The Relational Analysis of Belief Ascriptions and Schiffer’s Puzzle

Abstract

Using a variant of Schiffer’s puzzle regarding de re belief, I recently presented a new argument against the so-called Naive Russellian theory, consisting of the following theses: ($NR_{1}$) The propositions we say and believe are Russellian propositions, i.e., structured propositions consisting of the objects, properties, and relations our thoughts and speech acts are about; ($NR_{2}$) Names (and other singular terms) are directly referential terms, i.e., the propositional content of a name is just its referent; ($NR_{3}$) A sentence of the form ‘A believes/disbelieves that S’ is true in a context c if and only if the referent of A in c believes/disbelieves the proposition expressed by S in c. In this paper, I will argue that my variant of Schiffer’s puzzle is not only a problem for the Naive Russellian theory, but for every theory of belief ascriptions entailing ($NR_{3}$). Such theories are also called relational analyses of belief ascriptions. Here the main alternative to a Neo-Russellian theory, consisting of ($NR_{1}$) and ($NR_{2}$), is a Fregean theory, according to which the propositions we say and believe are Fregean propositions, i.e., structured propositions consisting of ways the objects, properties, and relations our thoughts and speech acts are about are presented to the speaker or agent. I will argue that such variants of the relational analysis are committed to principles very similar to the principles used by my Schiffer puzzle. Concluding, I will discuss Fregean and Neo-Russellian alternatives to the relational analysis, and I will argue that, although there are Neo-Russellian alternatives to the relational analysis which provide a solution to my variant of Schiffer’s puzzle, there seem to be no such Fregean alternatives.

1 Introduction

Using a variant of Schiffer’s (2006) puzzle regarding de re belief, in Rinner (2022) I recently presented a new argument against the so-called Naive Russellian theory, consisting of the following theses (see, e.g., Salmon 1986a/1986b, 1989, 2006, Braun 1998, 2006):¹²

($NR_{1}$):

The propositions we say and believe are Russellian propositions, i.e., structured propositions consisting of the objects, properties, and relations our thoughts and speech acts are about.

($NR_{2}$):

Names (and other singular terms) are directly referential terms, i.e., the propositional content of a name is just its referent.

($NR_{3}$):

A sentence of the form ‘A believes/disbelieves that S’ is true in a context c if and only if the referent of A in c believes/disbelieves the proposition expressed by S in c.³

First, I argue that the Naive Russellian theory is committed to the following principles regarding de re belief:⁴

The Exportation Principle

(EP) Necessarily, if $\alpha$ believes/disbelieves that $\psi _{[\beta ]}$, then $\beta$ is believed/disbelieved by $\alpha$ to be (something/someone) such that $\psi _{[it]}$.⁵

Frege’s Constraint

(FC) Necessarily, if an object o is rationally both believed and disbelieved by an agent k to be (something/someone) such that $\phi _{[it]}$, then there are modes of presentation m and $m'$ of o such that

• 1. o is believed by k to be (something/someone) such that $\phi _{[it]}$ under m,

• 2. o is disbelieved by k to be (something/someone) such that $\phi _{[it]}$ under $m'$, and

• 3. k takes m and $m'$ to be modes of presentation of different objects.⁶

Then, I go on to show that, together with the Naive Russellian theory and plausible assumptions, (EP) and (FC) lead to contradictions.

In this paper, I will argue that my variant of Schiffer’s puzzle is not only a problem for the Naive Russellian theory, but for every theory of belief ascriptions entailing ($NR_{3}$). Such theories are also called relational analyses of belief ascriptions. Here the main alternative to a Neo-Russellian theory, consisting of ($NR_{1}$) and ($NR_{2}$), is a Fregean theory, according to which the propositions we say and believe are Fregean propositions, i.e., structured propositions consisting of ways the objects, properties, and relations our thoughts and speech acts are about are presented to the speaker or agent (see, e.g., Frege 1892, 1918-19, Chalmers 2011, Recanati 2012). I will argue that such variants of the relational analysis are committed to principles very similar to (EP) and (FC), and that, together with the relational analysis and plausible assumptions, these principles lead again to contradictions. Concluding, I will discuss Fregean and Neo-Russellian alternatives to the relational analysis, and I will argue that, although there are Neo-Russellian alternatives to the relational analysis which provide a solution to my variant of Schiffer’s puzzle, there seem to be no such Fregean alternatives.

