In very brief detail, Frege’s problem centres upon the cognitive significance of true identity statements involving co-referring terms.272 For example, if ‘a = b’
and ‘a = a’ are both true, then how can the former differ from the latter in terms of truth, proposition (or circumstance) asserted and so cognitive significance? If a is identical to b, then, presumably, ‘a = b’ and ‘a = a’ say the same thing, assert the same proposition. Of course, the Kripkean response to these
272 Although the problem can also apply to standard, subject-predicate statements involving co-
questions might be something along the lines of the following. Whilst ‘a = b’ and ‘a = a’ have the same modal value (they are both necessary truths), they have different epistemic and cognitive values; they are (necessary) a posteriori and a
priori sentences respectively—thereby studiously avoiding the issue of
propositions, perhaps. Now, as I suggest throughout the foregoing, this very much fails to answer the Fregean problem; if ‘a = b’ and ‘a = a’ have the same modal value, if they are (or express) the same truth, circumstance or proposition (i.e. if they say the same thing; if they assert the very same arrangement of objects and attributes), and if propositions are the objects of belief, there is, fairly clearly, a strong sense in which they ought to have the same epistemic and cognitive value as well.273 As I try to demonstrate
throughout the previous chapter, this kind of response will not do. Very much in line with Chapter 5 then, my initial response to Frege’s problem is as follows. Widely understood, ‘a = b’ and ‘a = a’ express effectively the same (wide) proposition; they assert the same arrangement of objects and attributes, namely the self-identity of whatever object is named by a (or more contentiously the being of a by the object named by a/b); i.e. a = a or a = a. This proposition, of course, is necessarily true but also knowable on an a priori basis. Narrowly understood, on the other hand, ‘a = b’ and ‘a = a’ express different (narrow) propositions—they assert different circumstances; namely that some differently named object is (self-) identical (‘a = b’: xy [Ax By x = y]) or (arguably) that an identically named object is (self-) identical (‘a = a’:
x [Ax x = x]).274 Narrowly then, the relevant propositions are contingent
and a posteriori (as per my analysis of the necessary a posteriori). So my response to Frege’s problem is that there are (at least) two propositions, one necessary and a priori, and the other contingent but a posteriori. Widely, both assert the same necessary but a priori circumstance; narrowly, however, they express distinct but jointly a posteriori and contingent circumstances. So my analysis of Frege’s problem depends on which proposition ‘a = b’ is taken to
273 Unless of course, some difference in proposition is read off the apparent difference in
cognitive value. I also stop short of attributing any of this to Kripke, who states suspicion about propositions (1980, pp. 20-1) and refrains from offering a solution to his own version of the puzzle (1979, pp. 259 and 267 for example). Hence the ‘Kripkean’, in the main text, above.
274 Or, mutatis mutandis, !x... for both. I explain the predicate form (for the names) in the
assert. Widely it is the same proposition as ‘a = a’; narrowly however, it is not— and this is where the cognitive difference applies, since narrowly ‘a = b’ expresses an a posteriori as opposed to an a priori proposition.
Originally of course, Frege’s problem was posed as a question concerning the cognitive significance of true identity statements. If, on a fully worked out and very direct—‘Millian’—theory of reference, ‘a = b’ and ‘a = a’ express the same proposition, then we (or rather the Millian) would appear to be straight back at the beginnings of Frege’s problem. This being the case, the (very much related) problem of the intersubstitutivity of proper names in belief reports is often employed by Millians, so as to understand how ‘a = b’ and ‘a = a’ might express the same proposition, whilst differing in cognitive value or, perhaps better (according to such Millians), pragmatic significance.275 Such accounts
usually involve a three-way belief relation involving the original propositions as the ultimate objects of belief, with ‘guises’, ‘modes of presentation’ or ‘ways of believing’ acting as intermediaries between these and the believer a. So, returning to the Eminem and Slim Shady example, if a believes,
(2a) e = e
in virtue of assenting to,
(2) ‘Eminem is Eminem’,
a thereby also believes (however counter-intuitive it might appear prima facie)
(1a) e = s,
i.e. what is expressed by
(1) ‘Eminem is Slim Shady’,
275 I am thinking of course of theorists such as Salmon 1986, Soames 2002 (pp. 140-6 in
particular) and even (although he claims to be offering a solution at odds with Salmon’s) Braun 1998.
even if he does not assent to, or even dissents from, (1), since (2a) and (1a) are (pace a lot of what I have said so far) simply one and the same, singular proposition.
