Naive Russellians and Schiffer’s Puzzle

Neo-Russellians like Salmon and Braun hold that: (A) the semantic contents of sentences are structured propositions whose basic components are objects and properties, (B) names are directly referential terms, and (C) a sentence of the form ‘n believes that S’ is true in a context c iff the referent of the name n in c believes the proposition expressed by S in c. This is sometimes referred to as ‘the Naive Russellian theory’. In this talk, I will discuss the Naive Russellian theory primarily in connection with a problem known as Schiffer’s puzzle. Schiffer first presented the puzzle as an argument against the Naive Russellian theory. Schiffer’s argument proceeds in two steps. In step one, Schiffer argues that the Naive Russellian theory is committed to two principles regarding de re belief; the special-case consequence and Frege’s constraint. Then, in step two, Schiffer argues that the special-case consequence is not consistent with Frege’s constraint. Salmon and Braun reply to Schiffer’s argument that although the Naive Russellian theory is committed to Frege’s constraint, it is not committed to the special-case consequence. However, in this paper, I will argue with a new Schiffer-case that even if the Naive Russellian theory is not committed to the special-case consequence, it is still not consistent with Frege’s constraint. Concluding, I will discuss the possibility to reject Frege’s constraint within the Naive Russellian theory.


Introduction
Following the work of Marcus (1961), Donnellan (1970), Perry (1977), Kripke (1980) and Kaplan (1989), so-called Neo-Russellians like Salmon (1986aSalmon ( , b, 1989Salmon ( , 2006 and Braun (1998Braun ( , 2006 hold that: B Stefan Rinner stefan.rinner@lrz.uni-muenchen.de 1 Ludwig Maximilian University of Munich (MCMP), Munich, Germany (N R 1 ) The semantic content of a sentence S of a language L in a context c is a Russellian proposition; i.e. a structured proposition whose basic components are objects and properties. (N R 2 ) Names and other singular terms (pronouns, simple demonstratives, indexicals) function as directly referential terms; i.e. the semantic content of 'n is F' in a context c is the singular proposition o, , where o is the referent of the name n in c and is the property expressed by the predicate F in c. This is also known as the Neo-Russellian theory. 1 Moreover, Salmon and Braun advocate the following theory of belief reports: (N R 3 ) A sentence of the form 'n believes/disbelieves that S' is true in a context c iff the referent of the name n in c believes/disbelieves the proposition expressed by S in c. The theory consisting of (N R 1 ), (N R 2 ) and (N R 3 ) is sometimes referred to as 'the Naive Russellian theory '. 2 In this paper, I will discuss the Naive Russellian theory primarily in connection with a problem known as Schiffer's puzzle. Schiffer first presented the puzzle in (Schiffer 2006) as an argument against the Naive Russellian theory. Schiffer's argument proceeds in two steps. In step one, Schiffer argues that the Naive Russellian theory is committed to the following principles regarding de re belief, where α is any singular term of English, β is any proper name or other directly referential term of English, φ it is any English open sentence in which the pronoun 'it' occurs as a free variablealternatively 'he', 'she', 'him' or 'her' -and φ β is the same as φ it except for having occurrences of β wherever φ it has free occurrences of the relevant pronoun: The Special-Case Consequence (S): Necessarily, if α believes/disbelieves that φ β , then β is believed/disbelieved by α to be (something/someone) such that φ it . Frege's Constraint (FC): If an object o is rationally both believed and disbelieved by an agent k to be (something/someone) such that φ it , then there are two modes of presentation m and m such that (a) o is believed by k to be (something/someone) such that φ it under m, (b) o is disbelieved by k to be (something/someone) such that φ it under m , and (c) k does not recognise that m and m are modes of presentation of one and the same object.
1 As the name suggests, the Neo-Russellian theory goes back to Russell (1905Russell ( , 1910Russell ( -1911Russell ( , 1912. However, according to Russell, the only directly referential terms are so-called logically proper names; i.e. demonstratives like 'this' and 'that' which refer to sense-data or other objects of immediate acquaintance. 2 Note that not all Neo-Russellians accept (N R 3 ). For example, Crimmins andPerry (1989, Crimmins 1992) hold that 'believe' expresses a three-place relation holding between agents, Russellian propositions and contextually determined modes of presentation. The objection I am about to raise against the Naive Russellian theory is not an objection to Crimmins and Perry's theory of belief ascriptions. I will return to this later.
Then, in step two, Schiffer argues that together with plausible assumptions these principles lead to contradictions. Thus, if the Naive Russellian theory were committed to both the special-case consequence and Frege's constraint, this would refute the Naive Russellian theory. In Sect. 2, I will discuss Schiffer's argument in more detail.
In (Salmon 2006), Salmon agrees with Schiffer that together with plausible assumptions the special-case consequence and Frege's constraint lead to contradictions. However, Salmon replies to Schiffer's argument that although the Naive Russellian theory is committed to Frege's constraint, it is not committed to (S), but only to (S ), where α and β are again as before, ψ it is any standard English open sentence with monadic-predicational form, 'It'+V P, where V P is a monadic predicate 3 in which the pronoun 'it' does not occur free, and φ β is again the same as φ it except for having occurrences of β wherever φ it has free occurrences of the relevant pronoun: (S ) Necessarily, if α believes/disbelieves that ψ β , then β is believed/disbelieved by α to be (something/someone) such that ψ it .
