This is the real power of the Private Language Argument:
The question 'Is it possible to ask questions?' can have only one answer if it is a question. We might imagine, however, that it is something we could wonder about, non-linguistically. It would be like wondering whether it was possible to talk.
What would this 'wondering' be like?
It could be like privately articulating the question 'Is it possible to ask questions?' We could wonder whether any previous public questioning and answering we had done had really 'worked' - whether it had comprised real questions and answers. It's hard to separate this question from the question whether we had really been speaking at all in the past - whether we had understood what anything we thought we were saying meant. This is incomprehensible, but it has a specific incomprehensibility here: we could not know what we were 'privately' doing by asking ourselves 'Is it possible to ask questions?' as this private act depends upon the validity of the public practice of speaking - which we wish to query, or about which we have become sceptical.
What the PL argument says is that there cannot be some private language in which we could comprehensibly articulate these queries - e.g. about the possibility of asking questions or about whether it was really possible to talk to people.
The PLA can be reformulated in Davidsonian terms:
If some private language were to count as a language, we would have to be able to interpret it, or translate it, into the public language in which we are conducting our enquiry. I think this is what Wittgenstein meant by saying that otherwise we would not know what rules we were following or whether we were following them correctly.
If we can only render the concept of a rule intelligible in terms of intentionality (which I've argued for earlier), and we can only reliably attribute intentional states to interlocutors (from Kripke's paradox), then this result is what we would expect.
Another perspective on this: how would my (or your) having a thought in our private language be represented, and how would our thought be attributed to us, in the public language of our enquiry? If I say of someone that they have articulated the possibility that it might rain in their private language, then I might as well be saying of them that they thought it would rain.
I could say of someone 'she thinks in Polish', and imagine her thinking the Polish sentence for 'I think it will rain'. I can imagine her inventing a language which can be translated into our language, and using that language to say something that would translate as 'I think it will rain'. I cannot imagine her thinking it will rain, but somehow representing this in a language I cannot translate. Such a language might as well be random - have no rules, but just mean whatever she took for the moment it to mean. She might think it would rain, attach this thought to a noise, a colour, an unpleasant memory, her confusion about linear programming algorithms, and any of these would do. Anything at all could 'stand for' her thought that it would rain, and so anything could be 'translated' into our language of enquiry as 'I think it will rain', and different things could be translated so at different times. There could be no rules in this translation schema, and so it could not even be reliably applied from one occasion to another.
If we translated:
'X, on occasion Y translates from our language of enquiry into "It will rain" in Sophie's private language'
into Sophie's private language, we could not know whether our translation was correct.
And if we could not know whether our translation into Sophie's language was correct, we could not know whether the translation of any such statement back into our language of enquiry was correct, and so we could not know what anything in Sophie's 'language' meant.
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