A problem for the relational theory of propositional attitudes
Abstract.
The relational theory of propositional attitudes holds that attitude verbs, such as ‘believe’,
express binary relations between individuals and propositions. The theory predicts that
inferences such as the one from (1) Russell believed that mathematics reduces to logic,
and (2) That mathematics reduces to logic is Logicism, to (3) Russell believed Logicism,
are valid. A puzzling anomaly is that, for many attitude verbs other than ‘believe’, the
corresponding inferences are invalid. In some cases, the conclusions are not even
grammatical. I will show that even in belief reports substituting the proposition that p for the
clause that p can result in a truth-value change.
Keywords.
Belief, propositional attitudes, propositions, ‘that’-clauses.
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1. The relational theory and a puzzling phenomenon.
Belief reports are sentences of the form A believes that S, e.g.,
(1) Russell believed that mathematics reduces to logic.
Similarly, hope reports have the form A hopes that S. In general, we have reports for every
propositional attitude. The default theory of such reports is the relational theory, which
today appears to be endorsed by the vast majority of philosophers. Stephen Schiffer calls
it the face-value theory since
it is a theory which appears well motivated when belief reports are taken at face value, and
because the intuitive considerations which prima facie support the theory arguably give it the
default status of a theory that must be defeated if it is not to be accepted (Schiffer 2006: 267).
It consists of the following three theses:
Thesis 1. ‘Believe’ and all verbs of propositional attitudes are two-place predicates.
Thesis 2. Such predicates are flanked by two argument slots for singular terms, A and
‘that S’. (Phrases of the form ‘that S’ are called ‘that’ clauses.)
Thesis 3. ‘That’-clauses designate1 propositions.
1
Both proper names, that (directly) refer to objects and definite descriptions that (if proper) denote them can
designate the same thing, in so far as the truth value of the sentences where they occur depends on the
properties possessed by that thing and the relations it stands in.
2
The clause ‘that mathematics reduces to logic’ designates the proposition that
mathematics reduces to logic. Putting theses (1)-(3) together, we have that (1) is true just
in case Russell stood in the belief relation to that mathematics reduces to logic.
The theory is incomplete as it stands, since no account is given of what propositions are,
and must be supplemented by some account of them. It is on this issue that philosophers
mostly differ. Theses (1)-(3) are made plausible – it is claimed – by their being the most
straightforward way of accounting for the apparent validity of inferences such as:
(a) Harold believes everything that Russell says.
Russell says that mathematics reduces to logic.
So, Harold believes that mathematics reduces to logic.
(b) Russell believes that mathematics reduces to logic and so does Harold.
So, there is something that they both believe – to wit, that mathematics reduces to
logic.
(c) Harold believes Russell’s theory.
Russell’s theory is that mathematics reduces to logic.
So, Harold believes that mathematics reduces to logic.
If the logical form of these inferences are, respectively
(a’)
x(Fax  Gbx)
Fac
 Gbc,
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(b’)
Fab & Fcb
x (Fax & Fcx),
(c’)
Fab
b=d
 Fad,
then it is clear that they are valid and verbs of propositional attitudes are two-place
transitive verbs, flanked by slots for two singular terms. Theses (1) and (2) are then
established. As to thesis (3), no further argument seems to be needed: “If, as the facevalue theory has it, the displayed occurrence of [‘that mathematics reduces to logic’] is a
singular term, then, obviously, its referent is [that mathematics reduces to logic]” (Schiffer
2006: 269).
Now a puzzling phenomenon arises, first noted by Arthur Prior (1971) and much discussed
in recent years.2 Several devices exist in language to designate propositions, instances of
which are
(i) ‘Logicism’,
(ii) ‘Russell’s theory’
(iii) ‘The proposition that mathematics reduces to logic’,
(iv) ‘that mathematics reduces to logic’.
2
I shall only mention Kent Bach (1997), Jeffrey King (2002), Friederike Moltmann (2003), Stephen Schiffer
(2006), Tobias Rosefeldt (2008), Graeme Forbes (2009).
