A Puzzle about Belief Reports


I'd like to present a puzzle about belief reports that's been nagging at me for several years. I've subjected many friends and audiences to various abortive attempts at solving it. Now it's time to get it off my chest and let others try their hand at it.<1>

My puzzle is not to be confused with either Frege's or Kripke's. Frege's (1892) puzzle about attitude reports, which derived from his more famous puzzle about the informativeness of identity statments, concerns the effect of substitution of co-referring terms. Kripke's puzzle (1979) goes deeper than that, showing that there is a similar problem about belief reports even without substitution. In my view, their puzzles arise only on a certain seemingly innocuous assumption, that 'that'-clauses specify belief contents. More precisely, this 'Specification Assumption' says that for a belief report of the form 'A believes that p' to be true, the proposition that p must be among the things that A believes. Frege and Kripke, despite their radically different views on the semantics of 'that'-clauses in belief reports, share this popular assumption. My puzzle arises once it is rejected.

First I will use Kripke's Paderewski case, along with a simple linguistic observation, to call the Specification Assumption into question. Next I will briefly sketch the main options available, given the Specification Assumption, for solving Frege's substitution puzzle, and suggest that these options present an unpalatable dilemma. And then I will explain how giving up that assumption offers prospects for an intuitively more plausible approach to the semantics of belief reports (and attributions of other propositional attitudes). However, this approach must confront a puzzle of its own. For it turns out that every case is a Paderewski case, at least potentially.

1. The Specification Asssumption and Kripke's Puzzle

What could be more plausible than the supposition that a belief report of the form, 'A believes that p', is true only if the proposition that p is among the things that A believes? Belief reports of this form certainly appear to relate believers to things believed. Indeed, it is sometimes suggested that the clause 'that p' is a kind of singular term, whose reference is the proposition that p (the idea is that 'that' is a term-forming operator on sentences). Then we have a straightforward explanation of the apparent validity of such inferences as the following:

I1. Jerry believes everything Hilary says.             (x)(Shx -> Bjx)
    Hilary says that water is wet.                         Shp
    So, Jerry believes that water is wet.<2>               Bjp
If the clause 'that water is wet' is a term, then I1 has the form indicated on the right, in which case it is not only valid but formally valid. The analogous point seems to apply to the following inference:
I2. Art believes that Paderewski had musical talent.       Bap
    Bart believes that Paderewski had musical talent.      Bbp
    So, there is something both Art and Bart believe. (Ex)(Bax & Bbx)

But is it so clear that the 'that'-clause of a true belief report specifies something the believer believes? Consider Kripke's Paderewski case. On account of what Peter believes regarding a certain pianist, an utterance of (1) is true.

(1) Peter believes that Paderewski had musical talent.

Even so, an utterance of (2)

(2) Peter disbelieves that Paderewski had musical talent.

could be true too, because of what Peter believes regarding a certain statesman. It happens that these are the same man, Paderewski, but Peter does not realize this.<3> Kripke's puzzle is to explain how (1) and (2) can both be true (not that both would be uttered in the same context without qualification). They seem to have Peter believing and disbelieving the same thing. That's what they must do if the following inference is formally valid, with the form indicated:

I3. Peter believes that Paderewski had musical talent.      Bap
Peter disbelieves that Paderewski had musical talent.       Dap
So, there is something Peter believes and disbelieves. (Ex)(Bax & Dax)

Kripke's puzzle arises from the fact that Peter's problem is ignorance, not bad logic. But that can't be right if (1) and (2) really do have him believing and disbelieving the same thing, or, equivalently, believing contradictory things. How could he believe contradictory propositions (simultaneously and consciously) without being illogical?

Kripke is so pessimistic about finding a satisfactory way to say what Peter believes that he is led to lament, 'When we enter into [this] area, we enter into an area where our normal practices of interpretation and attribution of belief are subjected to the greatest possible strain, perhaps to the point of breakdown' (1979, pp. 268-9). I say there's no such strain, once we see through the illusion that (1) and (2) have Peter believing and disbelieving the same thing.

