I always seem to get confused when I get just passed the first third of pg 185 of Frege's On Concepts and Object. But there was a reductio raised in an earlier post (Wes) that I agreed with so I will talk about that. It has been summed up a few times already, so I will give a really short interpretation of Frege's argument before the reductio.
All the examples Frege gives seem to imply that anything which can be used as an adjective is a concept, and anything that cannot is an object. Concepts have instances in objects, but objects cannot have instances in concepts. When Kerry objects and says that there are situations where concepts seem to play the part of objects, Frege does two things: 1) he says that because of the inadaquacy of language certain paradox's will arise, 2) that there are situations where second-order concepts can have instances in first-order concepts.
I totally agree with the reductio Wes gives against Frege's work:
1. Frege uses the resources of language to explore language
2. The resources of language are inadaquate to fully explore language
3. Therefore, Frege is unable to fully explore language.
At first I considered, in Frege's defense, that he never actually claimed that he was going to fully explore language. He claimed that it was precisely because of this inadaquacy of language that he would not actually give a definition of his 'bedeutung'; he would only give a feeling of, or clues to, what it is like. Wouldn't this preface have to be applied then to everything that follows in Frege's argument?
4. Frege's concept-object distinction is central to his idea of Bedeutung
5. Frege's idea of Bedeutung is not fully fleshed out or defined, but is still useful
6. Therefore, Frege's concept-object distinction is not fully fleshed out or defined, but is still useful (4,5 MP)
However, upon review I think that 4 is backwards. Frege comes to his idea of what Bedeutung is precisely because of the relations between subjects, predicates, objects, and concepts. His argument for Bedeutung is like this:
7. Objects are incapable of being used as a grammarical predicate themselves.
8. Objects can play a role in part of a concept (ex: "no other than Venus" he says is a concept, and yet 'Venus' is part of that concept).
9. If the whole of the object were in the makeup of a concept, the object would in fact be a concept.
10. If 9, then part of an object must stay wholly an object while said object plays a role in a concept.
The part of the object which can only be an object is called the Bedeutung. This clearly shows that the idea of Bedeutung relies on the concept-object distinction. I cannot really think of a way to defend Frege from the reductio. I think he has to atleast concede that his concept-object distinction is sitting on unsound foundation.
Does this mean that he has to give up his position entirely though? If he admits to the fact that his concept-object distinction does a lot of the work, but is not consistent in a few specific instances where language gets weird and self-reflexive, it still may be a very useful theory. Couldn't you say his theory is workable pending further developments in the constructs of language. Lots of accepted theories rest on unstable grounds, such as the theory of gravity (where what we learn in school breaks down at quantum levels), or even the laws of thermodynamics (in recent cosmological models). What he cannot say however, is that his concept-object distinction is flawless and in no need of further development.