Since, according to Salmon, unlike the conjunction of (S) and Frege's constraint, the conjunction of (S ) and Frege's constraint does not lead to contradictions, Salmon concludes that Schiffer's argument does not refute the Naive Russellian theory. Braun (2006, 376) agrees with Salmon on this point.
In the first part of this paper (Sects. 2, 3, and 4), I will argue with a new Schiffer case that, just like the conjunction of (S) and Frege's constraint, the conjunction of (S ) and Frege's constraint leads to contradictions. Since, as we will see, the Naive Russellian theory is indeed committed to (S ), it will follow that, pace Salmon and Braun, Naive Russellians have to reject Frege's constraint.
In (Schiffer 2006, 364-365), Schiffer notes that prima facie Naive Russellians could reject Frege's constraint, and, instead, accept a version of Frege's constraint for propositional modes of presentation; i.e. Salmon's constraint. However, Schiffer (2006, 365) also notes that together with plausible assumptions Salmon's constraint leads to a similar problem as Frege's constraint. I will call this 'Schiffer's puzzle regarding de dicto belief'. The puzzle regarding de dicto belief was first presented by Schiffer in (Schiffer 1987, 463-466).
In the second part of this paper (Sects. 5, 6, and 7), I will argue that the new Schiffer case also undermines Salmon's solution to Schiffer's puzzle regarding de dicto belief in (Salmon 1989). Following this, I will argue with Schiffer (2006, 365-366) that the most promising way to solve Schiffer's puzzle regarding de dicto belief within the Naive Russellian theory is to take the propositional modes of presentation implied by Salmon's constraint to be public language sentences or to be sentences in a language of thought. However, concluding, I will argue that in connection with the new Schiffer case taking the propositional modes of presentation implied by Salmon's constraint to be public language sentences or to be sentences in a language of thought is problematic as well. It will follow that Naive Russellians have to come up with an alternative candidate for propositional modes of presentation which (a) satisfies Salmon's constraint, and (b) does not lead to a similar problem as Frege's constraint. This will be no easy task. Before I come to the new Schiffer case, I will briefly present Schiffer's original puzzle.

Schiffer's Puzzle
The starting point of Schiffer's puzzle is a problem regarding de re belief which also arises within the Naive Russellian theory. For example, both (1) and (2) can be true; e.g. if Ralph is disposed to sincerely and reflectively utter both 'Karol Wojtyła is Polish' and 'It is not the case that John Paul II. is Polish'.
(2) Ralph disbelieves that John Paul II. is Polish. 4 Moreover, it is very likely that according to the Naive Russellian theory de re belief is simply a special case of de dicto belief (belief that): If an agent k believes de dicto the singular proposition about o that it (he, she) is P, then it seems that o is believed by k to be (something/someone) such that it (he, she) is P. Schiffer calls this 'the special-case consequence' (Schiffer 2006, 362): (S) Necessarily, if α believes/disbelieves that φ β , then β is believed/disbelieved by α to be (something/someone) such that φ it .
(3) Karol Wojtyła is believed by Ralph to be (someone) such that he is Polish.
(4) John Paul II. is disbelieved by Ralph to be (someone) such that he is Polish.
Since John Paul II. = Karol Wojtyła, and since we can assume that Ralph is both a brilliant logician, i.e. that he is in principle in a position to notice and correct contradictory beliefs, and fully rational, i.e. that he would never let contradictory beliefs pass if he recognises them as such, this leads to the question how a brilliant logician like Ralph can rationally both believe and disbelieve an object o to be (something/someone) such that φ it . I will call this 'the problem of rationality regarding de re belief'. The received solution to the problem of rationality regarding de re belief says that Wojtyła is presented to Ralph by two modes of presentation m and m without him recognising that m and m are modes of presentation of one and the same person. Since Ralph believes Wojtyła to be Polish under m and disbelieves Wojtyła to be Polish under m , the solution continues, Ralph cannot be convicted of irrationality. Schiffer calls this 'Frege's constraint' (Schiffer 2006, 362) (b) o is disbelieved by k to be (something/someone) such that φ it under m , and (c) k does not recognise that m and m are modes of presentation of one and the same object.
Taken in its obvious intent, Frege's constraint appears to be a self-evident truth. For example, Salmon (2006, 370) argues that if an agent k rationally believes o to be (something/someone) such that φ it and disbelieves o to be (something/someone) such that φ it , then, in so doing, k takes o and o to be distinct. Insofar as k is rational, the argument continues, he/she thereby takes o and o differently, even if, in fact, o = o . However, in (Schiffer 2006), Schiffer shows that together with plausible assumptions the special-case consequence leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint. Thus, if the Naive Russellian theory were committed to both the special-case consequence and Frege's constraint, this would refute the Naive Russellian theory.
Take the above example of Ralph. From Ralph's disposition to sincerely and reflectively utter both 'Karol Wojtyła is Polish' and 'It is not the case that John Paul II. is Polish' we infer that both (1) and (2) are true. This means that we presuppose the following disquotational principles connecting sincere assertion and belief, where 'S' can be replaced, inside and outside quotation marks, by any standard English sentence lacking indexical or pronominal devices or ambiguities (Kripke 1979, 248-249): 6 (D P) If a normal English speaker is disposed to sincerely and reflectively utter 'S', then he/she believes that S. (D P ) If a normal English speaker is disposed to sincerely and reflectively utter 'It is not the case that S', then he/she disbelieves that S.