2 Schiffer Puzzles and the Naive Russellian Theory

Just like I did in Rinner (2022), Schiffer (2006) presents his puzzle regarding de re belief as an argument against the Naive Russellian theory. However, instead of the exportation principle, Schiffer uses a logically stronger principle, i.e., the so-called special-case consequence:⁷

The Special-case Consequence

(S) Necessarily, if $\alpha$ believes/disbelieves that $\phi _{\beta }$, then $\beta$ is believed/disbelieved by $\alpha$ to be (something/someone) such that $\phi _{it}$.

According to Schiffer, the Naive Russellian theory is committed to the special-case consequence. If an agent k believes de dicto the singular proposition about o that it (he, she) is P, then, the argument goes, o is believed by k (de re) to be (something/someone) such that it (he, she) is P.

Schiffer (2006, 363) then goes on to show that, together with Frege’s constraint, the special-case consequence leads to contradictions. For example, even a rational, normal English speaker who believes ‘Karol Wojtyła = John Paul II’ to be true could be disposed to sincerely and reflectively utter both (1) and (2), e.g., if the speaker has Fregean intuitions regarding the truth values of sentences such as (1) and (2).

• (1) Ralph believes that Karol Wojtyła is Polish.

• (2) It is not the case that Ralph believes that John Paul II is Polish.

Let us assume that Sally is such a speaker. Together with simple disquotational principles connecting sincere assertion and belief/disbelief, it would follow that both (3) and (4) are true.⁸

• (3) Sally believes that Ralph believes that Karol Wojtyła is Polish.

• (4) Sally disbelieves that Ralph believes that John Paul II is Polish.

If (3) and (4) are true, then, according to the special-case consequence, so are (5) and (6).

• (5) Karol Wojtyła is believed by Sally to be (someone) such that Ralph believes that he is Polish.

• (6) John Paul II is disbelieved by Sally to be (someone) such that Ralph believes that he is Polish.

From this, in turn, it would follow together with Frege’s constraint that Sally has two modes of presentation of Karol Wojtyła which she takes to be modes of presentation of different persons. However, since Sally believes ‘Karol Wojtyła = John Paul II’ to be true, we can assume that she does not have two such modes of presentation. This is Schiffer’s puzzle.

Even for a Naive Russellian such as Salmon the solution to the puzzle cannot be to reject Frege’s constraint. For instance, Salmon (2006, 370) points out that if an agent k rationally believes o to be (something/someone) such that $\phi _{it}$ and disbelieves $o'$ to be (something/someone) such that $\phi _{it}$, then, in so doing, k takes o and $o'$ to be distinct. Insofar as k is rational, they thereby take o and $o'$ differently, even if, in fact, $o=o'$. However, although Naive Russellians seem to be committed to Frege’s constraint, according to Salmon (2006), they are not committed to the special-case consequence, but to counter-instances of the special-case consequence. For instance, if (3) and (4) are true, then Sally both believes and disbelieves the singular proposition $\langle \langle$Ralph, $\langle$Karol Wojtyła, being Polish$\rangle \rangle$, believing$\rangle$. But she does not thereby both believe and disbelieve the singular proposition $\langle$Karol Wojtyła, being (someone) such that Ralph believes that he is Polish$\rangle$. Since this would be required for (5) and (6) to be true, according to the Naive Russellian theory, from the fact that (3) and (4) are true it does not follow that so are (5) and (6).

Even if the Naive Russellian theory is not committed to the special-case consequence, according to Salmon, it is still committed to the (weaker) exportation principle, where $\psi _{it}$ is any standard English open sentence with monadic-predicational form, ‘It’+VP, such that VP is a monadic predicate in which the pronoun ‘it’ does not occur free:

The Exportation Principle (EP) Necessarily, if $\alpha$ believes/disbelieves that $\psi _{\beta }$, then $\beta$ is believed/disbelieved by $\alpha$ to be (something/someone) such that $\psi _{it}$.

As Salmon (2006, 371) points out, VP is then a term for a particular property or singulary-functional concept F. Thus, an agent who believes the singular proposition expressed by ‘It’+VP under the assignment of a particular object o to the variable ‘it’ can be said to believe o to be F.

