David Brightly writes: "'Hamlet kills Polonious' is analyzed into the conjunctive sentence 'Hamlet exists &Hamlet kills Polonious.' Something that has been puzzling me is how this doesn't run foul of an infinite regress. Can you explain how interpretation of the second, inner 'Hamlet kills Polonius' differs from that of the first, outer instance, so that this doesn't happen?"
A good point. We could represent that the second proper name by a pronoun. Thus Ockham (the medieval one) says that 'chimaera est non-ens' (the chimera is a non-being) is to be analysed as 'chimaera est aliquid' et 'illud est non-ens' (the chimera is something and it is a non-being'), of which the first is false. Or we could represent it a bound variable thus
E x, x = Hamlet and x kills Polonius.
I don't think either is quite right. My position would be that a proper name, which tells us who the predicate applies to,adds a little bit of information to the word 'someone', which doesn't tell us who the predicate applies to. I.e. 'Someone kills Polonius' asserts the existence of a Polonius-killer. Then we can add a bit of information to the 'someone' by turning it into a proper name, as though the proper name were a sort of adjective. I.e.
Someone (Polonius) kills Hamlet.
Thus there is only one proposition, not two, and we avoid the regress. This raises the difficulty of exactly how a proper name can function as an adjective, logically speaking. More later, possibly.