Analogous principles can be formulated for French, German etc. Taken in their obvious intent, also (D P) and (D P ) seem to be self-evident truths. In particular, (D P) and (D P ) seem to be true of belief ascriptions of the form ' A believes that S'. For example, if a normal English speaker sincerely and reflectively utters 'Ralph believes that snow is white', we usually infer that the speaker believes that Ralph believes that snow is white. Similarly, if a normal English speaker sincerely and reflectively utters 'It is not the case that Ralph believes that snow is white', we usually infer that the speaker disbelieves that Ralph believes that snow is white. Therefore, just like Schiffer (2006), Salmon (2006), and Braun (2006), in what follows, I will simply assume that every instance of (D P) and (D P ) is true. Now, Schiffer (2006, 363) notes that in the above 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 (5); e.g. if the speaker has Fregean intuitions regarding the truth-values of sentences like (1) and (5).
(1) Ralph believes that Karol Wojtyła is Polish. (5) It is not the case that Ralph believes that John Paul II. is Polish.
Assume that Peter is such a speaker. Together with (D P) and (D P ), it would follow that both (6) and (7) are true.
(6) Peter believes that Ralph believes that Karol Wojtyła is Polish. (7) Peter disbelieves that Ralph believes that John Paul II. is Polish.
(8) Karol Wojtyła is believed by Peter to be (someone) such that Ralph believes that he is Polish. (9) John Paul II. is disbelieved by Peter to be (someone) such that Ralph believes that he is Polish.
From this, in turn, it would follow together with Frege's constraint that Karol Wojtyła is presented to Peter by two modes of presentation without him recognising that these are two modes of presentation of one and the same person. However, since Peter believes 'Karol Wojtyła = John Paul II.' to be true, we can simply assume that Karol Wojtyła is not presented to him by two modes of presentation without him recognising that these are modes of presentation of one and the same person. This is Schiffer's puzzle.
Schiffer's puzzle shows that together with plausible assumptions (S) leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint. Thus, if the Naive Russellian theory were committed to both (S) and Frege's constraint, Schiffer's puzzle would refute the Naive Russellian theory. However, in (Salmon 2006, 371-372), Salmon notes that although the Naive Russellian theory is committed to Frege's constraint, it is not committed to (S), but to counter-instances of (S). Therefore, next, I will discuss Salmon's solution to Schiffer's puzzle in more detail. Following this, I will argue with a new Schiffer case that even if the Naive Russellian theory is not committed to (S), it still leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint.

Salmon's Solution to Schiffer's Puzzle
One of Salmon's examples of a counter-instance of the special-case consequence is due to Kaplan (1986, 269-272). Kaplan notes that as a rational, normal English speaker Ralph could be disposed to sincerely and reflectively utter 'Karol Wojtyła is taller than John Paul II.'; i.e. if Ralph does not know that 'Karol Wojtyła' and 'John Paul II.' are names of one and the same person. Together with (D P), it would follow that (10) is true.
(10) Ralph believes that Karol Wojtyła is taller than John Paul II.
From this, in turn, it would follow together with (S) that (12) is true.
(12) Karol Wojtyła is believed by Ralph to be something z such that z is taller than z.
However, since Ralph cannot rationally believe Karol Wojtyła to be taller than himself, in our example, (12) cannot be true. Thus, if the Naive Russellian theory were committed to (S), Kaplan's example would already refute the Naive Russellian theory without any reference to Frege's constraint. However, Salmon notes that according to the Naive Russellian theory, (11) is true if and only if Ralph believes the singular proposition Karol Wojtyła, Karol Wojtyła , taller-than , whereas (12) is true if and only if Ralph believes the singular proposition Karol Wojtyła, being taller than oneself . Since the latter proposition has to be distinguished from the former, according to the Naive Russellian theory, there are circumstances in which (11) is true and (12) is false. 7 It follows that the Naive Russellian theory is not committed to (S), but to counter-instances of (S).
As Salmon (2006, 371-372) rightly points out, Schiffer's puzzle provides just another counter-instance of (S). If (6) and (7) are true, then, according to the Naive Russellian theory, Peter both believes and disbelieves the singular proposition Ralph, Karol Wojtyła, being Polish , believing . However, Peter does not thereby both believe and disbelieve the singular proposition Karol Wojtyła, being (someone) such that Ralph believes that he is Polish . For example, if Peter believes 'Karol Wojtyła = John Paul II.' to be true, then, as a rational, normal English speaker, he is not disposed to sincerely and reflectively utter both (13) and (14).
(13) Karol Wojtyła is (someone) such that Ralph believes that he is Polish. (14) It is not the case that John Paul II. is (someone) such that Ralph believes that he is Polish.
Since, according to the Naive Russellian theory, (8) is true if and only if Peter believes the singular proposition Karol Wojtyła, being (someone) such that Ralph believes that he is Polish , and (9) is true if and only if Peter disbelieves the singular proposition Karol Wojtyła, being (someone) such that Ralph believes that he is Polish , it follows that although, in the above example, both (6) and (7) are true, according to the Naive Russellian theory, (8) or (9) is not. Salmon (2006, 373) notes that there remains a bit of a mystery. Although the Naive Russellian theory is not committed to (S), it is still committed to (S ), where ψ it is any standard English open sentence with monadic-predicational form, 'It'+V P, such that V P is a monadic predicate in which the pronoun 'it' does not occur free: (S ) Necessarily, if α believes/disbelieves that ψ β , then β is believed/disbelieved by α to be (something/someone) such that ψ it .