This is where my variant of Schiffer’s puzzle enters the scene. As I point out in Rinner (2022), even a rational, normal English speaker who believes that the that-clauses in (1) and (2) designate the same proposition, could be disposed to sincerely and reflectively utter both (1) and (2), i.e., if they share the intuitions of Neo-Russellians such as Crimmins and Perry (1989, Crimmins 1992). Although these philosophers believe that the that-clauses in (1) and (2) designate the same proposition, they have strong intuitions that there are circumstances in which both (1) and (2) are true. As I argue in Rinner (2022), the same is true of (7) and (8).

• (7) That Karol Wojtyła is Polish is believed by Ralph.

• (8) That John Paul II is Polish is not believed by Ralph.

Thus, as a rational, normal English speaker who believes that the that-clauses in (7) and (8) designate the same proposition, Sally could be disposed to sincerely and reflectively utter both (7) and (8). Together with simple disquotational principles connecting sincere assertion and belief/disbelief, it would follow that both (9) and (10) are true.

• (9) Sally believes the following: That Karol Wojtyła is Polish is believed by Ralph.

• (10) Sally disbelieves the following: That John Paul II is Polish is believed by Ralph.

If (9) and (10) are true, then, according to the exportation principle, so are (11) and (12).

• (11) That Karol Wojtyła is Polish is believed by Sally to be something such that it is believed by Ralph.

• (12) That John Paul II is Polish is disbelieved by Sally to be something such that it is believed by Ralph.

From this, in turn, it would follow together with the Naive Russellian theory and Frege’s constraint that Sally has two modes of presentation of the (Russellian) proposition designated by the that-clauses in (11) and (12) which she takes to be modes of presentation of different propositions. However, since Sally believes that the that-clauses in (7) and (8) designate the same proposition, we can again assume that she does not have two such modes of presentation.⁹

In this way, my variant of Schiffer’s puzzle in Rinner (2022) shows that the Naive Russellian theory and Frege’s constraint already lead to contradictions together with the (weaker) exportation principle (EP). Before discussing possible solutions to my variant of Schiffer’s puzzle, next, I will argue that it is not only a problem for Naive Russellians, but for relational analyses of belief ascriptions in general. Among other things, this will suggest that the solution to the puzzle cannot simply be to reject the Neo-Russellian theory, consisting of the theses ($NR_{1}$) and ($NR_{2}$).

3 Schiffer Puzzles and the Relational Analysis

Ultimately, in my variant of Schiffer’s puzzle, I only use the following instance of the exportation principle when inferring (11) and (12) from (9) and (10), respectively.

($EP'$):

Necessarily, if $\alpha$ believes/disbelieves that that S is believed by A, then that S is believed/disbelieved by $\alpha$ to be something such that it is believed by A.

Now, it seems that not only Naive Russellians are committed to ($EP'$), but relational analyses of belief ascriptions in general. After all, in order for (9) and (10) to be true, Sally has to be acquainted with the propositions designated by the respective that-clauses, regardless of what these propositions are. From this, in turn, it seems to follow that the propositions are believed or disbelieved, respectively, by Sally to be something that is believed by Ralph.

Similarly, also Salmon’s argument for the relevant instances of Frege’s constraint seems to be independent of which theory of propositions is correct. If an agent k rationally believes a proposition p to be something that is believed by x and disbelieves a proposition $p'$ to be something that is believed by x, then, in so doing, k takes p and $p'$ to be distinct. Insofar as k is rational, they thereby take p and $p'$ differently, even if, in fact, $p=p'$.

An advocate of the relational analysis could respond that, although relational analyses are committed to both ($EP'$) and Frege’s constraint, my variant of Schiffer’s puzzle is only a problem for the Naive Russellian theory. After all, only if the that-clauses ‘that Karol Wojtyła is Polish’ and ‘that John Paul II is Polish’ designate the same proposition does it follow from (11) and (12) that there is a proposition p such that p is both believed and disbelieved by Sally to be something that is believed by Ralph. Indeed, according to a Fregean variant of the relational analysis, from (11) and (12) it only follows that there are propositions p and $p'$ such that p is believed by Sally to be something that is believed by Ralph, and $p'$ is disbelieved by Sally to be something that is believed by Ralph. Hence, even if p and $p'$ are not presented to Sally by two modes of presentation which she takes to be modes of presentation of different propositions, this does not contradict Frege’s constraint. However, it contradicts the following rationality principle regarding de re belief of which Frege’s constraint is an instance:

