I reply to the first argument of the four arguments for direct reference. The argument was that a proper name does not signify something that is repeatable, therefore does not signify a property. Therefore it signifies an object.
I reply: the argument relies on the assumption that a a term signifies either a property (which is repeatable) or an object (which is not). This is false. As I have argued before, the entire significance of a proper name is to signify that (if we are talking about anything at all) we are talking about a single thing. In other words, Fa and Ga imply that some F is G, if 'a' is functioning as a proper name. Thus it cannot signify anything repeatable like a property, by reason of its peculiar semantic function. 'Fa' and 'Ga' always imply that 'F' and 'G' apply to a single thing. Thus it makes no sense to say that this individual is Socrates on Tuesday, but that someone else is Socrates on Wednesday. Or that this individual is Socrates today, but might not have been Socrates.
Nor does a proper name signify an object. Sentences containing the same proper name, accepted in the same sense, are true of the same thing, if they are true at all. But they do not have to be true of anything at all, in order for us to understand this.