As Salmon points out (2006, 371), V P is then a term for a particular property or singulary-functional concept F. Thus, Salmon continues, if an agent believes the singular proposition expressed by 'It'+V P under the assignment of a particular object o to the variable 'it', the proposition has the simple structure o, F , so that the agent indeed believes o to be F. Moreover, Salmon notes that in the above example, as someone with Fregean intuitions, Peter could be disposed to sincerely and reflectively utter both (15) and (16).
(15) That Karol Wojtyła is Polish is believed by Ralph.
(16) That John Paul II. is Polish is not believed by Ralph.
Together with (D P) and (D P ), it would follow that both (17) and (18) are true. 7 See also (Salmon 1986b).
(17) Peter believes the following: That Karol Wojtyła is Polish is believed by Ralph.
(18) Peter disbelieves the following: That John Paul II. is Polish is believed by Ralph.
(19) That Karol Wojtyła is Polish is believed by Peter to be something such that it is believed by Ralph. (20) That John Paul II. is Polish is disbelieved by Peter to be something such that it is believed by Ralph.
Since, according to the Naive Russellian theory, both the proposition that Karol Wojtyła is Polish and the proposition that John Paul II. is Polish are the singular proposition Karol Wojtyła, being Polish , together with Frege's constraint, it would follow that the singular proposition Karol Wojtyła, being Polish is presented to Peter by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. But, since neither Karol Wojtyła nor the property of being Polish is presented to Peter by two modes of presentation without him recognising that these are modes of presentation of one and the same object/property, for a Naive Russellian, the question remains, how Karol Wojtyła, being Polish can be presented to Peter by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. I will call this 'Schiffer's puzzle for propositions'. Salmon (2006, 373-374) solves Schiffer's puzzle for propositions by arguing that Peter can mistake the singular proposition Karol Wojtyła, being Polish for two independent thoughts without taking one of its basic components in two different ways. For example, according to Salmon, if Peter has Fregean intuitions, then he mistakes the singular proposition Karol Wojtyła, being Polish for the Fregean thought m K W , being Polish and for the Fregean thought m K W , being Polish , where m K W and m K W are Ralph's modes of presentation of Karol Wojtyła. According to the Naive Russellian theory, this is a misconception. However, as Salmon puts it, "misconceiving is a way of taking" (Salmon 2006, 374).
So far, one may agree with Salmon. However, next, I will argue that there are instances of Schiffer's puzzle for propositions where the agent does not take the proposition in question for two independent thoughts. It will follow that, just like (S), (S ) leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint.

A New Schiffer Case
Let us assume that Harry is a rational, normal English speaker who believes that the that-clause in (1) and (15) and the that-clause in (5) and (16) designate one and the same proposition. Nevertheless, Harry could be disposed to sincerely and reflectively utter both (1) and (5); i.e. if he shares the intuitions of Neo-Russellians like Crimmins and Perry (Crimmins and Perry 1989;Crimmins 1992). Although these philosophers believe that the that-clause in (1) and the that-clause in (5) designate one and the same proposition, they have strong intuitions that there can be circumstances in which both (1) and (5) are true. Moreover, if Harry shares the intuitions of Neo-Russellians like Crimmins and Perry, as a rational, normal English speaker, he could even be disposed to sincerely and reflectively utter both (15) and (16); e.g. if he wants to explain to someone why Ralph does not speak Polish when he meets the Pope, although he is a childhood friend of him. Together with (D P) and (D P ), it would follow that both (21) and (22) are true.
(21) Harry believes the following: That Karol Wojtyła is Polish is believed by Ralph. (22) Harry disbelieves the following: That John Paul II. is Polish is believed by Ralph.
(25) That Karol Wojtyła is Polish is disbelieved by Harry to be something such that it is believed by Ralph.
From (23) and (25), in turn, it would follow together with Frege's constraint that the proposition that Karol Wojtyła is Polish is presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. However, since Harry believes that the that-clause in (15) and the that-clause in (16) designate one and the same proposition, we can simply assume that the proposition that Karol Wojtyła is Polish is not presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. Thus, even together with (S ), the Naive Russellian theory leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint.
The obvious solution to this version of Schiffer's puzzle seems to be that in the above example Harry neither believes nor disbelieves the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , but that he rather believes something along the lines of the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m and disbelieves something along the lines of the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m , where m and m are two distinct ways the singular proposition Karol Wojtyła, being Polish is presented to Ralph. From this, the solution continues, together with (S ), it would only follow that the singular proposition Karol Wojtyła, being Polish is believed by Harry to be something such that under m it is believed by Ralph and disbelieved by Harry to be something such that under m it is believed by Ralph, and not that the singular proposition Karol Wojtyła, being Polish is both believed and disbelieved by Harry to be something such that it is believed by Ralph. However, such a solution is not available to the Naive Russellians. According to (N R 3 ), both in 'That Karol Wojtyła is Polish is believed by Ralph' and in 'That John Paul II. is Polish is believed by Ralph' 'believe' expresses a two-place relation holding between agents and Russellian propositions. Therefore, according to the Naive Russellian theory, (21) is true if and only if Harry believes the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , and (22) is true if and only if Harry disbelieves the singular proposition Karol Wojtyła, being Polish , being believed by Ralph . Together with (S ), it would follow that the singular proposition Karol Wojtyła, being Polish is both believed and disbelieved by Harry to be something such that it is believed by Ralph.