The counter-intuitiveness suggested above is simply the idea that the very fact that a would not assent to, or would dissent from (1), is perhaps evidence that (2a) and (1a) are not precisely the same proposition; and consequently that (2) and (1) are not simply different modes or ways of believing ‘that’ singular proposition. Instead, I argue, the fact that a assents to (2) but not to (1) and that he is surprised to learn (1), reads some popular music press, updates his music collection (etc.), is strong evidence that (2a) and (1a) are, in some (narrow) sense, different propositions—even if they (widely) say the same thing. What I am getting at here is that in such cases, if a is insisting that he believes (2) and does not believe, or even disbelieves (1), I think that someone who refuses to give any credence to a’s reports of his own belief (and consequent action) states, must be in the grip of a philosophical theory; and the level of counter- intuitiveness is just too high a price to pay to secure such a theory. Instead, if a insists that he does not believe, or disbelieves (1) and especially if he then goes out of his way to understand whether (1) is true, there must be some (however narrow) truth to the claim that a believes (2)/(2a) and does not believe (1)/(1a); i.e. that (2a) and (1a) are distinct propositions (in some sense). After all, in such a scenario, a is very likely to assent to (2) and ¬(1). If ¬(1) asserts ¬(1a) (which seems very likely) and (2) asserts (1a) (which the defenders of the relevant theory would agree on, since they claim that (1a) is the same proposition as (2a)), then, quite clearly, a believes (1a) and ¬(1a), which is clearly problematic.276
As I suggest above, there is perhaps a way out of this apparent contradiction that is discussed in the literature. Salmon (2006) and Braun (2006) effectively insist that a (‘unaware’277 perhaps, that Eminem is Slim
Shady) could believe (1a) under one ‘guise’, mode or way, and disbelieve it
276 There is a sense here in which I am endorsing what Kripke calls the principle of disquotation
(DP). Since I discuss this with respect to Kripke’s puzzle, below, I set this issue aside for now. Suffice to say that belief (and precisely what sentences assert) is a very complex matter and there is a sense (the wide one) in which (DP) might be false, and another (narrow) in which it might apply.
under another; hence he would be ‘illogical, but not irrational’ (as per the title of Braun’s paper), in virtue of not believing a contradiction—at least not in an open, obvious manner. Schiffer (2006) replies that the contradiction cannot be so easily avoided, since it would be possible for b (aware that Eminem is Slim Shady) both to believe and disbelieve of a that a believes that Eminem is Slim Shady; thus the contradiction would resurface—b would be illogical and irrational, since b would not possess the relevant, different guises required to explain the contradiction. In slightly more detail, my version of this exchange is as follows.278
Alan and Brenda are two equally gifted logicians. Alan is unaware that ‘Eminem’ and ‘Slim Shady’ are co-referential, hence he is unwilling to assent to, and in fact denies, (1), whilst at the same time assenting to (2). Brenda is aware of the relevant co-referentiality and so assents to both (2) and (1). Applying the apparently uncontroversial principle of disquotation,
(DP) if an agent a sincerely and reflectively assents to a sentence s (in a context c), then a believes, at the time of c, what s expresses in c,279
it seems fair to conclude that Alan believes (2a) and disbelieves (1a), whilst Brenda believes both (2a) and (1a). This is perhaps a standard argument for a more descriptivist account of the significance of names; since it is possible to believe (2a) and disbelieve (1a), there must be a sense in which they are not the same proposition. In response to this however, the direct reference theorist can insist that Alan, whilst appearing to be illogical, is not in fact irrational, since he can ‘take’ Eminem to be identical to Slim Shady under one guise or mode of presentation, but not identical to Slim Shady under another; he can ‘take’ Eminem to have the property of being self-identical, even if he ‘takes’ Eminem to be distinct from Slim Shady.280 At this point, Schiffer objects that it would be
entirely possible that
278 As well as the authors cited in the text here, see Perry 1977 and Kaplan 1969.
279 Suitably amended from the original, to deal with sentences and what they might express in
different contexts and times. See Kripke 1979, pp. 248-9.
(3) Brenda believes that Alan believes that Eminem is Eminem and that he disbelieves that Eminem is Slim Shady,
but of course, since Brenda is aware that Eminem is Slim Shady, and since, according to the Millianism that Salmon advocates, she therefore does not possess two guises of Eminem. Therefore (3) appears to imply that
(4) Brenda believes and disbelieves that Alan believes that Eminem is Slim Shady.
