We can divide the following seven propositions into two groups, a datanic triad and a theoretical tetrad. The members of the datanic triad are just given -- hence 'datanic' -- and so are not up for grabs, whence it follows that to relieve ourselves of the ensuing contradiction we must reject one of the members of the theoretical tetrad. The funs starts when we ponder which one to reject. But first you must appreciate that the septad is indeed inconsistent.
D1. Sam believes that Cicero is a philosopher.
D2. Cicero is Tully.
D3. It is not the case that Sam believes that Tully is a philosopher.
T1. 'Cicero' and 'Tully' have the same denotation (are coreferential)
in all of their occurrences in the datanic sentences, both in the
direct speech and indirect speech positions.
T2. 'Is' in (D2) expresses strict, numerical identity where this has
the usual properties of reflexivity, symmetry, transitivity, and the
necessity of identity (if x = y, then necessarily, x = y).
T3. Cicero has the property of being believed by Sam to be a
T4. If x = y, then whatever is true of x is true of y, and vice versa.
(Indiscernibility of Identicals)
Now, do you see that this septad is pregnant with contradiction? By (T3), Cicero has a certain property, the property of being believed by Sam to be a philosopher. Therefore, given the truth of (T1) and (T4), Tully has that same property. But this implies the negation of (D3).
To remove the contradiction, we must reject one of the T-propositions. The D-propositions express the data of the problem. Obviously, they can't be rejected. Of course, nothing hinges on the particular example. There are countless examples of the same form. Someone could believe that 3 is one of the square roots of 9 without believing that one of the square roots of 9 is a prime number, even though 3 is a prime number.
The Fregean solution is to reject (T1). In (D1), 'Cicero' refers to its customary sense, not its customary referent, while in (D2), 'Cicero' refers to its customary referent. This implies that the antecedent of (T4) remains unsatisfied so that one cannot conclude that Tully has the property of being believed by Sam to be a philosopher.
A different solution, one proposed by Hector-Neri Castaneda, is achieved by rejecting (T2) while upholding the rest of the T-propositions. The rough idea is that 'Cicero' in all its occurrences refers to a 'thin' object, an ontological guise, a sort of ontological part of ordinary infinitely-propertied particulars. This ontological guise is not strictly identical to the ontological guise denoted by 'Tully,' but the two are "consubstantiated" in Castaneda's jargon.
This consubstantiation is a type of contingent sameness. Since Cicero and Tully are not strictly identical, but merely consubstantiated, the fact that Cicero has the property of being believed by Sam to be a philosopher does not entail that Tully has this property. So the contradiction does not arise. (Cf. The Phenomeno-Logic of the I, pp. 183-186)
Both solutions invoke what our friend 'Ockham' calls 'queer entities' using 'queer' in the good old-fashioned way. The Fregean solution requires those abstract entities called senses and the Castanedan solution posits ontological guises. Can 'Ockham' solve the problem while satisfying all his nominalistic scruples?
Can a man in a straight-jacket do the tango?