open sentence; and,
surely that is not the case.

Though (**E**’’) is not in conflict with (**C**),
it has another consequence which deserves attention. Consider, for instance, the
following sentence:

(i) It is possible that the number of planets is odd.

One would be inclined to say that the occurrence of ‘the
number of planets’ in (i) is not purely referential. But, if (**E**")
is true, and, the occurrence of ‘the number of planets’ in (i) is not purely
referential, then, given that ‘*x*’ is a variable,

(ii) It is possible that *x* is odd,

is not an open sentence. For, suppose that (ii) is an open
sentence. Then, surely, 9, the number of planets, satisfies it, and, since, (i)
express a true proposition, if (**E**’’) is true, then, the occurrence of
‘the number of planets’ in (i) is purely referential. Hence, if we are
inclined to say that (ii) is an open sentence and that the occurrence of ‘the
number of planets’ in (i) is not purely referential, we had better reject (**E**").
However, even if these are grounds for rejecting (**E**"), these are not
grounds for rejecting the following consequence of (**E**"):

(**E**) For any sentence ** S**, any non-vacuous
singular term , and any

It is worth noting that (**E**) is a weaker principle than
(**C**). Unlike (**C**), (**E**) does not guarantee the truth of (**D**).
If (**E**) is true, then, it is true that

(**D**’) for any sentences ** S** and

Consider, for instance, sentences (6), (7), and (8). Since (6) expresses a true proposition, for any variable , 9 satisfies

It is necessary that is odd,

if and only if, the number of planets, satisfies it. But,
since (7) expresses a true proposition, and (8) does not express a true
proposition, if (**E**) is true, then either the occurrence of ‘9’ in
(7), or the occurrence of ‘the number of Dlanets’ in (8) is not Durelv
referential. Of course. if, for some variable ,

It is necessary that is odd,

is an not open sentence, then, the occurrence of ‘9’ in
(7), and, the occurrence of ‘the number of planets’ in (8) fails to be
purely referential. But, it does not follow from (**E**), or from (**E**)
and the fact that (6) and (7) express true propositions and (8) does not, that
for some variable ,

It is necessary that is odd, is not an open sentence.

Now, (**E**) is in conflict with some of Quine’s remarks
about the concept of a purely referential occurrence. Apparently, Quine thinks
that not only (**C**) is true but the following stronger principle (**C**’)
is true as well:

(**C**’) For any sentence ** S**, any singular
term

If (**C**’) is true, then, the occurrence of ‘Giorgione’
in

(i) ‘Giorgione’ names a chess player,

is purely referential. But, surely, we want to say that, for
any variable *, ‘ ‘ *names a chess player,

is not a kind of sentence such that anything would either
satisfy it or its denial, that it is not an open sentence. But, if for any
variable , *‘ ‘ *names a chess player, is
not an open sentence, then, (**E**) is true only if (**C**’) is not
true.

(**E**) purports to give the necessary conditions of a
concept which I think, are of interest in discussions of referential opacity. I
propose that we accept (**E**), and that therefore (**C**’) should be
rejected. As for Quine’s remarks about (i), the intuitions which underlie it
are captured by another distinction that Quine draws attention to.

Quine writes:

In sentences there are positions where the term is used as a means simply of specifying its object, or purporting to, for the rest of the sentence to say something about, and there are positions where it is not. An example of the latter sort is the position of ‘Tully’ in:

(1) ‘Tully was a Roman’ is trochaic.