($FC'$):

Necessarily, if an object o is rationally believed by an agent k to be (something/someone) such that $\phi _{[it]}$, and an object $o'$ is rationally disbelieved by k to be (something/someone) such that $\phi _{[it]}$, then there is a mode of presentation m of o and a mode of presentation $m'$ of $o'$ such that

1.:

o is believed by k to be (something/someone) such that $\phi _{[it]}$ under m,

2.:

$o'$ is disbelieved by k to be (something/someone) such that $\phi _{[it]}$ under $m'$, and

3.:

k takes m and $m'$ to be modes of presentation of different objects.

Since Salmon’s argument for Frege’s constraint is primarily an argument for ($FC'$), which treats Frege’s constraint only as a special case, this is just as problematic, suggesting that my variant of Schiffer’s puzzle is ultimately a problem for relational analyses of belief ascriptions in general. Regardless of which theory of propositions is assumed to be true, together with ($EP'$) and ($FC'$), relational analyses lead to contradictions.

The solution to the puzzle cannot be to maintain that with respect to (7) and (8) Sally does not count as a normal English speaker, and that, therefore, from her sincere and reflective utterances of (7) and (8) it does not follow that both (9) and (10) are true. For instance, the intuitions of Neo-Russellians such as Crimmins and Perry show that even normal English speakers who believe that the that-clauses in (7) and (8) designate the same proposition can take (7) and (8) to express different propositions. Hence, if, according to the relational analysis, such speakers would not count as normal English speakers when it comes to sentences such as (7) and (8), this would in itself undermine the relational analysis of belief ascriptions.

An advocate of the relational analysis could object that in the above example Sally does not use (8) as it is standardly used, i.e., to reject the proposition (semantically) expressed by ‘That John Paul II is Polish is believed by Ralph’. For example, in order to explain within the Naive Russellian theory that rational, normal speakers can take both (1) and (2) to be true, Felappi (2022) claims that (2) can be used to metalinguistically reject (13) or what (13) pragmatically suggests.

• (1) Ralph believes that Karol Wojtyła is Polish.

• (2) It is not the case that Ralph believes that John Paul II is Polish.

• (13) Ralph believes that John Paul II is Polish.

According to this proposal, if Sally sincerely asserts both (7) and (8), she uses (8) to metalinguistically reject (14) (or what (14) pragmatically suggests).

• (7) That Karol Wojtyła is Polish is believed by Ralph.

• (8) That John Paul II is Polish is not believed by Ralph.

• (14) That John Paul II is Polish is believed by Ralph.

But then from Sally’s sincere assertions we can no longer infer that (10) is true, and, thus, my variant of Schiffer’s puzzle would be blocked.

Note that this solution would only be available to Naive Russellians as Fregeans standardly explain the fact that both (1) and (2) (and (7) and (8), respectively) can be true with the fact that the respective that-clauses designate different propositions. Hence, if Fregeans resorted to metalinguistic negation in order to explain that rational, normal speakers, such as Sally, can take both (7) and (8) to be true, this would undermine the Fregean explanation of the truth values of belief ascriptions such as (7) and (8). But even when it comes to the Naive Russellian theory a metalinguistic use of (2) or (8), respectively, is implausible. For instance, Felappi agrees with Naive Russellians such as Salmon (1986) that the reason why normal speakers have strong intuitions that there are circumstances in which (1) is true and (13) is false (and vice versa) is that they mistake certain pragmatic implications of (1) and (13), respectively, for semantic implications. But then these very same speakers should already take the standard use of (2) to reject these pragmatic implications of (13). After all, normal speakers take the standard use of (2) to reject the proposition semantically expressed by (13). Hence, if they mistake certain pragmatic implications of (13) for semantic implications of (13), then they should take the standard use of (2) to reject these pragmatic implications.¹⁰ Since these pragmatic implications are exactly why, according to Naive Russellians, normal speakers can take (13) to be false, even though they take (1) to be true, this would then explain that rational, normal speakers can be disposed to sincerely assert both (1) and (2) (and (7) and (8), respectively) when used with their standard meanings. This not only speaks against the existence of a metalinguistic use of (2) and (8) within the Naive Russellian theory, but above all suggests that even for Naive Russellians the solution to my variant of Schiffer’s puzzle cannot be to block the step from Sally’s sincere assertions of (7) and (8) to (9) and (10).