The alternative is to reject the Specification assumption and say that (1) and (2) are true but not because Peter believes and disbelieves the same thing. This is possible because the 'that'-clause they contain does not specify anything he believes or anything he disbelieves--it merely characterizes something he believes and characterizes something he disbelieves, and these needn't be the same thing. Compare the following sentences:

Peter likes a certain pianist.

Peter dislikes a certain pianist.

There is no implication here that Peter likes and dislikes the same pianist. Somewhat similarly, I suggest, (1) and (2) do not jointly imply that Peter believes and disbelieves the same thing. One and the same 'that'-clause, even though it expresses but one proposition, can characterize (as opposed to specify) two distinct belief contents. This entails that a belief report can be true even if the believer does not believe the specific proposition expressed by the 'that'-clause. With (1), for example, Peter must believe something such that Paderewski had musical talent, but he need not believe *that* proposition.

You might think that believing that p just *is* believing the proposition that p. After all, (2) seems equivalent to (2p),

(2p) Peter disbelieves the proposition that Paderewski had musical talent.

But the following are anything but equivalent:

(2') Peter suspects/fears/realizes that Paderewski had musical talent.

(2p') Peter suspects/fears/realizes the proposition that Paderewski had musical talent.

The oddity of (2p') should make one wonder whether 'that'-clauses in attitude contexts really do refer to propositions.

On the alternative 'descriptivist' view, 'that'-clauses in belief reports do not specify but merely characterize things believed. If this view is correct, inference I3 above does not have the indicated form and is not formally valid. But in that case inferences I1 and I2 do not have the forms indicated for them and are not formally valid either. That they are is an illusion due to the Specification Assumption. Once we abandon that assumption, we can see that even though their respective 'that'-clauses express the same proposition, (1) and (2) can both be true without Peter believing and disbelieving the same thing.

2. The Specification Asssumption and Frege's Substitution Puzzle

The pernicious effect of the Specification Assumption is evident if we consider the main options it allows for solving Frege's substitution puzzle. As we will see, it forces a dilemma on us: we must choose between a solution that requires terms mysteriously to acquire special semantic roles in belief contexts and one which implausibly rejects the intuitive explanation of why the puzzle arises in the first place.

Ordinarily, replacing one term with another, co-referring term does not and cannot affect truth value. For example, if 'Superman can fly' is true, then so is 'Clark Kent can fly'. But in belief contexts, substitution seems to affect truth value. Even though Clark Kent is Superman, substituting 'Clark Kent' for 'Superman' in (3)

(3) Lois has always believed that Superman can fly.

seems to turn a truth into a falsehood:

(4) Lois has always believed that Clark Kent can fly.

The puzzle is to explain why substitution can fail in belief (and other attitude) contexts. How can being embedded matter? Whatever the answer, it should reckon with the apparent fact that (3) and (4) have Lois believing two different things, that Superman can fly and that Clark Kent can fly. Because she can believe one without believing the other, the truth values of (3) and (4) can differ accordingly. The problem is how to explain all this, or else explain it away.<4>

It is natural to suppose that the 'that'-clause in a belief report specifies something the believer believes and that substitution can affect what is specified. The two traditional view suppose this.

FREGEAN: This view denies that terms occurring in embedded clauses have their 'customary' references. It claims that they refer instead to their (customary) senses (their 'indirect' references). The embedded sentence refers to the 'thought' (or 'Fregean proposition') that the person is being said to believe. Unembedded, the sentence would express the thought but not refer to it.<5>

METALINGUISTIC: Like the Fregean view, this view denies that terms occurring in embedded sentences have their customary references. It claims instead that such terms refer to themselves, or, alternatively, to their translations in the believer's language (or perhaps to their translations in his mental language). On such a quotationalist or sententialist view, belief reports relate believers not to propositions but to sentences (or mental representations).<6>