When a singular term is used in a sentence to specify its object, and the sentence is true of the object, then certainly the sentence will stay true when any other singular term is substituted that designates the same object. Here we have a criterion for what may be called purely referential position: the position must be subject to the substitutivity of identity. That the position of ‘Tully’ in (1) is not purely referential is reflected in the falsity of what we get by supplanting ‘Tully’ in (1) by ‘Cicero’.11

This passage presents a two-fold distinction: one, a
distinction among positions occupied by singular terms in a sentence, and, two,
a distinction among uses of singular terms in a sentence. Substitutability *Salva
veritate *of coreferential singular terms is offered as a criterion for
distinguishing those positions of a singular term in a sentence which are purely
referential from those which are not; but, what is apparently given as a
justification for this criterion is a claim which involves distinguishing those
uses of a singular term in a sentence which are a means simply of specifying its
object from those uses which are not. Quine has frequently referred to the
latter distinction as a distinction between a purely referential occurrence of a
singular term in a sentence and other kinds of occurrence. To avoid confusion
between Quine’s distinction among positions, and the associated distinction
among occurrences which is partially characterized in (**E**), let us agree
to use the phrase ‘reverentially transparent position’ in place of Quine’s
‘purely referential position’. I shall understand by ‘the position of an
occurrence of a singular term in a sentence ** S**’ the result of
deleting that occurrence of from

(**F**) For any sentence ** S**, any singular
term , and any

And, following Quine, I shall say that the position of an occurrence of a singular term in a sentence is reverentially opaque if and only if it is not reverentially transparent. The position of the occurrence of ‘9’ in ‘9 is odd’ is presumably reverentially transparent, but, the position of the occurrence of ‘9’ in

(7) It is necessary that 9 is odd,

is referentially opaque. Notice that the position of some
occurrence of a singular term in a sentence is reverentially opaque if and only
if (**A**) is false.

I shall say that a one-place sentential operator **O** is
reverentially transparent, if and only if, any position of** Z** of an
occurrence of a singular term in a sentence is reverentially transparent only if
**OZ** is
reverentially transparent; and, that a sentential operator is reverentially
opaque, if and only if, it is not reverentially transparent. The sentential
operators ‘It is true that’, and, ‘It is not the case that’, are
reverentially transparent; but ‘It is necessary that’ is reverentially
opaque, since ‘__ __is odd’ is reverentially transparent, but ‘It is
necessary that is odd’ is not.

The concept of referential transparency of a position, as one
would expect, is closely connected with that of purely referential occurrence.
Suppose that the position of an occurrence, *w*, of a singular term in a
sentence ** S**, is not reverentially transparent. Given (

Quine notes that the existence of reverentially opaque
positions shows not only that (**A**) is false, but that existential
generalization is the principle that:

(**G**) For any sentences ** S** and

As Quine notes, the existence of vacuous singular terms
falsifies (**G**); ‘There is no such thing as Pagasus’ expresses a true
proposition, but, ‘( *x*) There is no such thing as *x*’ does not
expresses a true proposition. (**G**) is also falsified by some pairs of
sentences consisting of (i) a sentence containing an occurrence of a singular
term which is not purely referential, and, (ii) an existential generalization of
such an occurrence of a singular term in that sentence. Consider, for instance,
(4). (4) expresses a true proposition, but, if (**G**) is true, then,

(4') ( *x*) *x* was so-called because of his size,

expresses a true proposition as well. But, surely we would
say that (4') does not express any proposition, and that, therefore, it does not
express a true proposition; and hence, (**G**) is false. And consider (2).
Since (2) expresses a true proposition, if (**G**) is true, then,

(2') ( *x*) ‘*x*’ contains nine letters,

expresses a true proposition as well. Now, it is not clear
what sense is to be made of (2). Perhaps, one is to think of (2) as expressing
the same proposition that ‘*x*’, the 24th letter of alphabet contains
nine letters. If so, (**G**) is false.

From considerations such as these, Quine appears to conclude that ‘if to a reverentially opaque context of a variable we apply a quantifier, with the intention that it govern that variable from outside reverentially opaque context, then what we commonly end up with is unintended sense or nonsense. . . . In a word, we cannot in general quantify into reverentially opaque contexts’.14 Making allowance for Quine’s allusion to unintended sense, Quine’s claim in this passage may be formulated as:

(**H**) An occurrence of a variable in a sentence may be
bound by a quantifier outside of that sentence only if the position of that
occurrence of the variable in the sentence is reverentially transparent.