4
Let us call terms like (i) proposition names (henceforth PNs), terms like (ii) and (iii)
proposition descriptions (henceforth PDs), and terms like (iv) ‘that’ clauses (henceforth
TCs). It would appear that any singular term t designating an object o and occurring in a
sentence s ought to be substitutable in s by any other singular term t’ referring to the same
o salva veritate. As far as the propositional attitude of belief is concerned, it seems that the
prediction is borne out: any one of the terms (i)-(iii) can be substituted for ‘that
mathematics reduces to logic’ in (1) Russell believed that mathematics reduces to logic,
without affecting its truth value. It is not so, however, with attitudes other than belief. For
instance, whereas
2. Russell hoped that mathematics reduces to logic
is true,
3. Russell hoped the proposition that mathematics reduces to logic
is not even grammatical. The same goes with other attitude verbs such as ‘wish’ and ‘say’,
which can be followed by TCs, but neither by PNs nor by PDs. For other attitude verbs,
such as ‘fear’, ‘suspect’, ‘feel’, ‘understand’, ‘announce’, ‘anticipate’, ‘ask’, ‘boast’, ‘caution’,
‘decide’, ‘discover’, ‘forget’, ‘notice’, ‘prefer’, ‘require’, ‘see’, ‘suggest’, ‘worry’, and
cognates of these, the same substitutions produce a grammatical sentence but are not
salva veritate. For instance,
4. Harold fears that mathematics reduces to logic
might well be true, but it is unlikely that
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5. Harold fears the proposition that mathematics reduces to logic
is true. It is no option to maintain the face-value theory of belief reports while denying it of
hope reports, fear reports, etc. Various remedies have been proposed.
Jeffrey King has claimed that proponents of the relational theory need not be too
impressed by the puzzling phenomenon. His argument, if I understand it correctly, is that,
even though the PD ‘the proposition that mathematics reduces to logic’ does in fact
designate the same proposition as the TC ‘that mathematics reduces to logic’, the steps
from (2) to (3) and from (4) to (5) are not valid, but neither are they of the form (c’). The
fact is, according to King, that ‘fear’, ‘feel’ and a whole class of attitude verbs are
ambiguous or polysemous and, depending on the syntactical category of their
complement, contribute different relations to the propositions expressed by the sentences
where they occur.
I claim that there are two classes of verbs of propositional attitude (that take both NP and S
complements) with the members of one class ambiguous in the way that we have claimed ‘fears’ is
and the members of the other univocal in the way that we have claimed ‘believe’ is (King 2002: 357).
King also maintains that there is independent evidence of ambiguity or polysemy for the
verbs of the former class since, for one thing, Harold needs not believe the proposition for
(5) to be true, whereas he does for (4). By contrast, there is no pre-theoretical intuition that
in such sentence pairs as
6. Russell believed that mathematics reduces to logic,
6
7. Russell believed the proposition that mathematics reduces to logic,
the occurrences of the verb ‘believe’ have different meanings. Thus, the puzzling
phenomenon is no longer puzzling and, he claims, does not undermine the relational
theory.
Stephen Schiffer points out that it does not generally hold true that every singular term t
designating an object o and occurring in a sentence s can be substituted in s by any other
singular term t’ referring to the same o salva veritate, or even salva significatione.
However, he takes inferences such as (c) and that from (6) to (7) to be valid.
Tobias Rosefeldt approaches the matter rather differently. He rejects the claim that TCs
are singular terms. There is no reason, therefore, to expect that, in general, they are
substitutable either with PDs or with PNs salva veritate and salva significatione. However,
if I understand him correctly, he too takes the step from (6) to (7) to be valid.
I shall not discuss how effective these defences of the face-value theory are against the
threat posed by the puzzling phenomenon. Rather, I intend to show that the puzzling
phenomenon has been underestimated. Everyone seems to agree that, even though some
attitude verbs are ambiguous or polysemous, and it is therefore to be expected that the
substitution of ‘that’ clauses by PDs in the corresponding reports does not preserve their
truth values, the class of univocal attitude verbs which admit both TCs and PDs as
complements, and for which inferences like (c) above are valid, is not empty. King,
Schiffer, Rosefeldt, and many others, all agree that the verb ‘believe’ is in that class.
A notable exception is Graeme Forbes:
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Believing a witness is believing what the witness says, and this in turn seems to consist in believing
or agreeing that p for some statement that p of the witness’s that you are judging. […] But
propositions themselves do not literally say anything, so claiming that you believe the proposition
that p is a category mistake, something necessarily false.
Nevertheless, it is in fact quite acceptable to say ‘{believe/doubt} the proposition that…’. The reason
this is so is that it is an apt figure of speech (Forbes 2009: 6).
However, even Forbes maintains that there are attitude verbs where an inference in the
style of (c) is straightforwardly correct: “Some verbs for mental operations on propositions
support interchange of clause [TC] and propositional description [PD] preserving literal
meaning: these include ‘accept’, ‘assert’, ‘assume’ and inference verbs such as ‘deduce’,
‘prove’, ‘infer’ and ‘establish’ (none of these appear to be substitution-resisting in their
transitive versions)”(Forbes 2009: 7).