Notice that both the Fregean and the metalinguistic views in effect reject the original terms of the substitution puzzle. They deny that substituting 'Clark Kent' for 'Superman' in a belief context really *is* a case of substituting one co-referring term for another--in such contexts the names do not have their usual references. This is the price these views are willing to pay in order to explain the effect of substitution (e.g., that the difference between (3) and (4) concerns what they have Lois believing). Unfortunately, these views do not give an independently motivated account of how and why such reference shifts should occur. One symptom of trouble is that in a sentence like (5),

(5) Lois believes that Clark Kent can't fly, but he can.

the pronoun 'he' refers to Clark Kent even though it is anaphoric on the embedded name, 'Clark Kent', which is supposed not to refer to Clark Kent in this context. This difficulty may be superficial, but it illustrates why positing a reference shift just doesn't ring true.

The contemporary approach is to avoid reference shifts and maintain that constituents of an embedded sentence have their usual references. But then, since 'Superman' and 'Clark Kent' have the same reference, it seems that the difference between (3) and (4) must consist in something other than what they have Lois believing. Indeed, the two main current views on the subject say precisely this. They both distinguish the 'how' from the 'what' of belief and claim that (3) and (4) differ not in what they have Lois believing but in how they have her believing it.<7> They both hold that an embedded sentence refers to a Russellian proposition, whose constituents are objects and properties (or relations).<8> Since the 'that'-clauses of (3) and (4) refer to the same proposition, the singular proposition that Superman/Clark Kent can fly, (3) and (4) as a whole have Lois believing the same thing.<9> Even so, utterances of (3) and (4) can differ in how they have her believing it. Speakers, by how they word the 'that'-clause in a belief report, convey information about ways of thinking of things and ways of taking propositions, but this information is part of the semantic content of the 'that'-clause. In particular, using 'Clark Kent' rather than 'Superman' conveys different information about how Lois thinks of the individual both names name, so that using a 'that'-clause containing one name rather than the other conveys different information about how she takes the proposition that he can fly.

The two views in question differ in how they regard the semantic status of such information.

NEO-RUSSELLIAN: On this view, such information is merely 'pragmatically imparted', as Salmon (1986) puts it (he proposes an ingenious explanation of how this information is readily confused with semantic content). This view rejects the anti-substitution intuition, at least as far as the semantic contents of belief reports are concerned. (4) does follow from (3): to believe that Clark Kent can fly *is* to believe that Superman can fly, at least under some way of taking that proposition.

HIDDEN-INDEXICAL: Alternatively, information about ways of taking propositions, even though it is conveyed only tacitly, *is* part of the semantic contents of belief reports.<10> Claiming this requires denying that (3) and (4) have the logical form they appear to have: 'believe' (or any verb of propositional attitude) expresses not a dyadic but a triadic relation, involving not only persons and propositions but also ways of taking propositions, to which utterances of belief sentences make tacit reference. Then (3) is true relative to one implicitly referred to way of taking the singular proposition that Superman/Clark Kent can fly, and (4) is false relative to another.<11>

Both views are counterintuitive. The neo-Russellian view implausibly rejects the anti-substitution intuition that gives rise to Frege's puzzle in the first place. This intuition is so strong that, as Mark Richard suggests, it would take 'bribery, threats, hypnosis, or the like ... to get most people' to think that (3) and (4) have Lois believing the same thing (1990, p. 125).<12> The hidden-indexical theory purports to respect the anti-substitution intuition, but in fact it claims, contrary to a key element of that intuition, that (3) and (4) do have Lois believing the same thing--they differ only in how they have her taking that proposition. Moreover, it provides no linguistic explanation of where the extra argument place comes from.<13>

If the four views considered (and their variants) exhaust the options available on the Specification Assumption, then collectively they pose a dilemma with respect to the anti-substitution intuition. The first two, in an effort to explain why (3) and (4) have Lois believing two different things, both posit theoretically unmotivated reference shifts. The last two avoid reference shifts but deny the basis of the intuition, namely that (3) and (4) have Lois believing two different things. Escaping this dilemma requires explaining, without positing reference shifts, how (3) can be true because of one thing Lois believes and how (4), if it were true, would be true because of something else she believes?<14>

