London Ed sends another batch of 'philolang' ruminations. My responses are in blue.
Bill's comment that the general/singular distinction should not be confused with the indirect/direct distinction brings us back to my original question about how we could get from one to the other. I think I have finally cracked it.
Define a general term as one which applies, or can apply, in the same sense or meaning, to more than one object. The Latin phrase is dicibilis de pluribus. Even when [a term] can apply to only one individual at one time (e.g., 'prime minister of England'), a general term is transferable: it could still apply to a different individual (after the next election) and even if it has always applied to the same individual ('the moon'), it still could apply, counterfactually, to a different heavenly object, or to more than one.
BV: So far, so good. I agree completely.
By contrast, a genuine singular term can only apply in the same sense or meaning to one individual. There are many people called 'John Smith', but this is not the same as them all being called ‘man’. The term 'man' applies to them all in the same sense or meaning, whereas the proper name applies to each of them with only one specific meaning, proper to each alone. Moreover, if we say "John Smith is prime minister", meaning a particular Smith, and then say "John Smith might not have been prime minister" or "John Smith will not be prime minister next year", then the same person is meant.
BV: This implies that 'the winner of the Boston Marathon in 1979' is not a genuine singular term despite the fact that it picks out exactly one individual, Bill Rodgers. (Someone other than Rodgers could have won it.) I am simply noting this implication.
Now ask about the relation 'applies to' which holds between a general term and several individuals, and between the singular term and a unique individual. Why should this hold? What makes the term and the individual(s) so related?
In the case of the general term, it is clearly the possession of an attribute corresponding to the term. E.g. if the term is 'F', then the statement 'this is F' is true or false for any individual signified by 'this', and the term 'applies to' the individual by definition if the statement is true, otherwise it does not apply.
BV: I would put it as follows. The general term 'F' applies to an individual x only if the attribute expressed by 'F' is instantiated by x. For example, the general term 'cat' applies to Max only if Max instantiates the property or attribute of being a cat.
So in the case of general terms the relation is 'accidental' or indirect, mediated either by the possession of the attribute – if being F is accidental, or by the existence of the individual, if being F is essential. (I.e. it is accidental that David Cameron falls under 'man' not because David Cameron could exist without being a man, which is impossible, but rather because Cameron could cease to exist. Indeed, all men, i.e. all humans, could cease to exist, yet the term 'man' would still have a meaning).
BV: This seems right although you are using 'accidental' in two different senses which is inelegant at the very least and could be misleading. The thought, though, is clear. The (general) reference of 'man' to Cameron is mediated by the property expressed by 'man.' Hence this general reference cannot be direct.
But in the case of singular terms, there is no attribute that an individual could possess, in virtue of which the term applies to them [to it]. Such an attribute would be untransferable, i.e. no other individual could possibly possess it, which is absurd. (I will omit other arguments which Bill has given – he is the main 'owner' of these arguments). Therefore the relation is not indirect via the possession of any attribute and (in the absence of any other candidate for the intermediary) the meaning of the singular term must be the object itself.
BV: This definitely seems to follow. My claim for a long time has been that there are no haecceity properties. There is no property H of x such that: (i) x instantiates H; (ii) nothing distinct from x instantiates H; (iii) nothing distinct from x could instantiate H. Given that there are no haecceity properties, no term can express one. Ergo, genuine singular reference is not routed through, mediated by, haecceities.
It follows that if a relation between a [genuinely] singular term and its bearer exists at all, i.e. if there is such a thing as a [genuine singular] reference relation, then it must be direct.
BV: I don't think this follows. What follows is a disjunctive proposition: either there are no genuinely singular terms or their reference is direct.
Note that while it is a datum that there are proper names, and a datum that there are grammatically singular terms, it is not a datum that there are genuinely singular terms as defined above. Suppose there are no genuinely singular terms. There would still be proper names such as 'David Cameron.' It is just that they would have to be understood in some other way, as, say, definite descriptions in disguise. But then they are not genuinely singular.
I think Ed has established nolens volens the above disjunctive proposition. Now consider this argument:
1. Either there are no genuinely singular terms or singular reference is direct.
2. If singular reference is direct, then any associated propositions must be Russellian as opposed to Fregean. For example, if 'Tom' in the sentence 'Tom is tall' refers directly, then the proposition *Tom is tall* is Russellian, i. e., it contains Tom himself as subject constituent and not a Fregean sense or mode of presentation of Tom.
3. There are no Russellian propositions.
4. Singular reference is not direct.
5. There are no genuinely singular terms.
Argument for (3):
6. If a proposition is Russellian, then its truth supervenes upon that unity of its constituents that makes it a proposition as opposed to a mere aggregate of its constituents. (Just as a sentence is not a list of its terms, a proposition is not an aggregate of its constituents.)
7. If truth supervenes upon proposition-making unity of constituents, then there are no false propositions.
8. If a proposition is Russellian, then it cannot be false.
9. There are false propositions.
3. There are no Russellian propositions.