That’-clauses as Existential Quantifiers

Abstract

Following Panaccio, 'John believes that p' is analysed as 'For some x such that x is true if and only if p, John believes x'. On this view the complement clause 'that p' acts as a restricted existential quantifier ('For some x such that x is true if and only if p') and it contributes a higher-order property.

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’That’-clauses as existential quantiers
François Recanati
To cite this version:
François Recanati. ’That’-clauses as existential quantiers. Analysis, Oldenbourg Verlag, 2004, 64
(3), pp.229-235. �ijn_00000493�

7
restriction of the domain of quantification. On this view the overall content of
the belief sentence ‘John believes that Peter is an eye-doctor’ is nothing
other than
[∃
p
: TRUE (
p
) iff EYE-DOCTOR (Peter)] BELIEVES (John,
p
)
but the variable
‘p’
only ranges over beliefs possessing the contextually
relevant property
F
.3
Institut Jean-Nicod (CNRS/EHESS/ENS)
1
bis
avenue de Lowendal, 75007 Paris, France
recanati@ehess.fr
References
Egré, P. forthcoming. A pragmatic approach to the problem of logical
omniscience.
Panaccio, C. 1996. Belief sentences: outline of a nominalistic approach. In
Québec Studies in the Philosophy of Science II
, eds. M. Marion and R. S.
Cohen, 265-77. Dordrecht : Kluwer.
Recanati, F. 2000.
Oratio Obliqua, Oratio Recta: An Essay on
Metarepresentation
. Cambridge, Mass. : MIT Press/Bradford Books.
3 Many thanks to Paul Egré, Neftali Villanueva Fernandez and Philippe
Schlenker for comments on an earlier version of this paper, and to Claude
Panaccio for inspiring the main idea.

6
is possible, and it might be said that this reading is
‘de re’
with respect to the
property expressed by ‘eye-doctor’:
[ιX : X = EYE-DOCTOR] [∃
p
: TRUE (
p
) iff X (Peter)] BELIEVES (John,
p
)
But the problem is that the
other
reading — the
de dicto
reading — has been
represented in such a way that it, too, allows substitution. It follows that
nothing, in our framework, captures the feature of belief sentences in virtue
of which substitution fails even for synonymous expressions.
I think that feature can (and should) be handled pragmatically. On a
pragmatic analysis, what the sentence compositionally articulates is only the
truth-conditional content of the ascribed belief. At that level, substitutivity
does
not
fail. But the context and the way the speaker phrases the report
impart extra information regarding the ascribee’s belief, and in particular the
ways she presumably thinks of the various objects and properties which her
belief concerns. Substitutivity fails, when it fails, because the expressions
that are used in giving the truth-conditions of the ascribed belief are
themselves contextual clues which may affect the further suggestions that
are conveyed, but not literally expressed, regarding that belief.
There are two types of pragmatic accounts of opacity in the literature.
One type of account says that the information that is ‘pragmatically
imparted’ rather than compositionally articulated does
not
affect the truth-
conditions of the report. The truth-conditions which such views ascribe to
belief reports are very different from the intuitive truth-conditions which they
seem to have, and this, I take it, is a serious defect of those approaches. The
other type of account says that the pragmatic suggestions in question find
their ways into the truth-conditions of the report. For example, we may argue
that the compositionally articulated content of ‘John believes that grass is
green’ is
freely enriched
through the contextual provision of additional
ingredients (‘unarticulated constituents’) in the restriction of the quantifier
— ingredients which I represent by means of the extra conjunct ‘
F
(
p
)’, in
which
‘F’
is a free variable:
[∃
p
: (TRUE (
p
) iff EYE-DOCTOR (Peter)) &
F
(
p
)] BELIEVES (John,
p
)
Intuitively, the property
‘F’
that is implicitly ascribed to John’s belief is the
property that its propositional constituents are thought of under such and
such modes of presentation.
If, for general methodological reasons, one does not like ‘free
enrichment’ or ‘unarticulated constituents’, an alternative analysis is available
which is less controversial but amounts to exactly the same thing. The
alternative analysis appeals to the universally accepted idea of a contextual

5
which would be my rendering of (the
de dicto
interpretation of) ‘John
believes that grass is green’ if ‘iff’ was construed as material equivalence,
‘GREEN (grass)’ can be replaced by any materially equivalent formula (e.g.
‘WHITE (snow)’) without affecting the truth-value of the whole. That is not
acceptable, for we cannot substitute ‘snow is white’ for ‘grass is green’ in
‘John believes that grass is green’.
The belief operator ‘John believes that’ posited by the Hintikka-Prior
analysis is intensional; it operates on the content of the complement
sentence, not on its extension. It follows that only a sentence expressing the
same proposition as the sentence ‘grass is green’ can substitute for it in
‘John believes that grass is green’. In the standard framework, the same
result is achieved by extensional means: the ‘that’-clause ‘that grass is green’
is taken to designate the content of the complement sentence ‘grass is
green’, hence only a sentence with the same content as ‘grass is green’ can
be substituted for it without modifying the reference of the ‘that’-clause. To
achieve that effect in our framework, we have to make the connective ‘iff’
suitably intensional, i.e., sensitive to the content of the sentence on the
right-hand-side, and not merely to its extension (its truth-value). Indeed,
when we say that what the speaker believes is true if and only if grass is
green, we describe a state of affairs, consisting of a certain object (grass)
having a certain colour (green), and we say that the belief is true in all and
only those situations in which
that state of affairs
obtains. The situations in
question may be partial, so even strict equivalence (equivalence in all possible
worlds) will not do. Which of the many proposals available in the logico-
philosophical literature best captures the intuitive content of ‘if and only if’ is
an issue which I will not address in this paper. I use the symbol ‘iff’ as a place-
holder, to record the need for a suitably intensional connective.
IV.
One might object that, even if we had such a connective, we still couldn’t
account for substitutivity failures in belief sentences. The sentence ‘John
believes that Peter is an eye-doctor’ will be rendered as:
[∃
p
: TRUE (
p
) iff EYE-DOCTOR (Peter)] BELIEVES (John,
p
)
Since ‘EYE-DOCTOR’ has the same content (expresses the same property) as
‘OPHTALMOLOGIST’, substitution is possible. Yet in the natural language
sentence ‘John believes that Peter is an eye-doctor’, substitution is blocked:
John may fail to realize that Peter is an ophtalmologist even if he believes
him to be an eye-doctor.
It will not do to appeal to the
de re/de dicto
distinction here. To be
sure, there is a reading of the natural language sentence in which substitution

4
[∃
p
: TRUE (
p
) iff GREEN (grass)] BELIEVES (John,
p
)
In this framework, semantic innocence is preserved as much as it is in
Davidson’s paratactic analysis: the sentence ‘grass is green’ makes its
standard contribution and is not recruited as a fragment of a complex name.
The standard view is rejected because (2) is rejected. But no discrepancy is
introduced between grammatical form and logical form. As for the above-
mentioned inferences, they can be accounted for quite easily:
John believes that grass is green,
Sam doubts whatever John believes,
Therefore, Sam doubts that grass is green
is now formalized as
[∃
p
: TRUE (
p
) iff GREEN (grass)] BELIEVES (John,
p
)
[∀
p
: BELIEVES (John,
p
)] DOUBTS (Sam,
p
)
[∃
p
: TRUE (
p
) iff GREEN (grass)] DOUBTS (Sam,
p
)
The
de re/de dicto
distinction also can easily be captured. The two
readings of a belief sentence with an embedded definite description, for
example,
John believes that the winner is African
will be represented respectively as
[de re reading]
[ι
x
: WINNER (
x
)] [∃
p
: TRUE (
p
) iff AFRICAN (
x
)] BELIEVES (John,
p
)
and as
[de dicto reading]
[∃
p
: TRUE (
p
) iff [ι
x
: WINNER (
x
)] AFRICAN (
x
)] BELIEVES (John,
p
)
III.
In the above formulas I have used the symbol ‘iff’ without saying which logical
connective it stands for. One thing is sure: the connective in question cannot
be material equivalence. If it were, we would fail to capture an essential
property of belief sentences. In
[∃
p
: TRUE (
p
) ≡ GREEN (grass)] BELIEVES (John,
p
)

3
she has a belief with certain truth-conditions, that is, a belief that is true iff
such and such is the case. We can therefore analyse ‘John believes
that grass
is green’
as ‘John believes
something that is true iff grass is green’
(Panaccio
1996: 266-7). This means that we can treat a ‘that’-clause as, in effect, a
restricted existential quantifier, and paraphrase it as ‘For some
p
such that
p
is true iff S’ (where
‘p’
now is an
objectual
variable ranging over truth-
evaluable entities, and ‘S’ stands for the sentence embedded in the ‘that’-
clause). ‘John believes that grass is green’ is therefore equivalent to
[∃
p
: TRUE (
p
) iff GREEN (grass)] BELIEVES (John,
p
)
that is, ‘for some
p
such that
p
is true iff grass is green, John believes
p’
.
The semantic contribution of a quantified noun phrase is standardly
treated as a higher-order property, predicated of the property expressed by
the nuclear sentence. Similarly, the semantic contribution of ‘that grass is
green’ in ‘John believes that grass is green’ can be viewed as a higher-order
property, predicated of the property expressed by ‘John believes ξ’. That
higher-order property is the property a property has when it is possessed by
at least one entity true iff grass is green. It can be represented as
λX λ
x
[(∃
p
: TRUE (
p
) iff GREEN (grass)) X (
x
,
p
)]
This, then, is the semantic content of ‘that grass is green’.2 To get the
content of ‘believes that grass is green’ we apply that higher-order property
to the first-order relation that is the semantic content of ‘believes’:
λX λ
x
[(∃
p
: TRUE (
p
) iff GREEN (grass)) X (
x
,
p
)] (BELIEVES)
What we thereby get is a property of individuals, namely the property of
believing something that is true iff grass is green:
λ
x
[(∃
p
: TRUE (
p
) iff GREEN (grass)) BELIEVES (
x
,
p
)]
When this first-order property is applied to John, we get
λ
x
[(∃
p
: TRUE (
p
) iff GREEN (grass)) BELIEVES (
x
,
p
)] (John)
that is,
2 To get the semantic content of ‘that’, we need only to add another lambda
abstractor and to replace the formula ‘GREEN (grass)’ by a sentential
variable:
λσ λX λ
x
[(∃
p
: TRUE (
p
) iff σ) X (
x
,
p
)]