To appreciate how this can be, compare Lois's situation with that of Perry White, Clark Kent's editor at the Daily Planet. For him, believing that Clark Kent can fly amounts to the same thing as believing that Superman can fly. This is so because he was party to Superman's Clark Kent ploy in the first place. Perry has always believed that Superman can fly and also that Clark Kent can fly, but that is in virtue of only one belief of his. No wonder Perry believes that only one individual can fly. Things would be different with Lois even if she came to believe that Clark Kent can fly. Suppose she saw Clark, attired in a grey suit, suddenly soar into the air but she was still so smitten with Superman that she did not make the obvious inference. We would describe her as now believing that Clark Kent can fly, but the belief that makes this so would be distinct from her longstanding belief that Superman can fly. Together they lead her to believe that two individuals can fly. Unlike her, Perry believes that only one individual can fly.

3. Giving up the Specification Assumption: A New Puzzle

Why does it take bribery, threats or hypnosis to get most people to think that (3) and (4) say the same thing? The reason is very simple. (3) and (4) have Lois believing two different things. It's not that she believes the same thing in two different ways--she believes two different things. An analogous point explains what's puzzling about the Paderewski case. The puzzle here concerns what Peter believes, not how he believes it. (1) is true because Peter believes one thing, and (2) is true because he disbelieves something else. So, we might ask, how can this be, if the same 'that'-clause occurs in both? That is my puzzle.

The solution *begins* with the rejection of the Specification Assumption. Once we realize that the 'that'-clauses in (1) and (2) do not specify anything Peter believes and disbelieves, we can see that (1) and (2) do not express relational propositions, of the form 'Bap' and 'Dap' respectively. 'Believes' and 'disbelieves' express dyadic relations all right, and Peter is one of the terms of that relation, but there is no reference to, or specification of, the other term of that relation. For the only thing that could be the other term is the proposition that Paderewski had musical talent, but that is not what Peter believes or disbelieves. What he believes is something that requires the truth of that proposition, but that proposition is not what he believes. Similarly, what he disbelieves is something that requires the truth of that proposition (he believes something that requires the falsity of that proposition). But neither what he believes nor what he disbelieves is specified by the 'that'-clause in (1) and (2). The puzzle, then, is to explain what makes (1) and (2) true anyway.

A solution must answer three questions:

Q1: What is the relation between the proposition expressed by the 'that'-clause

in a true belief report and the belief(s) that it characterizes?

Q2: How can propositionally equivalent 'that'-clauses characterize different beliefs?

Q3: How can they characterize different beliefs in one context (as with Lois) and

the same beliefs in another context (as with Perry)?

It is important to realize that my puzzle about belief reports is not limited to isolated cases like Paderewski. It is epidemic--every case is a Paderewski case, at least potentially. Kripke thinks that the puzzle cases are special cases (he is reluctant to draw conclusions from them because 'hard cases make bad law'), but there is nothing special about 'that Paderewski had musical talent'--it is a perfectly ordinary 'that'-clause. Similar puzzles arise with belief reports whose 'that'-clauses express general propositions rather than singular ones. For *any* 'that'-clause 'that S', there could be circumstances in which someone believes that S and disbelieves that S without being illogical. For it need not specify anything that he both believes and disbelieves.