Since the position of the occurrence of ‘*x*’ in
"‘*x*’ contains nine letters", and, the position of the
occurrence of *x*’ in ‘*x* was so-called because of his size’
are both reverentially opaque, if (**H**) is true, the second occurrence of
‘*x*’ in (2) and, the second occurrence of ‘*x*’ in (4'), both
fail to be bound by the initial quantifiers in (2') and(4 )respectively.

(**H**) is to be distinguished from the claim that if an
occurrence of a singular term in a sentence is not purely referential, then,
existential generalization on that occurrence is unwarranted. The latter is
suggested by the pairs of sentences (2) and (2'), and (4) and (4'), and Quine, I
think, endorses it; but, it is the stronger (**H**), which articulates Quine’s
frequently repeated assertion that there is no quantification into reverentially
opaque contexts.

1. 2.

Is (**H**) true?

In a recent paper Kaplan writes:

I have concluded that in 1943 Quine made a mistake. He
believed himself to have given a proof of a general theorem regarding the
semantical interpretation of any language that combines quantification with
opacity. The purported theorem says that in a sentence, if a given position,
occupied by a singular term, is not open to substitution by co-designative
singular terms salva *veritate, *then that position cannot be occupied by a
variable bound to an initially placed quantifier. The proof offered assumes that
quantification receives its standard interpretation. But the attempted proof is
fallacious. And what is more, the theorem is false.15

Kaplan goes on to reconstruct the alleged proof as follows:

Step 1: A purely designative occurrence of a singular term , in formula is one in which is used solely to designate the object. (This is a definition)

Step 2: If has a purely designative occurrence in , then the truth-value of depends only on what designates, not how designates. (From 1)

Step 3: Variables are devices of pure reference, they cannot have non-purely designative occurrences. (By standard semantics)

Step 4: If and *ß* designate the same thing, but and
differ in truth-value, the occurrences of , in and *ß *in *ß* are
not purely designative. (From 2)

Now assume (5.1): and *ß* are co-designative singular
terms, and and *ß* differ in truth-value, and (5.2):* *is a variable
whose value is the object designated by and *ß*.

Step 6: Either and differ in truth-value or *ß* and
differ in truth-value. (From (5.1) since and *ß* differ.)

Step 7: The occurrence of in fg is not purely designative. (From 5.2, 6, and 4)

Step 8: is semantically incoherent. (From 7 and 3)16

Kaplan notes:

All but one of these steps seem to me to be innocuous. That
is step 4 which, of course, does *not *follow form 2. All that follows from
2 is that at least one of the two occurrences is not purely designative. When 4
is corrected in this way, 7 no longer follows. The error of 4 appears in later
writings in a slightly different form. It is represented by an unjustified shift
from talk about *occurrences *to talk about *positions. *Failure of
substitution does show that some occurrence is not purely referential. (Shifting
now from ‘designative’ language of ‘Notes on Existence and Necessity’ to
the ‘referential’ language of ‘Reference and Modality’). From this it is
concluded that the context (read ‘position’) is reverentially opaque. And
thus what the context expresses ‘is in general not a trait of the object
concerned, but depends on the manner of referring to the object’. Hence, ‘we
cannot properly quantify into a reverentially opaque context.’17

If we understand the notation of ‘* *‘ in Step 4 as
standing for any sentence ** S** which contains one or more occurrences
of a singular term , and ‘

** S**:

Suppose, moreover, that the position of the displayed
occurrence of in ** S** is not reverentially transparent. Then, there
is a sentence

** S’**:

and, there is an assignment ** I** relative to which
=

** S’’**:

and suppose that, relative to ** I**, the value of

(**J**) an occurrence of a variable in a sentence may be
bound by a quantifier outside the sentence only if that occurrence is purely
referential,

then, the occurrence of in ** S**’’ may not be
bound by a quantifier outside of

Are (**D**) and (**J**) true? To answer this question
we need to know what is for an occurrence of a singular term in a sentence to be
purely referential. Quine remarks: ‘Failure of substitutivity reveals merely
that the occurrence to be supplanted is not purely referential’. I formulated
this claim in Section 1.1 as (**C**). It is easily seen that (**C**) is
true if and only if (**D**) is true. Perhaps, it would be thought that (**C**)
is one half of a definition of ‘a purely referential occurrence’. It would
then be argued that if (**C**) is a truth of definition, (**D**) must be
true. But, as we have seen, if (**D**) and (**J**) are true, (**H**) is
true; and surely, the argument would go on, (**J**) is a truth of standard
semantics; hence, (**H**) is true.

