The paradigms of direct reference are the indexicals and the demonstratives. The English letter 'I' is not the English word 'I,' and the word 'I' -- the first-person singular pronoun -- has non-indexical uses. But let's consider a standard indexical use of this pronoun. Tom says to Tina,
I am hungry.
Tom refers to himself directly using 'I.' That means: Tom refers to himself, but not via a description that he uniquely satisfies. The reference is not routed through a reference-determining sense. If you think it is so routed, tell me what the reference-determining sense of your indexical uses of the first person singular pronoun is. I wish you the best of luck.
As I understand it, to say of a singular term that it is directly referential is not to say that it lacks sense, but that it lacks a reference-determining sense. The indexical 'now' does have a sense in that whatever it picks out must be a time, indeed, a time that is present. But this very general sense does not make a use of 'now' refer to the precise time to which it refers. So 'now' is directly referential despite its having a sense.
Consider the demonstrative 'this.' Pointing to a red-hot poker poker, I say 'This is hot!' You agree and say 'This is hot!' We point to the same thing and we say the same thing. The same thing we say is the proposition. The proposition is true. Neither the poker nor its degree of heat are true. The reference of 'this' is direct. It seems to follow that the poker itself is a constituent of the proposition that is before both of our minds and that we agree is true. The poker itself, not an abstract and immaterial surrogate or representative of the material poker. But then propositions are Russellian as opposed to Fregean. The poker itself, the whole infinitely-propertied nasty metallic rod, not an abstract surrogate such as a Fregean sense, is a constituent of the proposition.
How can this be? I grasp the proposition expressed by 'This is hot!' So I grasp its constituents. (Assumption: I cannot grasp or understand a proposition unless I understand its logical parts.) But how is it possible for my poor little finite mind to grasp the hot poker in all its infinitely-propertied reality? Here is an aporetic triad for your consideration:
The proposition is in or before my mind. The hot poker itself is a constituent of the proposition. The hot poker itself is not in or before my mind.
How will you solve this bad boy? Each limb is highly plausible but they cannot all be true.
The first limb is well-nigh datanic. Since I understand the proposition expressed by 'This is hot' asserted while pointing to a hot poker, the proposition is before my mind.
The second limb is plausible because the meaning of 'this' is exhausted by its referent. Surely 'this' lacks a reference-determining or Fregean sense. Since no Fregean sense is the subject-constituent of the proposition, it must be the Fregean referent that is the subject-constituent. That implies that the proposition is not Fregean but Russellian.
The third limb is extremely plausible because a finite intellect cannot have present to it an infinitely-propertied object. For example, the poker is hot and perceived to be hot and is therefore determinate with respect to being hot or not hot; but as perceived by me it is indeterminate with respect to the exact degree of being hot, even though in reality it must have some definite degree of being hot or other.
So that's the puzzle. How do we solve it? Note to London Ed: Tell me whether you think the problem as set forth is genuine as opposed to pseudo. If genuine, how would you solve it?
My tendency is to reject the second limb and affirm that all propositions are Fregean. If all propositions are Fregean, then no proposition has as a constituent an infinitely-propertied material object such as a red-hot poker.
But if I say this, then it seems that I cannot say that the reference of 'this' is direct. But if not direct, then mediated by a Fregean sense. What then is the sense of 'this'? It seems obvious that it cannot have a Fregean sense.
Perhaps the solution is to say that the reference of 'this' is direct all right, but not to an infinitely-propertied chunk of physical reality, but to an incomplete object, something like what Hector-Neri Castaneda calls an "ontological guise" or what Husserl calls a noema. But if these incomplete objects are not to be mediating items standing between the mind and the infinitely-propertied massive chunk of physical reality, then these incomplete objects or ontological guises must be constituents, ontological parts of the massive chunk, "consubstantiated" guises that constitute a complete mind-independent existent.