It might seem that the problem here is merely one of insufficient detail. Make the 'that'-clause more specific in one way and you can say what Peter believes; make it more specific in another way and you can say what he disbelieves. Yes, we could embellish (3) and say that Peter believes that Paderewski the pianist had musical talent and embellish (4) and say that he disbelieves that Paderewski the statesman had musical talent, but ultimately this strategem does not work. Suppose that Peter hears two recordings, a beautiful performance of Rachmaninov and a horrible jazz improvisation, both by Paderewski. Then it wouldn't do any good to say that Peter believes that Paderewski the pianist had musical talent, because we could just as well have said that he disbelieves that Paderewski the pianist had musical talent. We could say that Peter believes that Paderewski the classical pianist had musical talent but that he disbelieves that Paderewski the jazz pianist had musical talent. But this ploy won't ultimately work either. Suppose Peter hears a recording of an atrocious performance of Mozart (by Paderewski) after the gorgeous performance of Rachmaninov. We could say that Peter disbelieves that Paderewski the classical pianist had musical talent, but this would not distinguish what he disbelieves from what he believes. We would need to say that Peter disbelieves that Paderewski the classical pianist playing Mozart had musical talent, and that Peter believes that Paderewski the classical pianist playing Rachmaninov had musical talent. ... When it comes to saying what someone believes, we can always say more but, it seems, we can never say enough.

This deepens my puzzle about belief reports. Not only do 'that'-clauses merely characterize belief contents, they are not inherently capable of fully specifying the contents of beliefs. Any belief report is potentially a Paderewski case. What, then, are belief contents, such that their contents can't be specified fully by 'that'-clauses, and how *can* belief contents be specified fully? Now that's a puzzle.<15>

Copyright Kent Bach 1997



Bach, K. 1994. Conversational impliciture. Mind & Language 9: 124-62.

Crimmins, M. 1992. Talk about Beliefs. Cambridge, MA: MIT Press.

Forbes, G. 1990. The indispensability of sinn. Philosophical Review 99: 535-563.

Frege, G. 1892. On sense and reference. In Translations of the Philosophical Writings

of Gottlob Frege, ed. P. Geach and M. Black. Oxford: Blackwell.

Kripke, S. 1979. A puzzle about belief. In Meaning and Use, ed. A. Margalit.

Dordrecht: Reidel.

Richard, M. 1990. Propositional Attitudes: An Essay on Thoughts and How We Ascribe

Them. Cambridge: Cambridge University Press.

Salmon, N. 1986. Frege's Puzzle. Cambridge, MA: MIT Press.

Schiffer, S. 1977. Naming and knowing. Midwest Studies in Philosophy 2: 28-41.

Schiffer, S. 1992. Belief ascription. Journal of Philosophy 89: 490-521.


1. To make my puzzle clear, in giving the necessary but, I hope, familiar background I will often either omit details or relegate them to the endnotes and give references.

2. Contrary to philosophical legend, water is not wet--it only makes things wet.

3. As Kripke describes the situation, Peter uses the name 'Paderewski' for what he takes to be two different individuals, but it is inessential to the problem that Peter even be familiar with the name. Uses of (1) and (2) could be prompted by Peter's reaction to two different photographs, for example. Frege's substitution puzzle is also not essentially about names the believer uses.

4. One thing to keep in mind is this. If you utter 'Superman can fly', you thereby say, and express the belief, that Superman can fly. However, you are not saying that you are saying this or that you believe this. If you uttered 'Clark Kent can fly' instead, your utterance would have the same propositional content but you would not be expressing the same belief. But you are not talking about the belief--you are talking about Clark Kent (or Superman). Ordinary statements express beliefs but, unlike belief reports, are not about beliefs.

5. Frege held that the referent of an unembedded sentence is a truth value (the True or the False), but one could hold, more plausibly, that it is a proposition, of the sort composed of the referents of the constituents of the sentence, and still be something of a Fregean. To be sure, this would be not a 'Fregean' but a 'Russellian proposition'. Even so, as a Fregean one could still hold that the sentence *expresses* a Fregean proposition, or what Frege himself called a 'thought'.

6. A more extreme version of the metalinguistic view denies that constituents of embedded sentences refer at all and that belief reports relate believers to anything at all. I will ignore this view in what follows. Obviously such a view is not committed to the Specification Assumption. The most glaring difficulty with such a view is that it has to treat each belief-predicate (of the form 'believes that S') as semantically primitive.