Now, I think that if (**J**) is to appear as a premise in
any argument for (**H**), we had better not construe (**C**) as a truth of
definition. Notice that according to (**C**), an occurrence of a singular
term in a sentence is purely referential only if its position in that sentence
is reverentially transparent. But, if (**C**) is a truth of definition, then,
it is a truth of definition that if

(**J**) an occurrence of a variable in a sentence may be
bound by a quantifier outside the sentence only if that occurrence is purely
referential

then

(**J**’) an occurrence of a variable in a sentence may
be bound by a quantifier outside that sentence only if the position of that
occurrence of the variable in that sentence is reverentially transparent.

And (**J**’) is (**H**). Hence, if (**C**) is a
truth of definition (**J**) can appear as a premise in an argument for (**H**)
only on pain of circularity.

In section 1.1, I proposed that we accept (**E**). I
argued that (**E**) is a weaker principle than (**C**); that though (**D**)
is a consequence of (**C**), it is not a consequence of (**E**). If (**E**)
is true then it is true that

(i) if a sentence S contains an occurrence of a singular term a, and

(ii) if ** S**’ is the result of substituting

(iii) relative to some assignment ** I**, =

(iv) it is not the case that relative to ** I**,

(v) either *z* or the corresponding occurrence of *ß *in
** S**’ is not purely referential.

But it is not a consequence of (**E**) that given (i) -
(iv), both *z* and the corresponding occurrence of *ß *in ** S**’
are not purely referential. What Kaplan describes as ‘the error of step 4’
is presumably the error of thinking that (

1.3

Quine has observed that if we try to apply existential generalization to

(7) It is necessary that 9 is odd,

we obtain

( *x*) It is necessary that *x* is odd.

But, as he asks rhetorically, what is this object which is necessarily odd? In the light of (7) it is 9, but in the light of

(6) 9 = the number of planets,

and

(13) It is not necessary that the number of planets is odd,

it is not. Now, it is not clear why these observations are
relevant to (**H**). Perhaps, as Cartwright says, we should construe Quine as
pointing out that a double application of existential generalization to a
conjunction of (6) and (7) with (13) yields

(14) ( *x*) ( *y*) (*x* = *y*. It is
necessary that *x* is odd. It is not necessary that *y* is odd).18

But now consider the schema:

(9) ( *x*) ( *y*) (*x*=*y* (Fx Fy)).

If

(10) ( *x*) ( *y*) (*x*=*y* (it is
necessary that *x* is odd it is necessary that *y* is odd))

is an instance of (9), then (14) is in conflict with (**B**),
the claim that the universal closure of every instance of (9) expresses a true
proposition. Thus, given that (**B**) is true, either (10) is not an instance
of (9), or (14) does not express a true proposition. Now, presumably the
principle of existential generalization whose double application to the
conjunction of (6) and (7) with (13) yields (14) is this:

(G) for any sentences ** S** and

Since the conjunction of (6) and (7) with (13) expresses a
true proposition, given that (**B**) is true, either (**G**’) is false
or (10) is not an instance of (9). Now, I think that it should be granted that
(10) is an instance of (9) if and only if

(15) It is necessary that *x* is odd,

is an open sentence. Hence, I think that it should be granted
that, given that (**B**) is true, either (**G**’) is false or (15) is
not an open sentence. However, I do not see why this is any evidence for (**H**).
That (**G**’) is false is established by the facts that

(4) Giorgione was so-called because of his size,

expresses a true proposition, but

(4') ( *x*) *x* was so-called because of his size,

does not express any proposition, and hence does not express
a true proposition. What is needed to establish (**H**) is an argument which
shows that any apparent counterexample to (**G**’) involves an attempt to
bind an occurrence of a variable which is not in an open sentence.

