London Ed wants to discuss the Paderewski example in Saul Kripke's "A Puzzle About Belief." But before doing so we should see if we agree on some preliminary points. Knowing Ed, he will probably find a way to disagree with a good chunk what I am about to say. So I expect we will get bogged down in preliminaries and never proceed to Paderewski. We shall see. Kripke references are to Philosophical Troubles, Oxford 2011.
Belief de re and belief de dicto
Kripke makes it clear that he is concerned only with belief de dicto in the paper in question (128). So we need to understand the restriction. The following I take to be constructions expressive of belief de re.
Cicero is believed by Tom to be a Roman
Cicero is believed to be a Roman by Tom
Cicero is such that Tom believes him to be a Roman
Tom believes, of Cicero, that he is a Roman
De re means: of or pertaining to the res, the thing, where 'of' is an objective genitive. De dicto means: of or pertaining to the dictum, that which is said (dico, dicere, dixi, dictum), where the 'of' is again an objective genitive. A dictum is the content of an assertive utterance. It is a proposition, what Frege called a thought (ein Gedanke), not a thinking, but the accusative of a thinking. I am not assuming a Fregean as opposed to a Russellian theory of propositions. But we do need to speak of propositions. And Kripke does. For the time being we can say that propositions are the objects/accusatives/contents of such propositional attitudes as belief. Of course they have other roles to play as well.
What makes the above sentences de re is that they ascribe a property to Cicero as he is in himself, and not as he appears before the mind of Tom. Or at least that is the way I would put it. Because of this the following argument is valid:
Cicero is believed by Tom to be a Roman
Cicero = Tully
Tully is believed by Tom to be a Roman.
The presiding principle is the Indiscernibility of Identicals: if x = y, then whatever is true of x is true of y and vice versa. So if Cicero = Tully, and the former is believed by Tom to be a Roman, then Tully is also believed by Tom to be a Roman. This is so even if Tom has never heard of Tully, or has heard of him but has no opinion as to his identity or non-identity with Cicero. But the following argument, whose initial premise is expressive of belief de dicto, is invalid:
Tom believes that: Cicero is a Roman.
Cicero = Tully
Tom believes that: Tully is a Roman.
The conclusion does not follow in the de dicto case because (i) Tom may never have heard of Tully and neither believes nor disbelieves anything about him, (ii) or Tom has heard of Tully but has no opinion about his identity or non-identity with Cicero. What this example suggests is that codesignative singular terms are not everywhere intersubstitutable salva veritate. The Latin phrase means: in a truth-preserving manner. De dicto belief contexts are thus contexts in which intersubstitutability of coreferential names appears to fail. Thus if we substitute 'Tully' for 'Cicero' in the initial premise, we turn a truth into a falsehood despite the fact that the two names refer to the same man.
What this suggests, in turn, is that there is more to the semantics of a proper name than its reference. It suggests that names have both sense and reference. It suggests that what Tom has before his mind, the proposition toward which he takes up the propositional attitude of belief, does not have as subject-constituent Cicero himself, warts and all, but a mode of presentation (Frege: Darstellungsweise) of the man himself, a sense (Sinn) that determines the reference to the man himself.
Before proceeding, we note the difference between the de re
There is someone Tom believes to be a faithful husband
and the de dicto
Tom believes that: there are faithful husbands.
The first entails the second, but the second does not entail the first. For if one believes that there are faithful husbands, one needn't believe, of any particular man, that he is a faithful husband. What one believes is that some man or other is a faithful husband. Tom: "I'm sure there are faithful husbands; I just can't name one."
A problem for a Millian theory of proper names
Kripke tells us that on a "strict Millian view . . . the linguistic function of a proper name is completely exhausted by the fact that it names its bearer . . . ." (127) Whether or not this is the view of the historical J. S. Mill is of no present concern. The Millian view contrasts with the Fregean view according to which names have reference-determining senses. The problem posed for Millian names by de dicto belief may be set forth as an aporetic tetrad:
a. There is no semantic difference between codesignative Millian proper names.
b. If (a), then 'a is F' and 'b is F' express the same proposition where 'a' and 'b' are both Millian and codesignative.
c. A person who believes a proposition cannot doubt or disbelieve that same proposition.
d. There are countless cases in which a person believes a proposition of the form a is F while doubting or disbelieving a proposition of the form b is F even when a = b.
This foursome is clearly inconsistent. But each of the limbs, with the exception of the first, is extremely plausible if not undeniable. So the natural solution is to jettison (a) and with it Millian semantics for proper names. But this is what the Millian Kripke is loath to do. He has already convinced himself that ordinary proper names are rigid designators whose designation does not depend on reference-determining senses.