Naive Russellians could respond that although, as a normal English speaker who shares the intuitions of Crimmins and Perry, Harry could be disposed to sincerely and reflectively utter both (1) and (5), the same is not true of (15) and (16). But I see no reason why a rational, normal English speaker who has strong intuitions that there can be circumstances in which both (1) and (5) are true should be immune to think the same of (15) and (16)? According to Naive Russellians, the speaker would be mistaken either way, but in neither case this seems to preclude that normal English speakers sometimes have these intuitions. Moreover, it does not seem to make any difference whether Harry uses (1) and (5) or (15) and (16) (15) and (16), and that, therefore, according to the Naive Russellian theory, from Harry's sincere and reflective utterances of (15) and (16) it does not follow together with (D P) and (D P ) that both (21) and (22) are true. 8 For example, an advocate of the Naive Russellian theory could argue that according to the Naive Russellian theory Harry does not take (15) and (16) to express the very propositions that they in fact express. Otherwise, the argument goes, since Harry believes that the that-clause in (15) and the that-clause in (16) designate one and the same proposition, he would notice that (15) and (16) express contradictory propositions. However, since, in the above example, it is not assumed that the Naive Russellian theory is true, but rather that Harry believes that the that-clauses in (15) and (16) express one and the same proposition, from the fact that according to the Naive Russellian theory Harry does not count as a normal English speaker with respect to (15) and (16), it does not follow that, in the world of the example, Harry does not count as a normal English speaker with respect to (15) and (16), and only the latter would block the steps to (21) and (22). Moreover, the intuitions of Neo-Russellians like Crimmins and Perry show that even normal English speakers who believe that the that-clauses in (15) and (16) designate one and the same proposition can have strong intuitions that there can be circumstances in which both (15) and (16) are true. Thus, if, according to the Naive Russellian theory, such speakers would not count as normal English speakers when it comes to sentences like (15) and (16), this would by itself undermine the Naive Russellian theory.
We see that the new Schiffer case shows that even together with (S ) the Naive Russellian theory leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint. Since the Naive Russellian theory is indeed committed to (S ), it follows that, pace Salmon (2006) and Braun (2006), Naive Russellians have to reject Frege's constraint. In (Schiffer 2006, 364-365), Schiffer notes that prima facie Naive Russellians could reject Frege's constraint, and, instead, accept a version of Frege's constraint for propositional modes of presentation. Therefore, next, I will discuss Schiffer's proposal in more detail. In this connection, we will see that Frege's constraint for propositional modes of presentation leads to a similar problem as (FC); i.e. Schiffer's puzzle regarding de dicto belief.

Schiffer's Puzzle Regarding De Dicto Belief
Naive Russellians not only have to explain how a brilliant logician like Ralph can rationally both believe and disbelieve Karol Wojtyła to be Polish. They also have to explain how a brilliant logician like Ralph can rationally both believe and disbelieve the singular proposition Karol Wojtyła, being Polish . I will call this 'the problem of rationality regarding de dicto belief'. In order to solve the problem of rationality regarding de dicto belief, in addition to Frege's constraint, Naive Russellians also accept a version of Frege's constraint for propositional modes of presentation: 9 (SC) If a proposition p is rationally both believed and disbelieved by an agent k, then there are two modes of presentation m and m such that (a) p is believed by k under m, (b) p is disbelieved by k under m , and (c) k (rationally) takes m and m to be modes of presentation of distinct propositions. I will call this 'Salmon's constraint'. Following Salmon's constraint, Naive Russellians would argue that in the above example the singular proposition Karol Wojtyła, being Polish is presented to Ralph by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. Since Ralph believes the proposition under one mode of presentation and disbelieves it under the other, the explanation goes, Ralph cannot be convicted of irrationality. Now, Schiffer (2006, 364-365) notes that since Naive Russellians already accept Salmon's constraint for propositional modes of presentation, prima facie, they could simply reject Frege's constraint. For example, following Salmon's constraint, Naive Russellians could claim that although the singular proposition Karol Wojtyła, being Polish is not presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition, the singular proposition Karol Wojtyła, being Polish , being believed by Ralph is still presented to him by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition. Since Harry believes the proposition under one mode of presentation and disbelieves it under the other, the solution continues, Harry cannot be convicted of irrationality. However, Schiffer (2006, 365) also notes that together with plausible assumptions Salmon's constraint leads to a similar problem as Frege's constraint.
According to Schiffer, prima facie, the only reasonable construal of the propositional modes of presentation implied by Salmon's constraint is that they are structured entities whose basic components are modes of presentation of the basic components of the Russellian propositions of which the propositional modes of presentation are modes of presentation:

(A) If an agent k believes/disbelieves a proposition p under a mode of presentation m,
then m is a structured entity whose basic components are modes of presentation of the basic components of p.