Cartwright notes:

Perhaps Quine is to be understood rather as follows: It would be counter to astronomy to deny

(16) ( *y*) (*y* = Phosphorus *y* = Hesperus),
and an application of existential generalization to the
conjunction of (16) with

(17) astro Hesperus = Phosphorus

would yield

(18) ( *x*) ( *y*) (*y* = Phosphorus *y*
= *x*). astro *x* = Phosphorus).

Again, no one could reasonably deny

(19) ( *y*) (*y* = Phosphorus *y* =
Phosphorus),

and an application of existential generalization to the conjunction of (19) with

(20) - astro Hesperus = Phosphorus

would yield

(21) ( *x*) ( *y*) (*y* = Phosphorus *y*
= *x*).

- astro Hesperus = Phosphorus).

Consider, then, the thing identical with Phosphorus. Is it a thing such that it is a truth of astronomy that it is identical with Phosphorus? In view of (18) and (21), no answer could be given. There is some one thing identical with Phosphorus. But there is no settling the question whether it satisfies ‘astro x = Phosphorus’. To permit quantification into opaque constructions is thus at odds with the fundamental intent of objectual quantification.19

Cartwright sees in this reasoning an argument in defence of (**B**).
Surely the conjunction of (18) and (21), he suggests, is not true; for if it
were, the question: ‘Is the thing identical with Phosphorus such that it is a
truth of astronomy that it is identical with Phosphorus?’ would be
intelligible, but no answer could be given to it. However, seen as an argument
for (**H**), this reasoning, I believe, is invalid. The last sentence, i.e.
‘To permit quantification into opaque constructions is thus at odds with the
fundamental intent of objectual quantification’ does not follow from the rest.
Consider, for instance, the following argument:

Perhaps Quine is to be understood rather as follows: It would be counter to history to deny

(16') ( *y*) (*y* = Reagan *y* = the president
of the U.S.),

and an application of existential generalization to the conjunction of (16') with

(17') It was not the case in 1972 that the president of the U.S. was identical with Reagan,

would yield

(18') ( *x*) ( *y*) (*y* = Reagan *y* = *x*).
It was not the case in 1972 that *x* was identical with Reagan.)

Again, no one could reasonably deny

(19') ( *y*) (*y* = Reagan *y* = Reagan),

and an application of existential generalization to the conjunction of (19) with

(20') It was the case in 1972 that Reagan was identical with Reagan,

would yield

(21') ( *x*) (( *y*) (*y* = Reagan *y* = *x*).
It was the case in 1972 that *x* was identical with Reagan.)

Consider, then, the thing identical with Reagan. Is it a
thing such that it was the case in 1972 that it was identical with Reagan? In
view of (18) and (21), no answer could be given. There is some one thing
identical with Reagan. But there is no settling the question whether it
satisfies ‘It was the case in 1972 that *x* was identical with Reagan’.
To permit quantification into opaque constructions is thus at odds with the
fundamental intent of objectual quantification.

Surely we must resist the suggestion that no answer could be given to the question ‘Is the thing identical with Reagan such that it was the case in 1972 that it was identical with Reagan?’ The question is intelligible; there is indeed such a thing identical with Reagan; and there is little doubt that this thing is such it was the case in 1972 that it was identical with Reagan. The conjunction (18') and (21') is not unintelligible; it is false.

Now, it ought to be noted, as both Quine and Cartwright would emphasize, that the intelligibility of this question or the intelligibility of the conjunction of (18') and (21') is not guaranteed simply by the intelligibility of quantification and the intelligibility of the role of ‘It was the case in 1972 that’ as an operator on close sentences. Cartwright notes:

The symbol "°" is sometimes so used that ° count as true if and only if itself is necessary. If that is all there is to go on, we have no option but to count the `°’ construction opaque and hence

(i) ( *x*) ( *y*) (*x* = *y* (°*x*
= *x* °*x* = *y*))

unintelligible. But (ii),

(ii) ( *x*) °(*x* = *x*)

and

(iii) ( *x*) ( *y*) (*x* = *y* °*x*
= *y*)

are witnesses to a contemplated transparent ‘°’ -construction.