I now show, to the contrary, that both ‘believe’ and these other verbs are most likely to be
substitution-resistant. The reason why they are has nothing to do with syntactic matters
and grammaticality, since all these verbs can be followed by both TDs and PDs as
complements indifferently, while preserving their literal meaning. If, even for those verbs,
inferences such as (c) above are invalid, this is fairly strong evidence that that the same
goes for all attitude verbs. This result does throw some doubt on the relational theory,
since it makes it hard to maintain that TCs of the form that p designate what the
corresponding PDs, ‘the proposition that p’, designate, and it is unlikely that the latter can
stand for anything other than propositions.
2. The case of Zoltan the monolingual Hungarian.
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In order to ascribe a belief to a person, we look at her behaviour and, in particular, at her
linguistic behaviour – first of all, her assertions. A principle that licenses going from her
assertions to her beliefs is the Disquotation Principle, a clear formulation of which is to be
found in (Kripke 1979: 112-13]. There are as many statements of the principle as there are
languages. Here is a rough statement of it for English. Let S be a normal English speaker,
reflective and sincere, and let p be an English sentence lacking indexical or pronominal
devices or ambiguities. Then
(Weak) Disquotation Principle for English: If S assents to ‘p’ then S believes that p.
Taken in its obvious intent, the principle appears to be a self-evident truth but, in what
follows, we need not assume that it is true. All that we need is that some Zoltan or other
believes it.3 Let Zoltan be a monolingual Hungarian, who only knows a few words of
English. Here are all the English words and phrases he knows: the connective if … then
…, the phrases assent to, believe that, and the proposition expressed by. In addition, he
knows that English is an SVO language. Zoltan is also a distinguished philosopher, who
happens to believe the Weak Disquotation Principle firmly. It is to be noted that, even with
his limited knowledge of English, he understands, and believes, the Weak Disquotation
Principle for English in the form given above.
Suppose that, on a certain occasion, he is witness to a man, Donald, whose name he
knows, assenting to the English sentence ‘The Earth moves’. Zoltan believes that Donald
is a normal speaker of English, reflective and sincere (no need to know English in order to
3
The character Zoltan was introduced by Schiffer in (2003).
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believe that). Moreover, Zoltan correctly identifies the sentence ‘The Earth moves’ as an
English sentence, even though he does not know what it means. 4 He then concludes
(11) Donald assents to ‘The Earth moves’.
He firmly believes (11), which he understands perfectly well, his limited knowledge of
English notwithstanding. (12) is therefore also true:
(12) Zoltan believes that Donald assents to ‘The Earth moves’.
Now he applies the rules of universal instantiation and modus ponens, which he knows to
be valid, to the Weak Disquotation Principle for English and to (11) – both of which he
believes – and infers the conclusion
(13) Donald believes that the Earth moves.
Premises and conclusions of inferences are entities apt to be believed. Since, in general,
indexical and content-sensitive expressions can occur in sentences, which have to be
evaluated in their contexts before they can enter into inferences as premises or
conclusions, premises and conclusions are not just sentences. I assume that anyone who
is willing to endorse the relational theory will agree that they are propositions. Zoltan infers
the proposition that Donald believes that the Earth moves, as the conclusion of that simple
argument. It might be added, as an intermediary, and indubitable, step that he infers the
proposition expressed by ‘Donald believes that the Earth moves’ – remember that he
4
Suppose he is also told that ‘The Earth moves’ is an English sentence lacking indexical or pronominal
devices or ambiguities.
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understands the PD “the proposition expressed by ‘Donald believes that the Earth moves’”
perfectly well. Given that it is the same as the proposition that Donald believes that the
Earth moves, the latter is what he infers.
Given that he has obtained that conclusion from premises he believes by means of
principles that he knows to be valid and, presumably, he trusts his own logical acumen at
least as far as this simple argument is concerned, he also believes the proposition
expressed by ‘Donald believes that the Earth moves’, i.e., the proposition that Donald
believes that the Earth moves.
We therefore have both
(14) Zoltan infers the proposition that Donald believes that the Earth moves,
and
(15) Zoltan believes the proposition that Donald believes that the Earth moves.
However, it is doubtful, to say the least, that we can conclude from this that (16) holds:
(16) Zoltan believes that Donald believes that the Earth moves.
Zoltan has no idea of what it is that Donald believes, as he lacks the necessary knowledge
of English to know the content of Donald’s belief. He does not even know that Donald said
something concerning the Earth. One might take the following as a general principle: a
sentence of the form S1 believes that S2 believes that p cannot be true unless S1 knows
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what S2 believes – i.e., the content of S2’s belief. This principle is perhaps not indubitable
as it is, but at least it stands a good chance of being true. Schiffer, for one, endorses it. He
even goes as far as using it to provide conclusive evidence that the sententialist theory of
belief ascriptions cannot possibly be true.5 Similar principles, with the attitude verbs
‘assert’, ‘assume’, ‘deduce’, ‘prove’, ‘infer’, ‘establish’ substituted for the first occurrence of
‘believes’, are equally plausible.