2
of inference, I have suggested handling it by appealing to sentential
quantification, along the following lines:
John_believes-that (grass is green)
∀
p
(John_believes-that (
p
) → Sam_doubts-that (
p
))
Sam_doubts-that (grass is green)
I still think Davidson’s paratactic analysis and the Prior-Hintikka analysis
fare better than the standard view in certain respects. The standard view
treats ‘that’-clauses as complex names referring to propositions, and that
arguably threatens semantic innocence.1 On both the Davidson and the Prior-
Hintikka view, the embedded sentence is
not
treated as a fragment of such a
name, but it remains a
bona fide
sentence — hence innocence is preserved.
Yet I am worried by the disappearance of ‘that’-clauses, which is a
consequence of their analyses. The disappearance of ‘that’-clauses
introduces an unwelcome discrepancy between grammatical form and logical
form. As far as the
grammar
is concerned, there isn’t much doubt that ‘that’-
clauses exist, and that their behaviour is (to some extent) similar to that of
noun-phrases. This, it seems, argues in favour of the standard view.
Or does it? An intermediate position may be available. One can
acknowledge the grammatical status of ‘that’-clauses as noun-phrases (or,
more accurately, as complementizer phrases similar in many respect to NPs),
while resisting the innocence-damaging claim that they are referential
expressions. To give a trivial example, quantified noun-phrases such as ‘most
children in the park’ are noun-phrases, but they are not referential
expressions. Therefore it is worth considering what would result if we decided
to treat ‘that’-clauses on the same pattern. In this way we could
acknowledge the grammatical reality of ‘that’-clauses, without accepting the
standard view and its unwelcome consequences.
II.
Can ‘that’-clauses be considered as quantified phrases? Why not? To say that
someone believes something is to say that she has a belief with a certain
content. To ascribe a content to a belief is to ascribe it certain truth-
conditions. Therefore, to say that someone believes something is to say that
1 For me ‘semantic innocence’ covers not only the requirement of semantic
constancy, but also a requirement of syntactico-semantic correspondence :
expressions of distinct grammatical categories should make semantic
contributions of different types. I am indebted to Paul Egré for discussion of
this point, both in conversation and in writing (Egré forthcoming). Thanks
also to Neftali Villanueva.

1
‘That’-clauses as existential quantifiers
FRANÇOIS RECANATI
I.
The following assumptions jointly constitute the
standard view
regarding the
logical form of belief reports:
(1) ‘believe’ and other propositional attitude verbs denote relations
between an agent and a truth-bearing entity (a ‘proposition’);
(2) ‘that’-clauses are referential expressions which denote propositions.
On this view ‘John believes that grass is green’ has the form
aRb
. The name
‘John’ and the ‘that’-clause ‘that grass is green’ are both referential
expressions, whose respective denotata fill the two argument-places in the
relation denoted by the verb. In this way we can account for the validity of
inferences such as
John believes that grass is green,
Sam doubts whatever John believes,
Therefore, Sam doubts that grass is green.
This is formalized as
BELIEVES (John, that_grass_is_green)
∀
x
(BELIEVES (John,
x
) → DOUBTS (Sam,
x
))
DOUBTS (Sam, that_grass_is_green)
Several philosophers have expressed dissatisfaction with the standard
view, on various grounds. Two alternatives have been put forward. One is
Davidson’s paratactic theory, which rejects (2). Davidson analyses attitude
reports like ‘John believes that grass is green’ as consisting of two
juxtaposed sentences: ‘John believes that’ (where ‘that’ is a demonstrative),
and ‘grass is green’. The second alternative, advocated by Prior and Hintikka,
treats ‘John believes that’ as a sentential operator analogous to modal
operators both syntactically and semantically. On this view, not only are
‘that’-clauses deprived of any linguistic reality (as on Davidson’s analysis),
but the verb ‘believes’ itself is no longer treated as denoting a first-order
relation. Hence both (1) and (2) are rejected.
I am among those who have expressed dissatisfaction with the
standard view, and in my book
Oratio Obliqua, Oratio Recta
I have argued in
favour of the Prior-Hintikka sort of view. Regarding the above-mentioned type