I just found an excellent paper by Tim Crane - "The Singularity of Singular Thought". Today I will say some things I like about the paper, tomorrow some things I don't like so much.
Crane begins by picking up a remark by Quine that "a singular term is one that ‘purports to refer to just one object’". This suggests to Crane that a singular term is one that appears or ‘claims’ to be doing something – referring to just one object, and which still appears to do this even if there is no such object. Readers of Beyond Necessity will understand that I find this attractive. Common sense suggests that a proper name, together with many other types of singular terms, has the same semantics whether or not there is an object corresponding to it. The semantics of proper names, I have argued, is object independent.
The difficulty, as Crane acknowledges, is to explain how this is consistent with the distinction between singular and general thought, which any adequate theory of mind must account for. As I suggested in some earlier posts, there are apparently strong arguments showing that we can only explain the distinction by invoking semantic dependency on objects. Singular thoughts (according to these arguments) are precisely those which depend for their existence on the existence of the objects they are about. John McDowell defines a singular thought as ‘a thought that would not be available to be thought or expressed if the relevant object, or objects, did not exist’.
Crane's objective is a theory of singular thought - of which he provides only a brief sketch - which accommodates the distinction between singular and general thought, "but which also takes seriously the idea that a singular thought might merely purport to refer. In other words, a thinker can think about a particular object and yet fail to refer to that object in thought.”