Now the intelligibility of such a construction is not guaranteed simply by an antecedent understanding of quantification and of the opaque ‘°’ -construction.20

And Quine remarks:

The important point to observe is that granted an understanding of modalities (through uncritical acceptance, for the sake of argument, of the underlying notion of analyticity), and given an understanding of quantification ordinarily so-called, we do not come out automatically with any meaning for quantified modal sentences.21

I think that it ought to be conceded that for any
reverentially opaque operator O, if all there is to go on about **O**, is
that for any closed sentence, ** S**,

(i) It is not the case that** S**
is true if and only if

and quantification is understood, we are not guaranteed any understanding of

(ii) ( *x*) It is not the case that *x* is odd. For
surely,

(iii) ( *x*) ‘*x* is odd’ is not true

does not count as an explanation of (ii). What is obviously needed is an explanation of the role of ‘It is not the case that’ as an operator on an open sentence. But now suppose that

(22) It is not the case that *x* is odd,

is specified as an open sentence, and the problem of
determining which sequences, if any, satisfy this open sentence is somehow to be
settled. It seems to me that it would not be a necessary condition for settling
this problem that the position of the occurrence of ‘*x*’ in (22) be
counted as reverentially transparent; for, I am inclined to think that this
problem is to be settled independently of any considerations about what singular
terms (other than the variables) or what kinds of singular terms (other than the
variables) are available. The point is not that there is some doubt about the
referential transparency of the position of the occurrence of ‘*x*’ in
(22); it is rather that the referential transparency of this position is not a
necessary condition for settling the problem of determining which sequences, if
any, satisfy (24). Similarly, suppose that

(15) It is necessary that *x* is odd,

and

(23) It was the case in 1972 that x was identical with Reagan,

are specified as open sentences, and the problem of
determining which sequences, if any, satisfy these open sentences is somehow to
be settled. It is not a necessary condition for settling this problem that the
positions of the occurrences of ‘*x*’ in (15) and (23) respectively be
counted as reverentially transparent. Why is it, then, claimed, as Quine
apparently does, that ‘to permit quantification into opaque constructions is
thus at odds with the fundamental intent of objectual quantification’.

One cannot help but think that at issue are some principles
of instantiation and generalization. Given that (**B**) is true, if (15) is
an open sentence, and the position of the occurrence of ‘*x*’ in (15)
is not reverentially transparent then the following principle of existential
generalization is not true:

(**L**) For any sentences ** S** and

If the position of the occurrences of ‘*x*’ in (15)
is not reverentially transparent then there are singular terms and *ß*
such that

= *ß*. It is necessary that is a odd. It is not
necessary that is *ß* odd

expresses a true proposition. But if (15) is an open sentence, then surely

*x* = *y*. It is necessary that *x* is odd. It is
not necessary that y is odd

is an open sentence as well. And if (**L**) is true, then

(14) ( *x*) ( *y*) (*x* = *y*. It is
necessary that *x* is odd. It is not necessary that *y* is odd)

expresses a true proposition. But (14) conflicts with (**B**).
Granted that (**B**) is true, either (**L**) is not true or (15) is not an
open sentence in which the position of the occurrence of ‘*x*’ is
reverentially transparent.

