Full Idea
The idea that concepts can be formed by abstraction from the Given just is the idea of private ostensive definition. So the Private Language Argument just is the rejection of the Given, in so far as it bears on the possibilities for language.
Clarification
'Ostensive' definition involves pointing
Gist of Idea
Forming concepts by abstraction from the Given is private definition, which the Private Lang. Arg. attacks
Source
John McDowell (Mind and World [1994], I.7)
Book Reference
McDowell,John: 'Mind and World' [Harvard 1996], p.20
A Reaction
I'm not clear why the process of abstraction from raw impressions shouldn't be a matter of public, explicit, community negotiation. We seem to be able to share and compare fairly raw impressions without much trouble (discussing sunsets).