Full Idea
Wittgenstein's point is that if I search for foundations in what can only be known to me, then the belief that I have discovered those foundations will also fall victim to Descartes' demon.
Clarification
He said a private language, with one speaker, was a logical impossibility
Gist of Idea
Wittgenstein makes it impossible to build foundations from something that is totally private
Source
Roger Scruton (Modern Philosophy:introduction and survey [1994], 5.3)
Book Reference
Scruton,Roger: 'Modern Philosophy: introduction and survey' [Sinclair-Stevenson 1994], p.54
A Reaction
Why should foundations based in wider society or a language community fare any better? Getting a lot of people to agree won't trouble the demon too much. Flat earthers.