Moreover, it is very likely that according to such a construal of the propositional modes of presentation implied by Salmon's constraint something like Frege's constraint holds for the basic components of the Russellian propositions of which the propositional modes of presentation are modes of presentation: Polish , believing is presented to Peter by two modes of presentation without him recognising that these are modes of presentation of one and the same object/property. Thus, together with (B) and Salmon's constraint, it would follow that Peter does not rationally both believe and disbelieve the singular proposition Ralph, Karol Wojtyła, being Polish , believing . However, as we have seen above, Naive Russellians are committed to the claim that Peter rationally both believes and disbelieves the singular proposition Ralph, Karol Wojtyła, being Polish , believing . This is Schiffer's puzzle regarding de dicto belief. 10 In order to solve Schiffer's puzzle regarding de dicto belief, Naive Russellians either have to show that (A) does not commit them to (B), or they have to reject (A) and 10 In his formulation of the puzzle, Schiffer uses the following principle: give an alternative construal of the propositional modes of presentation implied by Salmon's constraint that does not commit them to (B). In (Schiffer 2006), Schiffer discusses the first possibility, whereas, in (Salmon 1989) and (Salmon 2006), Salmon seems to suggest the second possibility. I will start with Salmon's proposal.

Salmon's Solution to the Puzzle Regarding De Dicto Belief
Schiffer first presented the puzzle regarding de dicto belief in (Schiffer 1987, 463-466). Arguably, the puzzle regarding de dicto belief and the puzzle regarding de re belief are simply two versions of one and the same puzzle. This is why, in (Salmon 1989, 267-268), Salmon can solve the puzzle regarding de dicto belief in a similar way as Schiffer's puzzle for propositions. According to Salmon, Peter can believe the singular proposition Ralph, Karol Wojtyła, being Polish , believing without thinking of Karol Wojtyła or the property of being Polish in a certain way; e.g. if he mistakes the singular proposition Karol Wojtyła, being Polish for a Fregean thought. Thus, according to Salmon, if Peter rationally both believes and disbelieves the singular proposition Ralph, Karol Wojtyła, being Polish , believing , he can mistake the singular proposition Karol Wojtyła, being Polish for two independent thoughts without taking one of its basic components in two different ways. Moreover, in so doing, Peter could take the singular proposition Ralph, Karol Wojtyła, being Polish , believing in two different ways without taking one of its basic components in two different ways. Therefore, if Salmon is right, Salmon's constraint neither commits Naive Russellians to ( A) nor to (B).
Even if Salmon's constraint does not commit Naive Russellians to ( A), it seems to commit them to something along the lines of ( However, just like the conjunction of (B) and Salmon's constraint, the conjunction of (B ) and Salmon's constraint is not consistent with the Naive Russellian theory. Take again the example of Harry. Since the singular proposition Karol Wojtyła, being Polish is not presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition, in the example of Harry, neither the singular proposition Karol Wojtyła, being Polish nor the property of being believed by Ralph is presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same object/property. Thus, together with (B ) and Salmon's constraint, it would follow that Harry does not rationally both believe and disbelieve the singular proposition Karol Wojtyła, being Polish , being believed by Ralph . However, as we have seen above, again, Naive Russellians are committed to the claim that Harry rationally both believes and disbelieves the singular proposition Karol Wojtyła, being Polish , being believed by Ralph .
Naive Russellians could respond that although in the example of Harry the singular proposition Karol Wojtyła, being Polish is not presented to Harry by two modes of presentation without him recognising that these are modes of presentation of one and the same proposition, the same is not true of the property of being believed by Ralph. For example, Naive Russellians could argue that in the example of Harry the property of being believed by Ralph is presented to Harry 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 distinct ways the singular proposition Karol Wojtyła, being Polish is presented to Ralph. However, if Harry mistakes the property of being believed by Ralph for the property of being believed by Ralph under m, then it is very likely that Harry does not ascribe to Karol Wojtyła, being Polish the property of being believed by Ralph, but the property of being believed by Ralph under m; i.e. that Harry does not both believe and disbelieve the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , but that he rather believes the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m and disbelieves the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m . Again, this is the obvious solution to the new Schiffer case. However, as we have seen above, such a solution to the new Schiffer case is not available to Naive Russellians.
At this point, Naive Russellians may opt for the second possibility to solve Schiffer's puzzle regarding de dicto belief, i.e. to show that (B) does not follow from (A) (or that (B ) does not follow from (A )). According to Schiffer (2006, 365-366), the most promising way to accept ( A) without being committed to (B) is to take the propositional modes of presentation implied by Salmon's constraint to be public language sentences or to be sentences in a language of thought. In the next section, I will argue that the same is true of ( A ) and (B ). However, concluding, I will argue that in connection with the new Schiffer case taking the propositional modes of presentation implied by Salmon's constraint to be public language sentences or to be sentences in a language of thought is problematic as well.

Propositional Modes of Presentation as Sentences
According to a sententialist view of the propositional modes of presentation implied by Salmon's constraint, the singular proposition Ralph, Karol Wojtyła, being Polish , believing is presented to Peter both as the proposition expressed by (1) and as the proposition expressed by (26) (or as the proposition expressed by a Mentalese translation of (1) and (26) (respectively)). 12 (1) Ralph believes that Karol Wojtyła is Polish. (26) Ralph believes that John Paul II. is Polish.
First of all, this would preserve (A), since sentences are structured entities whose basic components are expressions designating the basic components of the Russellian propositions expressed by them. Moreover, Schiffer (2006, 365-366) notes that even if Peter believes 'Karol Wojtyła = John Paul II.' to be true, he may still rationally take (1) and (26) to express distinct propositions; e.g. if Peter has Fregean intuitions. Therefore, according to Schiffer, taking the propositional modes of presentation implied by Salmon's constraint to be public language sentences or to be sentences in a language of thought would be a way for Naive Russellians to accept (A) without being committed to (B).