The apparent problem, of course, is that because Brenda does not possess the two, distinct guises of Eminem, (4) does appear to attribute irrationality to Brenda. The suggested resolution being to adopt something more akin to a descriptivist semantics. Unfortunately for Schiffer, the argument here is a little quick. The point being, what (3) really implies is not (4) (at least not without a great deal of detailed debate) but something more like
(5) Brenda believes that Alan believes that Eminem is Eminem (under Alan’s guise of ‘Eminem’) and that Alan believes that Eminem is not Eminem (under Alan’s guise of ‘Eminem,’ and ‘Slim Shady’),
which, of course, is fairly innocuous for the direct reference theorist.281
Now, it would be possible to spend much time debating the intricacies of this argument. In what follows, I set this debate aside, focusing instead on a simpler, clearer and more direct objection to simple Millianism, as follows. If we accept (DP) in addition to all of the assent claims (prior to (3)) above, as well as a Salmonesque Millianism about proper names, we get the following situation:
(6) Alan assents to (2) [Premise]
(7) Alan believes (2a) [From (DP) and (6)]
281 Even if there is a deeper issue as to the nature of guises. As I am not a (simple) direct
reference theorist, and as the ‘descriptive’ aspect of my account deals with this issue, I set this worry aside presently.
(8) (2a) is the same proposition as (1a) [Millianism]
(9) Alan believes (1a) [(7) and (8)]
(10) Alan does not assent to (1) [Premise]
(11) Alan does not believe (1a) [Salmon’s claim.282 Also deriv-
able from a suitably modified (DP)283 and (10)]
This is all well and good so far, since the Millian can make the same points concerning belief and non- (or dis-)belief of (1a) as before; (9) and (11) do not expose an irrationality, since Alan believes and disbelieves (1a) under different guises. Having said this however, accepting all of the same points and principles, we also get:
(12) Alan assents to ¬(1) [Premise]
(13) Alan believes ¬(1a) [(DP) and (12)]
(14) ¬(1a) is the same proposition as ¬(2a) [Millianism]
(15) Alan believes ¬(2a) [(13) and (14)]
In short, the anti-Millian urges that given all of the relevant assumptions, a case can be made for the claim that Alan believes (2a), (1a), ¬(1a) and ¬(2a) (and despite the sentence expressing ¬(2a) appearing to be very clearly a priori).284
At this point the Millian might attempt to make all of the same manoeuvres as before—Alan believes the relevant ‘contradictions’ under suitable guises,
282 Salmon 2006, pp. 369-70. 283 Perhaps:
(CON-DP) If an agent a sincerely and reflectively denies (or withholds assent from) a sentence s (in a context c), then a disbelieves (or does not believe), at the time of c, what s expresses in c.
284 McKay and Nelson (2008, §5) introduce a similar objection; if Lois Lane believes that (a)
Superman is stronger than Clark Kent, and if names are inter-substitutable salva veritate, then Lois also believes that (b) Superman is stronger than Superman and (c) Kent is stronger than Superman. Salmon (1992) and McKay (1991) attempt to resolve this paradox, but, to my mind, both papers fail to address the central concern; that there is no clear, Millian reason for favouring Lois’s (or Alan’s) rational beliefs over her ‘irrational’ ones. In addition, as I urge throughout (and as McKay and Nelson admit), that Lois would seek help from Superman, but not Kent, in strength-requiring situations, is at least prima facie evidence that she believes (a) but not (c)—or (b) for that matter. As McKay and Nelson also go on to suggest, the force of the objection rests on the strength of the claim that explanatory, predictive and rational concerns are an essential part of a full solution to Frege’s problem (and Kripke’s puzzle); a claim which I argue for throughout.
thereby retaining his rationality—however, the problem now is that applying Millianism and (DP) alone, does not appear to provide any reasoned motivation for favouring Alan’s belief in (2a), say, over his belief in ¬(2a), or his belief in ¬(1a), for example, over his belief in (1a) (both of which choices would resolve the apparent contradiction). My account on the other hand, can motivate just such reasons; I can argue that there is a strong (narrow) sense in which (2a) and (1a) are distinct propositions, and in which Alan’s assent to (2) but not (1) is strong evidence that he (narrowly) believes (2a) and ¬(1a); hence Alan (narrowly) believes neither (1a) nor ¬(2a). In addition, since rationality is grounded in the metaphysical and since Alan is rational, I can claim that there is a strong sense in which Alan cannot (rationally and widely) believe either ¬(2a) or ¬(1a), since (widely) both ¬(2a) and ¬(1a) are metaphysically impossible; and Alan cannot be rational and believe an impossibility. Thus I can argue that (11) and (15) do not follow; (8) and (14) (i.e. strong Millianism) should be rejected at the expense (at least initially, or perhaps widely) of (DP).285 That
said, the issue of (DP) and its narrow and wide truth or falsehood very much concerns Kripke’s puzzle. So, having discussed Frege’s problem and its propositional attitude-ascriptional variant, let us move on to this second puzzle, and the nature of (DP), in slightly greater detail.