I don't intend this post to be my comment paper, but I thought one (in particular) distinction brought up in class was interesting. Consider the sentences:
(H) Harry likes horses.
(C) Harry likes chickens.
Suppose margaret asserts all of (H), (C) and (&). Margaret asserts that Harry likes horses. Therefore there is some thing that is asserted by Margaret using the sentence (H). That is the thing asserted by (H). Fine.
By asserting (&), Margaret asserts the same thing about horses and chickens: that Harry likes them. Therefore there is some thing asserted of horses, and some thing asserted of chickens, and those two are one and the same thing.
From these two little facts we drew the distinction between the 'thing asserted' and the 'predication'. If this is a genuine distinction, then 'asserted' is ambiguous (or the other thing) about these two uses. I don't think this is in fact a genuine distinction. I believe the 'thing asserted' is just a special case of predication.
Consider (H) again. There is another thing asserted. It's asserted that the non-symetrical liking relation holds between Harry and horses. There's a third thing asserted, that liking horses applies to Harry. The liking relation is asserted of two things, Harry and horses (in that order). However the inclination to draw a distinction between asserting of (two things) and asserting of (one thing) isn't so pressing. I'd like to say that simple assertion is just a case of asserting of (0 things). It's not unheard of in logic to treat propositions as 0-place predicates. The idea seems exactly right to me.
One could say that there's a genuine distinction, since simple assertions are truth evaluable, while predicates aren't. I'd simply respond that the addicity of the predicate (whether it's firts, second place etc.) is simply the number of things that the predicate must be applied to in order to evaluate truth. Treatment of propositions as 0-place predicates falls neatly in line. If this is all right then we have a collapse of assertion-of and assertion, and we have a hint as to what propositions might be.
If anyone wants a formal argument, I guess it would go like this:
(1) There's no ambiguity in the word 'assert' between uses where it's used to speak of assertion of an individual or assertion of multiple individuals.
(2) (1) -> (3)
(3) Addicity of predication doesn't cause ambiguity in the word 'assert'
(4) 0-place predication makes sense.
(7) There's no ambiguity in the word 'assert' when asserting things of individual(s) or asserting things of no individuals