Prima facie, it would also be a way for Naive Russellians to accept (A ) without being committed to (B ). For example, Naive Russellians could argue that even if 12 For a discussion of a sententialist view of the propositional modes of presentation implied by Salmon's constraint see (Braun 1998). The view that propositional modes of presentation are sentences in a natural language seems to be most plausible if the natural language sentences only individuate the propositional modes of presentation implied by Salmon's constraint without equating the two. Moreover, both Schiffer and Braun prefer the version according to which the propositional modes of presentation implied by Salmon's constraint are sentences in a thinker's language of thought, since it applies without finagling to unexpressed beliefs. Prof. Braun has informed me (in personal correspondence) that although he finds the view according to which the propositional modes of presentation implied by Salmon's constraint are sentences in a language of thought plausible, he does not fully commit himself to this view, because he does not fully commit himself to the view that there is something like a language of thought. However, he would say that the propositional modes of presentation implied by Salmon's constraint are structured entities in the way described in ( A ). Note that although the sentences of a speaker's public language are abstract entities, the same is, arguably, not true of the sentences of a speaker's language of thought. For example, according to Braun (1998), the sentences of a thinker's language of thought are realised in his head and bear causal roles with respect to each other. Nevertheless, according to Braun, just like sentences of a public language, these mental sentences express propositions because of their structures and because their constituents refer to individuals and express properties and relations.
Harry believes that the that-clause in (15) and the that-clause in (16) designate one and the same proposition, he may still rationally take (15) and (27)  However, for an advocate of a sententialist view, the question remains, how a rational, normal English speaker like Harry can take (15) and (27) (or their Mentalese translations) to express distinct propositions, although, according to the Naive Russellian theory, both (15) and (27) express the singular proposition Karol Wojtyła, being Polish , being believed by Ralph . I will call this 'the problem of normal speakers'.
The problem of normal speakers is a problem Naive Russellians have to solve anyway. However, I will argue that within a sententialist view of the propositional modes of presentation implied by Salmon's constraint the standard Naive Russellian solutions to the problem of normal speakers are not an option. This will suggest that, ultimately, a sententialist view of the propositional modes of presentation implied by Salmon's constraint does not provide a solution to the problem of normal speakers, and that, therefore, a sententialist view of the propositional modes of presentation implied by Salmon's constraint is not an option for Naive Russellians.
According to a sententialist view, Harry can rationally believe and disbelieve the singular proposition Karol Wojtyła, being Polish , being believed by Ralph because he believes the proposition via (15) (or its Mentalese translation), disbelieves the proposition via (27) (or its Mentalese translation), and rationally takes (15) and (27) to express distinct propositions. As said above, such a solution to the problem of rationality regarding de dicto belief leads to the question, how Harry can rationally take (15) and (27) (or their Mentalese translations) to express distinct propositions, although, according to the Naive Russellian theory, both (15) and (27) express the singular proposition Karol Wojtyła, being Polish , being believed by Ralph . Naive Russellians standardly solve this problem by claiming that although Harry takes both (15) and (27) to express the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , he does so under distinct modes of presentation, m and m , without him recognising that these are modes of presentation of one and the same proposition. 13 But then m and m would, ultimately, explain how Harry can rationally accept (15) and the negation of (27), viz. (16), although, according to the Naive Russellian theory, the two sentences express contradictory propositions; i.e. m and m would, ultimately, explain how Harry can rationally believe and disbelieve the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , and not (15) and (27) (or their Mentalese translations). Since this contradicts a sententialist view of the propositional modes of presentation implied by Salmon's constraint, sententialists have to provide an alternative solution to the problem of normal speakers.
In order to solve the problem of normal speakers, Naive Russellians sometimes claim that although both (15) and (27) express the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , even a normal English speaker like Harry could take (15) to express a proposition p and (27) to express a proposition q such that p = q; i.e. if the speaker mistakes certain pragmatic implications of (15) and (27) regarding the way Ralph believes Karol Wojtyła, being Polish for their semantic implications. 14 However, if Harry does not take both (15) and (27) to express the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , it is very unclear how he can believe the proposition via (15) and disbelieve the proposition via (27) as a sententialist view of the propositional modes of presentation implied by Salmon's constraint claims. This suggests that within a sententialist view also a pragmatic solution to the problem of normal speakers is not an option.
An advocate of a sententialist view of the propositional modes of presentation implied by Salmon's constraint could claim that Harry can rationally take (15) and (27) (or their Mentalese translations) to express distinct propositions because for Harry the two sentences have different inferential properties. However, since, in addition to (15) and (16), Harry also accepts (28) (or its Mentalese translation), it is very unclear how Naive Russellians could explain that for Harry (15) and (27) have different inferential properties.
(28) (The proposition) that Karol Wojtyła is Polish = (the proposition) that John Paul II. is Polish.