As I point out in Rinner (2022), the obvious solution to my variant of Schiffer’s puzzle is to claim with Crimmins and Perry (1989, Crimmins 1992) that Sally believes something along the lines of the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m\rangle$ and disbelieves something along the lines of the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m'\rangle$, where m and $m'$ are two different ways the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$ is presented to Ralph.¹¹ Together with principles such as (EP) and ($EP'$), it would then only follow that the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$ is believed by Sally to be something that is believed by Ralph under m and disbelieved by Sally to be something that is believed by Ralph under $m'$, which would not require that Sally has two different modes of presentation of $\langle$Karol Wojtyła, being Polish$\rangle$. However, such a solution is not available to advocates of a relational analysis. According to ($NR_{3}$), both in (9) and (10) ‘believe’ and ‘disbelieve’ express two-place relations holding between agents and propositions. Thus, together with principles such as (EP) and ($EP'$), from (9) and (10) it only follows that the proposition that Karol Wojtyła is Polish is believed by Sally to be something that is believed by Ralph, and that the proposition that John Paul II is Polish is disbelieved by Sally to be something that is believed by Ralph. According to ($FC'$), this would then require that the propositions are presented to Sally by two modes of presentation which she takes to be modes of presentation of different propositions (see Rinner 2022).

An advocate of the relational analysis could respond that, although the propositions designated by the that-clauses in (11) and (12) are not presented to Sally by two modes of presentation which she takes to be modes of presentation of different propositions, the same is not true of the property of being believed by Ralph. For example, it could be argued that the property of being believed by Ralph is presented to Sally both as the property of being believed by Ralph under m and as the property of being believed by Ralph under $m'$, where m and $m'$ are two different ways the propositions designated by the that-clauses in (11) and (12) are presented to Ralph. However, if Sally mistakes the property of being believed by Ralph for the property of being believed by Ralph under m or $m'$, respectively, then, as I point out in Rinner (2022), this seems to be tantamount to saying that Sally does not ascribe to the proposition that Karol Wojtyła is Polish the property of being believed by Ralph, but rather the property of being believed by Ralph under m. Again, this is the obvious solution to my variant of Schiffer’s puzzle. However, as we have seen in this section, such a solution is not available to advocates of a relational analysis of belief ascriptions.

All of this suggests that in order to block my variant of Schiffer’s puzzle advocates of a relational analysis have to reject ($EP'$) or ($FC'$). However, next, I will argue that, independent of whether they accept a Neo-Russellian or a Fregean theory of propositions, for advocates of a relational analysis the solution to my variant of Schiffer’s puzzle can neither be to reject ($EP'$) nor to reject ($FC'$).

4 Rejecting Exportation or Frege’s Constraint

As I point out in Rinner (2022), prima facie, Naive Russellians could simply reject Frege’s constraint and, instead, accept Salmon’s constraint (see, e.g., Salmon 1986a/1986b, 1989, 2006):

(SC):

Necessarily, if a proposition p is rationally both believed and disbelieved by an agent k, then there are modes of presentation m and $m'$ of p such that

(a):

p is believed by k under m,

(b):

p is disbelieved by k under $m'$, and

(c):

k takes m and $m'$ to be modes of presentation of different propositions.

Thus, although Sally does not have two modes of presentation of the singular proposition designated by the that-clauses in (7) and (8), the singular proposition expressed by (7) is nevertheless presented to her by two modes of presentation which she takes to be modes of presentation of different propositions. Since Sally believes the proposition under one mode of presentation and disbelieves it under the other, the explanation goes, she cannot be convicted of irrationality.

Against this solution, I object that in order for Sally to have two modes of presentation of the singular proposition expressed by (7) one of its propositional constituents has to be presented to her in two different ways. In other words, if (SC) is true, then, according to the Naive Russellian theory, so are Frege’s constraint and ($FC'$). For a more detailed discussion of this argument I refer to Rinner (2022).

