How does Wittgenstein's argument against recognizing private sensations work?

Question

Wittgenstein writes in his Philosophical Investigations in paragraph 270:

Let us imagine a use for the entry of the sign "S" in my diary. I discover that whenever I have a particular sensation a manometer shows that my blood-pressure rises. So I shall be able to say that my blood-pressure rises without using any apparatus. This is a useful result.

This seems okay to me. Surely we can establish a correlation (if it exists, and otherwise prove that there is no correlation) between sensation "S" and a rise in blood-pressure. Moreover, it is very well imaginable that if I sense "S" I can prevent better some of the nasty and potentially dangerous side effects of high blood-pressure by taking some medication more timely. In this manner the sensation is useful, beyond the mere information of having high blood-pressure, something you could not care less for if without consequence. But now Wittgenstein continues...

And now it seems quite indifferent whether I have recognized the sensation right or not. Let us suppose I regularly identify it wrong, it does not matter in the least. And that alone shows that the hypothesis that I make a mistake is mere show.

I do not understand how this continuation follows from his preceding remarks. It is rather counterintuitive and calls for an explanation I think. Naturally, if I am not able to distinguish between a multitude of sensations, how can I then possibly observe a correlation (except in the case that all those sensations indicate high blood-pressure, but then it is still useful, since obviously we do not always have high blood pressure)?

Answer 1

Wittgenstein is not denying that the correlation is useful, he acknowledges as much in the first passage. What he means is that the correlation is established in a way that does not allow for any independent checking of sensation's authenticity. What way is there to tell if the sensation is the 'right one' other than observing the rising blood pressure? We only have sensation's 'word' for it. With a truly private diary the "S" is all there is, by construction there is no possibility of mistakes. And if there is no rising blood pressure then it is not that we identified the sensations 'wrong', there is simply an imperfect correlation or no correlation at all. We can have "S" publicly linked to rising blood pressure with a possibility of mistakes, or we can have private "S" without it, but we can not have the same "S" be both.

This is why in the end he says:"And that alone shows that the hypothesis that I make a mistake is mere show. (We as it were turned a knob which looked as if it could be used to turn on some part of the machine; but it was a mere ornament, not connected with the mechanism at all)". Another example he gives, in PI 266, is that it is pointless to buy several copies of the same newspaper to assure yourself that what it says is true, "justification consists in appealing to something independent" (PI 265).

See Fogelin's commentary in Taking Wittgenstein at His Word and Did Wittgenstein consider the possibility of a private language with public content? for more on the private language argument.