According to the Naive Russellian theory, (15) is a simple logical consequence of (27) and (28); i.e. it follows from (27) and (28) (15) and (28). Therefore, since we can simply assume that Harry is a brilliant logician who is familiar with the substitution of identicals, according to the Naive Russellian theory, for Harry, (15) and (27) should have the same inferential properties; i.e. according to a inferentialist solution to the problem of normal speakers, Harry should take (15) and (27) to express one and the same proposition. Naive Russellians could respond that Harry takes (15) and (27) (or their Mentalese translations) to express distinct propositions because for Harry the two sentences have different causal properties. 15 According to such a solution, although Harry accepts (28), the two sentences (15) and (27), nevertheless, have different causal properties in Harry's mind; i.e. while the latter may cause him to think of a pope, the former may not. However, since Harry is both a brilliant logician and fully rational, it is very unclear how (15) and (27) can have different causal properties in Harry's mind if for Harry the two sentences are logically equivalent. Moreover, even if the two sentences had different causal properties in Harry's mind, it is still not clear that this would be sufficient for Harry to take (15) and (27) to express distinct propositions. For example, it seems that even for a speaker who knows that 'Karol Wojtyła = John Paul II.' is true the two sentences (29) and (30) can have different causal properties, since the latter may cause the speaker to think of a Polish pope, whereas the former may not. However, since the speaker knows that 'Karol Wojtyła = John Paul II' is true, this would not be sufficient for him to take (29) and (30) to express distinct propositions. Thus, in order to solve the problem of normal speakers, an advocate of a causal solution would have to provide a more detailed account of what it means for two sentences to have different causal properties. Since no such solution has been well-elaborated in the literature, yet, I have to leave a more detailed discussion of a causal solution to the problem of normal speakers for future work.
We see that within a sententialist view of the propositional modes of presentation implied by Salmon's constraint the standard solutions to the problem of normal speakers are not an option. Moreover, neither the inferentialist solution nor the causal solution seems to provide a solution to the problem of normal speakers when it comes to the new Schiffer case. This suggests that, ultimately, a sententialist view of the propositional modes of presentation implied Salmon's constraint does not provide a solution to the problem of normal speakers. Thus, it seems that Naive Russellians have to come up with an alternative candidate for the propositional modes of presentation implied by Salmon's constraint which (a) satisfies (A) (or (A )), and (b) does not commit them to (B) or (B ). Since no such candidate seems to be available, this undermines the Naive Russellian theory.

Conclusion
Let us recap: The new Schiffer case shows that even together with (S ) the Naive Russellian theory leads to instances of the problem of rationality regarding de re belief that violate Frege's constraint. Since the Naive Russellian theory is indeed committed to (S ), it follows that, pace Salmon and Braun, Naive Russellians have to reject Frege's constraint. Schiffer notes that prima facie Naive Russellians could reject Frege's constraint, and, instead, accept a version of Frege's constraint for propositional modes of presentation; i.e. Salmon's constraint. However, Schiffer also notes that together with (A) and (B) Salmon's constraint leads to a similar problem as Frege's constraint. This was Schiffer's puzzle regarding de dicto belief. The new Schiffer case shows that, pace Salmon, the solution to Schiffer's puzzle regarding de dicto belief cannot simply be to reject ( A) and (B), and, instead, accept (A ) and (B ). Rather, Naive Russellians have to come up with a candidate for propositional modes of presentation which (a) satisfies (A) (or (A )), and (b) does not commit them to (B) or (B ). For Naive Russellians, the most promising way to accept (A) and (A ) without being committed to neither (B) nor (B ) is to claim that the propositional modes of presentation implied by Salmon's constraint are public language sentences or sentences in a language of thought. However, for Naive Russellians, such a sententalist view of the propositional modes of presentation implied by Salmon's constraint leads to the problem, how Harry can rationally take (15) and (27) (or their Mentalese translations) to express distinct propositions, although he believes that the that-clause in (15) and the that-clause in (27) designate one and the same proposition. Since it is very unclear how an advocate of a sententialist view of the propositional modes of presentation implied by Salmon's constraint could explain this, it seems that Naive Russellians have to come up with an alternative candidate for the propositional modes of presentation implied by Salmon's constraint which (a) satisfies (A) (or (A )), and (b) does not commit them to (B) or (B ). Since no such candidate seems to be available, this undermines the Naive Russellian theory.
At this point, a possible way out for Naive Russellians could be to reject both ( A) and (A ). For example, Naive Russellians could claim that the propositional modes of presentation implied by Salmon's constraint are simple, unstructured entities. However, although such a proposal is not ruled out by the arguments presented in this paper, there is also no well-elaborated theory of such simple propositional modes of presentation in the literature. Therefore, it is very unclear, whether such a proposal would, ultimately, provide a solution to Schiffer's puzzle. I will leave a more detailed discussion of simple, unstructured propositional modes of presentation in connection with Schiffer's puzzle for future work.
Finally, note that neither Schiffer's original puzzle nor the new version of Schiffer's puzzle presented in this paper is a problem for the Neo-Russellian theory in general. For example, although Crimmins and Perry (1989;Crimmins 1992) accept (N R 1 ) and (N R 2 ), they reject (N R 3 ), and, instead, hold that 'believe' expresses a three-place relation holding between agents, Russellian propositions and contextually determined modes of presentation. Therefore, Crimmins and Perry could claim that in the new Schiffer case Harry neither believes nor disbelieves the singular proposition Karol Wojtyła, being Polish , being believed by Ralph , but that he rather believes something along the lines of the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m and disbelieves something along the lines of the singular proposition Karol Wojtyła, being Polish , being believed by Ralph under m , where m and m are two distinct ways the singular proposition Karol Wojtyła, being Polish is presented to Ralph. Since, as we have seen above, such a solution to the new Schiffer case is not available to the Naive Russellians, in connection with the new Schiffer case, Crimmins and Perry's version of the Neo-Russellian theory is preferable to the Naive Russellian theory advocated by Salmon and Braun.