(1) That it is translatable into a public language, or
(2) That it is not.
If (1), then the language is not private in any relevant sense. Even if we do not require the translation schema to be spelled out, the 'owner' of the language must agree about the public translations.
If (2), we have no basis for calling the 'private language' a language at all. We identify languages on the basis of inter-translatability (Davidson, Quine, radical translation).
Whether or not this is a helpful restatement of Wittgenstein's exact position, it seems to be both conclusive and fundamental.
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