Another possibility for Naive Russellians to reject Frege’s constraint seems to be to resort to Crawford’s (2004) analysis of belief, which is usually seen as a Russellian alternative to Salmon’s constraint. Accordingly, the fact that a normal speaker can be disposed to sincerely and reflectively assert ‘Karol Wojtyła is Polish’ without being disposed to sincerely and reflectively assert ‘John Paul II is Polish’ is not explained by the fact that the singular proposition expressed by the two sentences is presented to the speaker in two different ways. Instead, Crawford points out that, although such a speaker believes the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$, they also (mistakenly) believe that they do not believe this very proposition. Hence, according to Crawford, the speaker’s situation can be represented by (15) and (16).

• (15) Believes (speaker, $\langle$Karol Wojtyła, being Polish$\rangle$).

• (16) Believes (speaker, $\langle \langle$speaker, $\langle$Karol Wojtyła, being Polish$\rangle \rangle$, does not believe$\rangle$).

Put more simply, the speaker believes they do not believe something they in fact believe.

According to Crawford, if the Neo-Russellian theory is correct, then there is nothing unacceptably counterintuitive about this fact. After all, according to Neo-Russellians, the contents of our thoughts are not necessarily transparent to us, which is why we can fail to keep track of the objects of our beliefs. Arguably, however, the fact that the contents of our thoughts are not necessarily transparent to us is precisely what has to be explained by a Neo-Russellian theory. Hence, Crawford’s analysis has to be supplemented by such an explanation. Since the only explanation on the market seems to be Salmon’s explanation using propositional modes of presentation and Salmon’s constraint, this seems to commit Crawford to something along the lines of Salmon’s constraint, which is why the problems mentioned in Rinner (2022) in connection with Salmon’s constraint also apply to Crawford’s analysis.

For Fregeans, on the other hand, it is not even an option to replace ($FC'$) and Frege’s constraint with something along the lines of Salmon’s constraint, since for them the two-place belief relation is not the existential generalization of a three-place relation holding between agents, propositions, and propositional modes of presentation. Rather, for Fregeans, the two-place belief relation is a relation holding between agents and Fregean propositions, i.e., structured propositions consisting of modes of presentation of the objects, properties, and relations our thoughts and speech acts are about (see, e.g., Frege 1892, 1918-19). Therefore, it is very likely that for Fregeans an object o is believed/disbelieved by an agent x to be F only if x believes/disbelieves a proposition consisting, among other things, of a mode of presentation of o.¹² This, in turn, would commit Fregeans to at least some version of ($FC'$).

Against (EP) and ($EP'$), prima facie, Fregeans could object that, since Sally mistakenly believes that the that-clauses in (7) and (8) designate the same proposition, from her sincere utterances of (7) and (8) we cannot infer that the propositions designated by the respective that-clauses are believed or disbelieved, respectively, by Sally to be something that is believed by Ralph. However, if Sally mistakenly believed that ‘Karol Wojtyła = Benedict XVI’ is true, from her sincere utterances of ‘Karol Wojtyła is Polish’ we would nevertheless infer that Karol Wojtyła is believed by Sally to be Polish. Hence, the fact that Sally mistakenly believes that the that-clauses in (7) and (8) designate the same proposition does not in itself establish that the propositions designated by the that-clauses in (7) and (8) are not believed or disbelieved, respectively, by Sally to be something that is believed by Ralph.

For Fregeans, the main problem posed by my variant of Schiffer’s puzzle seems to be that Sally, as a normal English speaker, takes the that-clauses in (7) and (8) to designate one and the same proposition, although, according to these philosophers, the embedded sentences of (7) and (8) express different propositions.

• (7) That Karol Wojtyła is Polish is believed by Ralph.

• (8) That John Paul II is Polish is not believed by Ralph.

After all, normal English speakers should take standard English sentences to express exactly the very propositions they in fact express in English. Together with the fact that the embedded sentences of (7) and (8) express different propositions, this should then explain that rational, normal speakers can be disposed to sincerely assert both (7) and (8). This problem is largely independent of whether Fregeans are committed to both ($FC'$) and ($EP'$), suggesting again that for Fregeans the solution to my variant of Schiffer’s puzzle cannot simply be to reject ($FC'$) or ($EP'$).

Similarly, for Neo-Russellians, the main problem seems to be that Sally, as a normal English speaker, takes (7) and (14) to express different propositions, although she takes the respective that-clauses to designate one and the same proposition.

• (7) That Karol Wojtyła is Polish is believed by Ralph.

• (14) That John Paul II is Polish is believed by Ralph.