Can this argument be resisted before it reaches its last step – e.g., by claiming that one
cannot believe a proposition of the form ‘the proposition that p’ unless one is also prepared
to believe that p? This would amount to rejecting (14) and (15). But it would also make the
relational theory empty, simply because, on this construal, no independent meaning can
be attached to the phrase ‘stand in the belief relation with a proposition’. The consequence
of Theses (1)-(3), that ‘S believes that p’ is true iff S stands in the belief relation with the
proposition that p, would merely amount to stating that ‘S believes that p’ is true iff S
believes that p. Moreover, we would be left completely in the dark as to the use of PNs
5
“[W]hile each version of sententialism will have its own unique flaws, there is one they all share, and I doubt
that it is surmountable. A theorist who eschews contents in favour of things that merely have content must
say that a person will believe one of those things S just in case she is in a belief state that has the same
content as S. For example, if believing that the earth moves is standing in the belief relation to the sentence
‘the earth moves’, then my utterance of ‘Galileo believed that the earth moves’ will be true just in case
Galileo was in a belief state whose content matched that of ‘the earth moves’. The problem every
sententialist account of propositional attitudes confronts comes to this for the example at hand: no one can
know that Galileo believed that the earth moves without knowing what Galileo believed, the content of his
belief, but one (e.g., a monolingual speaker of Hungarian) can know that Galileo was in a belief state whose
content was the same as the content of ‘the earth moves’ without having any idea of what Galileo believed,
of the content of his belief” (Schiffer 2003: 47).
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and PDs (other than those of the form ‘the proposition that p’) in such sentences as
‘Russell believed Logicism/Relativity Theory/ his own favourite proposition’.
If inferences such as (c) above never hold good, this might amount to a decisive objection
to the relational theory of attitude ascriptions. For one thing, the evidence available for the
theory is considerably weakened. It mainly consisted in the alleged validity of inferences
such as (a)-(c) above. Now (c) must be dropped. What is really worrying, however, is that
it is hard to maintain that TCs refer to propositions, in the face of the fact that the
substitution of ‘that p’ for ‘the proposition that p’ is not salva veritate, even in cases where
the grammaticality of the containing sentence is not affected and neither ambiguity nor
polysemy can be detected in such verbs as ‘believe’ and ‘infer’. That bona fide terms like
‘the proposition that p’ do refer to propositions is not be to doubted.
It has been diagnosed by Forbes that the reason why the step from
4. Harold fears that mathematics reduces to logic
to
5. Harold fears the proposition that mathematics reduces to logic
fails to preserve truth is that “switching from clausal to transitive verbs changes the way in
which the proposition determined by the ‘that’-clause stands to the state” (2009: 11). The
state of fear ascribed to Harold by (4) is one whose content is that mathematics reduces to
logic. On the other hand, the proposition that mathematics reduces to logic is the object
(theme – in Forbes’ terminology) of the event described by (5), whose agent is Harold. The
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distinction appears to be well observed in the case of fear and applies equally to belief: the
proposition that Donald believes that the Earth moves is the object of Zoltan’s belief in
(15), whereas that Donald believes that the Earth moves is the content of his belief in (16).
If Forbes is on the right track, then what the argument above shows, in my opinion, is that
something is seriously amiss in the relational theory, which conflates the two roles of
propositions as contents and as objects of propositional attitudes.
References
Bach, Kent. 1997, “Do Belief Reports Report Belief?”, Pacific Philosophical Quarterly 78:
215-41.
Forbes, Graeme. 2009, “Content and Theme in Attitude Ascriptions”,
http://www.eecs.umich.edu/~rthomaso/lpw11/forbes.pdf.
King, Jeffrey. 2002, “Designating Propositions”, Philosophical Review 111, 3: 341-71.
Kripke, Saul. 1979, “A Puzzle About Belief”, in A.Margalit (ed.), Meaning and Use, Reidel,
Dordrecht.
Moltmann, Friederike. 2003, “Propositional Attitudes Without Propositions”, Synthese 135:
77-118.
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Rosefeldt, Tobias. 2008, “’That’-Clauses and Non-Nominal Quantification”, Philosophical
Studies 137: 301-333.
Schiffer, Stephen. 2003, The Things We Mean, Oxford University Press, Oxford and New
York.
Schiffer, Stephen. 2006, “Propositional Content”, in E.Lepore and B.Smith (eds.), Oxford
Handbook of Philosophy of Language, Oxford University Press, Oxford and New
York.
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