The Ostrich maintains:
1. Proper names have a (context dependent) sense. Context dependent, because ‘Mars’ can mean the god, or the planet, depending on context.
2. The object itself cannot be part of the sense, although the mainstream view is that it is.
BV: What is being called the mainstream view, I take it, is the direct reference view according to which the semantics of a proper name is exhausted by its reference. That is, there is nothing more to the meaning of a proper name than its referent. There is not, in addition to the referent, a (reference-mediating) sense that the name has whether or not it has a referent. This implies that an empty (vacuous) name has no meaning.
The formulation of (2) leaves something to be desired. If we distinguish sense from reference/referent, as we must, then it is trivially true that the object, the planet Mars say, cannot be part of the sense. What's more, (2) misrepresents the mainstream view. No direct reference theorist holds that proper names have reference-mediating senses. No such theorist can be maintaining that the object itself is part of a reference-mediating sense. So (2) might be read like this:
2*. The object itself cannot be part of the MEANING of the name, although the mainstream view is that it is.
The trouble with (2*) is that it is false. Surely Mars is part of the MEANING of 'Mars' inasmuch as Mars is the referent of 'Mars.'
The Ostrich's argument seems to perish at this point of an equivocation on 'sense' as between 'sense' in the sense of Frege's Sinn and MEANING where the latter embraces both Sinn und Bedeutung, both sense and reference in Fregean jargon.
3. Nor can the sense signify some property, or collection of properties. Not a collection, for the reasons Kripke has cogently argued. Not a single ‘haecceity’, for the reasons you have argued.
BV: Right, if you mean sense as opposed to reference/referent.
4. The only remaining candidate (in my view) is that a proper name acquires its meaning via anaphora (i.e. ‘back reference’). In all cases.
BV: What do you mean by 'meaning'? Do you mean sense as opposed to reference/referent? My verdict is that your argument is still too murky to be evaluated.