Again, this suggests that for Neo-Russellians the solution to my variant of Schiffer’s puzzle cannot simply be to reject ($FC'$) or ($EP'$). Rather, the puzzle seems to show that both Fregeans and Neo-Russellians have to look for alternatives to the relational analysis of belief ascriptions. Therefore, concluding, I will briefly discuss possible alternatives to the relational analysis for both Fregeans and Neo-Russellians. I will argue that, although there are Neo-Russellian alternatives to the relational analysis which provide a solution to my variant of Schiffer’s puzzle, there seem to be no such Fregean alternatives.

5 Rejecting the Relational Analysis

As we have seen in Section 3, the obvious solution to my variant of Schiffer’s puzzle seems to be that Sally believes something along the lines of the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m\rangle$ and disbelieves something along the lines of the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m'\rangle$, where m and $m'$ are two different ways the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$ is presented to Ralph. From this it would then only follow that the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$ is believed by Sally to be something that is believed by Ralph under m and disbelieved by Sally to be something that is believed by Ralph under $m'$, which would not require that Sally has two different modes of presentation of $\langle$Karol Wojtyła, being Polish$\rangle$. However, such a solution was not available to advocates of a relational analysis, since for these philosophers both in (9) and (10) ‘believe’ and ‘disbelieve’ express two-place relations holding between agents and propositions. For example, according to Naive Russellians, both (9) and (10) are true if and only if Sally believes or disbelieves, respectively, the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph$\rangle$.

This suggests that in order to solve my variant of Schiffer’s puzzle Neo-Russellians have to replace ($NR_{3}$) with something along the lines of a contextualist analysis of belief ascriptions, according to which ‘believe’ and ‘disbelieve’ express three-place relations holding between agents, propositions, and contextually determined propositional modes of presentation (see, e.g., Crimmins & Perry 1989, Crimmins 1992).

($NR_{3}'$):

A sentence of the form ‘A believes/disbelieves that S’ is true in a context c if and only if the referent of A in c believes/disbelieves the proposition expressed by S in c under a contextually determined mode of presentation of the proposition expressed by S in c.

Accordingly, (9) is true if and only if Sally believes the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m\rangle$ (under a contextually determined mode of presentation), and (10) is true if and only if Sally disbelieves the singular proposition $\langle \langle$Karol Wojtyła, being Polish$\rangle$, being believed by Ralph under $m'\rangle$ (under a (different) contextually determined mode of presentation). As said above, this would not require that Sally has two different modes of presentation of the singular proposition $\langle$Karol Wojtyła, being Polish$\rangle$, thus blocking my variant of Schiffer’s puzzle.

The debate between Naive Russellians and contextualists was largely based on intuitions regarding the truth values of sentences such as (1), (2), (7), and (8). My variant of Schiffer’s puzzle, on the other hand, provides an argument against the Naive Russellian theory and for a contextualist version of the Neo-Russellian view which is not based on speaker intuitions. After all, the puzzle only assumes that there are speakers with contextualist intuitions, something that has already been proven by the existing debate between Naive Russellians and contextualists.

This leads us to the question whether a contextualist solution to my variant of Schiffer’s puzzle is also available to Fregeans. Indeed, Fregeans sometimes reject ($NR_{3}$) in order to account for the fact that ascriber and ascribee can associate different modes of presentation with the expressions used in the embedded sentence of a belief ascription. A possible explanation is here that a sentence of the form ‘A believes that S’ is true if and only if the referent of A believes a proposition that stands in a contextually determined relation R to the proposition expressed by S (see, e.g., Chalmers 2011).

($NR_{3}''$):

A sentence of the form ‘A believes/disbelieves that S’ is true in a context c if and only if there is a proposition p such that p stands in a contextually determined relation R to the proposition expressed by S in c, and the referent of A in c believes/disbelieves p.

However, just like ($NR_{3}$), such an analysis leads to my variant of Schiffer’s puzzle. According to ($NR_{3}''$), (7) is true if and only if Ralph believes a proposition that stands in R to p(‘Karol Wojtyła is Polish’), and (8) is true if and only if Ralph does not believe a proposition that stands in R to p(‘John Paul II is Polish’).¹³ Hence, the fact that Sally takes both (7) and (8) to be true would not be compatible with the fact that, as a rational agent, Sally does not have a mode of presentation m of p(‘Karol Wojtyła is Polish’) and a mode of presentation $m'$ of p(‘John Paul II is Polish’) such that she takes m and $m'$ to be modes of presentation of different propositions.

