On Reference: An Aporetic Septad

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
   philosopher.
   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?

Comments

[Edward Ockham]

This post comes uncomfortably close to the previous two about intentionality, and I am not sure we have satisfactorily reached consclusions on either.

In any case, Ockhamistas reject T3, obviously.

[Edward Ockham]

>> By (T3), Cicero has a certain property, the property of being believed by Sam to be a philosopher.

It is manifest and obvious and self-evident that there is no such property. It is a 'queer property', if you like. No scientific examination of Cicero, or his remains or anything like that, would uncover the existence of such a property. Whatever you believe, takes place in your brain cells. This is an effect of something external, and cannot, qua belief, impact the outside reality in any way. (Perhaps the belief may result in an action - e.g. my beliefs about David Cameron my result in an email to my MP, which may result in my doing something. But the belief on its own cannot affect Cameron in any way).

[Edward Ockham]

If I might say, Bill, you are not really picking up on the real weaknesses of the Ockhamist position. I discuss this here http://ocham.blogspot.com/2010/12/album-fuit-disputaturum.html .

[Steven]

I would deny D3. I think that's breaking the rules, but I am young and restless.

Sam does believe Tully is a philosopher, he just doesn't use the name "Tully" for whatever reason. I remember Nathan Salmon suggesting something like this in a paper of his on Frege's sense and reference paper.

[Steven]

Perhaps we should distinguish between different ways of expressing a person's belief that. There is an objective way and a subjective way: in the objective way, we describe a person's belief in terms that they might not use but we would, given what we know; in the subjective way, we describe a person's belief in the words they would use themselves, as they would report it "from the inside".

We might say Julius Ceasar believes that Scintilla is beautiful, or that he believes that Scintilla pulchra est. Obviously Julius Ceasar did his believing and his speaking in Latin, so he would deny that he believes "Scintilla is beautiful", because he doesn't know what that means. But to be pulchra is just to be beautiful. In the objective way, he believes Scintilla is beautiful, but not subjectively described.

So also, we can understand D1 objectively or subjectively. Objectively, D1 entails D2. Subjectively, it doesn't, because Sam might have never heard of the name Tully, but I don't see what kind of contradiction is supposed to follow from D1 being understood subjectively.