7. Both theories, though anything but Fregean--they claim that 'that'-clauses refer to Russellian propositions, not Fregean ones--still exploit Frege's notion of 'mode of presentation.' They distinguish individuals from ways of thinking of them, and (Russellian) propositions from ways of taking them. Ways of taking Russellian propositions (modes of presentation of them) are essentially Fregean propositions, or thoughts.

8. In the case of (3) and (4), this is a 'singular' proposition, so-called because its subject constituent is an individual (or sequence of individuals). The simplest form of such a proposition may be represented as a sequence of the form: <a,F>.

9. This assumes that proper names such as 'Clark Kent' and 'Superman' are devices of direct reference, even as they occur in belief contexts. You might turn the point around and argue that the two 'that'-clauses refer to different propositions, hence that names are not devices of direct reference, at least in belief contexts. Rejecting the Specification Assumption, as we will do later, makes this issue moot. The alternative is to deny, e.g., that (3) is true because Lois believes the singular proposition its 'that'-clause expresses. One could deny this on grounds first given by Schiffer (1977), namely that singular propositions cannot comprise complete contents of beliefs.

10. This proposal was first advanced by Schiffer (1977) and has since been developed in detail by Crimmins (1992). It claims, in effect, that belief sentences fail to express complete propositions independently of context, that they are semantically incomplete (for discussion of this notion, see Bach 1994). Significantly different versions have been proposed by Forbes (1990) and by Richard (1990).

11. (4) could be true relative to the way of taking that proposition relative to which (3) is true. However, because 'Clark Kent' is being used rather than 'Superman', a typical utterance of (4) would refer to a different way of taking that proposition, and relative to that way of taking it (4) is false.

12. Only the neo-Russellian view regards the inference from (3) to (4) as formally valid, having the following form:


k = s

So, Bl<k,F>

The trouble is, taking I4 to have this form is tantamount to rejecting the anti-substitution intuition.

13. This is one of several objections brought by Schiffer (1992) against the hidden-indexical theory. He calls this the 'logical form' problem. There is a related grammatical form problem: the hidden-indexical theory seems to violate the principle of Compositionality, which says, roughly, that the meaning of a sentence is determined by its syntactic structure and the meanings of its constituents. There is no evident syntactic basis for the alleged device (the "hidden" indexical) of tacit reference. The hidden-indexical theory at least respects the principle of Semantic Innocence, which says that embedding expressions in particular constructions, such as 'that'-clauses in belief reports, does not change their meaning or reference. These principles and how they tie in to Frege's puzzle are discussed in Crimmins (1992, ch. 1). The Fregean and the metalinguistic views, with their claim of a reference shift, violate Semantic Innocence. Crimmins also explains the relevance of the principle of Direct Reference, which denies that determinants of reference, as opposed to the referents themselves, enter into semantic contents). Notice that Semantic Innocence is logically independent of Direct Reference, although proponents of the former generally endorse the latter.

14. How do the four types of theory sketched above fare with the Paderewski case, which does not involve substitution? Here, it seems, the referentially shifty approaches have a real problem, inasmuch as (1) and (2) contain identical 'that'-clauses. The Fregean and metalinguistic views would like to claim that Peter is being said to believe one thing and to disbelieve something else. Its strategy in the substitution case was to claim that substitution (e.g. of 'Clark Kent' for 'Superman') changes the reference in a belief context. But the same move is not available in the Paderewski case, where there is no substitution. There is no linguistic difference between the 'that'-clauses of (1) and (2), nothing to capture the difference between what Peter is being said to believe and what he is being said to disbelieve. The neo-Russellian and the hidden-indexical theories claim that (1) and (2) have Peter believing and disbelieving the same proposition, but under two different ways of taking it. The trouble with this claim, quite simply, is that (1) and (2) *seem* to have Peter believing one thing and disbelieving something else. The puzzle with Peter seems to be what he believes, not how he believes it. The challenge in solving that puzzle is to reckon with the fact that there is no difference between the 'that'-clauses of (1) and (2), nothing to mark the difference between what Peter believes and what he disbelieves.

15. Thanks to David Sosa for his very helpful advice.