Note that for advocates of ($NR_{3}''$) the solution cannot be to maintain that the contextually determined relation R varies between Sally’s utterance of (7) and her utterance of (8). On the most plausible reading the contextually determined relation R is some kind of similarity relation holding between propositions. However, the degree of similarity does not change simply by changing the embedded sentence as both (7) and (8) can in principle be used with various degrees of similarity. Rather, the degree of similarity depends on several factors of the context of utterance. For instance, the fact that a speaker sincerely utters both (7) and (8) is usually said to lead to a fairly high degree of similarity for both the contextually determined relation of (7) and the contextually determined relation of (8). But then, according to ($NR_{3}''$), the same should be true of Sally’s utterances in my variant of Schiffer’s puzzle.

This emphasizes again that, according to Fregeans, the fact that rational, normal speakers can be disposed to sincerely and reflectively accept both (7) and (8) must primarily be explained by the fact that their embedded sentences express different propositions. Normal speakers should then assign to the embedded sentences of (7) and (8) exactly the very propositions they in fact express. Hence, as I said at the end of the last section, for Fregeans, the main problem posed by my variant of Schiffer’s puzzle is that Sally, as a normal English speaker, takes the embedded sentences of (7) and (8) to express one and the same proposition, thus undermining the Fregean explanation of speakers’ intuitions regarding the truth values of sentences such as (7) and (8).

The problem remains if Fregeans reject ($NR_{3}''$) and, instead, maintain that agents have so-called vicarious modes of presentation, simulating the modes of presentation of other agents (see, e.g., Recanati 2012). According to such a proposal, when speakers use a referring expression embedded in a belief ascription of the form ‘A believes that S’ the expression is not used with its normal sense or mode of presentation, but with the vicarious mode of presentation that the speaker ascribes to the referent of A. Ultimately, however, such a proposal is very similar to the relational analysis of belief ascriptions, the only difference being that the proposition expressed by the embedded sentence consists of vicarious modes of presentation. Therefore, Fregeans would again have great difficulties explaining how a rational, normal English speaker can be disposed to sincerely and reflectively utter both (7) and (8) without taking their embedded sentences to express different propositions.

All of this suggests that the Fregean theory does not provide a solution to my variant of Schiffer’s puzzle, independent of whether it is advocated together with a relational or a contextualist analysis of belief ascriptions. Hence, although my variant of Schiffer’s puzzle provides an argument against the Naive Russellian theory, it speaks in favor of a contextualist version of the Neo-Russellian theory, which replaces the relational analysis ($NR_{3}$) with a contextualist analysis along the lines of ($NR_{3}'$). In this way, Neo-Russellians can block my variant of Schiffer’s puzzle without rejecting the weak exportation principles or Frege’s constraint.

6 Concluding Remarks

The primary aim of this paper was to show that the variant of Schiffer’s puzzle presented in Rinner (2022) is not only a problem for Naive Russellians, but for relational analyses of belief ascriptions in general. First of all, relational analyses seem to be committed to the exportation principle for that-clauses ($EP'$). In addition, I have argued that Frege’s constraint is just an instance of an equally plausible rationality principle regarding de re belief, i.e., ($FC'$). Starting from this, we have seen that, just like the conjunction of ($EP'$), Frege’s constraint, and the Naive Russellian theory, the conjunction of ($EP'$), ($FC'$), and the relational analysis leads to contradictions. Since for advocates of the relational analysis the solution can neither be to reject ($EP'$) nor to reject ($FC'$), this undermines the relational analysis of belief ascriptions. Concluding, possible alternatives to the relational analysis for both Neo-Russellians and Fregeans were discussed. Since, unlike the Neo-Russellian theory, the Fregean theory does not provide a solution to my variant of Schiffer’s puzzle, independent of whether a relational or a contextualist analysis of belief ascriptions is assumed to be true, the puzzle not only provides an argument against relational analyses of belief ascriptions, but also against Fregean theories of propositions. In this way, the present paper speaks in favor of a contextualist version of the Neo-Russellian theory, according to which attitude verbs such as ‘believe’ express three-place relations holding between agents, Russellian propositions, and contextually determined propositional modes of presentation.¹⁴