(**L**) is closely related to the following principle of
universal instantiation:

(**M**) For any sentences ** S** and

Again granted that (**B**) is true, if (15) is an open
sentence in which the position of the occurrence of ‘*x*’ is not
reverentially transparent, then, (**M**)is false. If the position of the
occurrence of ‘*x*’ in (15) is not reverentially transparent, then
there are singular terms and *ß *such that

= *ß*. It is necessary that is a
odd. It is not necessary that is *ß *odd.

expresses a true proposition. But granted that (**B**) is
true, if (15) is an open sentence, then

(10) ( *x*) ( *y*) (*x* = *y* (it is
necessary that *x* is odd it is necessary that *y* is odd)

is an instance of (9) which expresses a true proposition. But
if (**M**) is true, and (10) expresses a true proposition, then for any
non-vacuous singular terms and *ß*,

= *ß *(It is necessary that is a odd it is not
necessary that is *ß *odd)

expresses a true proposition. But that conflicts with the
claim that there are singular terms and *ß, *such that

= *ß*. It is necessary that is a
odd. It is not necessary that is *ß *odd

expresses a true proposition. Hence, if (**B**) is true,
either (**M**)is false, or (15) is not an open sentence in which the position
of the occurrence of ‘*x*’ is reverentially transparent. It is readily
seen that given that (**B**) is true, if (**M**) is true then (**H**)
is true. For given that (**B**) is true, if (**M**) is true then the
positions of the free occurrences of a variable in any open sentence are
reverentially transparent. But, then, (**H**) is true, since, surely it is
only the free occurrences of a variable in an open sentence which may be bound
by a quantifier outside of that open sentence.

But is (**M**) true? It seems to me that (**M**) is not
a principle which is fundamental to the intent of objectual quantification.
Objectual quantification is best understood in terms of satisfaction of open
sentences, and it appears to me that the problems of determining what it is for
a sequence to satisfy an open sentence are to be settled independently of any
considerations about what kinds of singular term other than the variable are
available. It seems, then, that it is not required for an understanding of
objectual quantification that the principle that the position of an occurrence
of a free variable in an open sentence is reverentially transparent is true. But
since, this principle is true if (**M**) is true, a defense of (**M**) is
not to be found in any appeal to the fundamental intent of objectual
quantification.

**NOTES**

This paper is based on my Ph.D. thesis entitled "Identity and Quantification" (Cambridge, MA: MIT, 1985). I am indebted, for their assistance, to George Boolos, and Judy Thomson; I have also benefitted from comments on an earlier draft of this paper by Tom Patton, and Scott Soames.

1. "Notes on Existence and Necessity", *Journal
of Philo-sophy* (1943), p. 127.

2. "Quantifiers and Propositional Attitudes",
reprinted in *Reference and Modality*, edited by Leonard Linsky (Oxford:
Oxford, 1971), pp. 102-03.

3. *From a Logical Point of View*, second edition (New
York: Harper and Row, 1963), p. 139.

4. In any sentence which contains expressions such as "It is not the case that", and "It is necessary that", etc., which generate structural ambiguity, I interpret these expressions as operators on "their complement sentences, rather than as modifying the copular or the verb phrase of their complement sentences.

5. See note 4.

6. A proposition *x* falsifies a proposition *y* if
and only if *x *is true and *x* entails the denial of *y*.

7. *Word and Object* (Cambridge, MA: MIT, 1970), pp.
167-68. I have changed the notation and the numbering to conform to this essay.

8. *From a Logical Point of View*, p. 139.

9. *Word and Object*, pp. 141-42.

10. *From a Logical Point of View*, p. 140.

11. *Word and Object*, pp. 141-42.

12. The use of the word "position" here, corresponds to the way Quine sometimes uses "context".

13. *From a Logical Point of View*, p. 145.

14. *Ibid.*, p. 148.

15. David Kaplan, "A Historical Note on Quine’s Argument Concerning Substitution and Quantification", unpublished, pp. 3-4. This paper has been incorporated in a longer unpublished paper entitled "Opacity", in the Library of Living Philosophers’ volume on Quine.

16. *Ibid.*, p. 6.

17. *Ibid.*, pp. 6-7.

18. Richard Cartwright, "Indiscernibility
Principles" in *Mid-west Studies in Philosophy*, vol. 4, edited by
French, Uchling and Wettstein (University of Minnesota, 1979), pp. 302-03.

19. *Ibid.*, p. 303.

20. *Ibid.*, p. 304.

21. *From a Logical Point of View*, p. 150.