There are numerous interpretations of precisely what Wittgenstein's Private Language argument is, where it begins and ends in Philosophical Investigations, what its target is, and whether it is successful...so it was nice to discover Stewart Candlish's one sentence summary of it in Edward Craig (ed.) The Shorter Routledge Encyclopedia of Philosophy:
' ...a language in principle unintelligible to anyone but its user would necessarily be unintelligible to the user also, because no meanings could be established for its signs'
I've had a go at a short summary in my book Philosophy: The Classics too...
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