Full Idea
Wittgenstein's claim is that the assumption that the reference is private (being observable to one person alone) is incompatible with the hypothesis that the sense is public.
Gist of Idea
If the reference is private, that is incompatible with the sense being public
Source
report of Ludwig Wittgenstein (Philosophical Investigations [1952], §293) by Roger Scruton - Short History of Modern Philosophy Ch.19
Book Reference
Scruton,Roger: 'A Short History of Modern Philosophy' [ARK 1985], p.282
A Reaction
An illuminating summary, showing the link between the private language argument and modern 'externalism' about the meaning of concepts (e.g. Idea 4099). I still don't find Wittgenstein's claim conclusive. Something is definitely private.
Related Idea
Idea 4099 If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane]