Does Wittgenstein's Private Language Argument (PLA) commit the fallacy of question begging?

Question

Following up from a question I previously posted, does the following objection quoted from Solomon Radley's blog, succeed in showing that the argument begs the question?

It looks like the PLA is question begging. Generally, a reductio argument doesn’t demonstrate the falsity of a single proposition – it shows that a group of propositions leads to a contradiction, but leaves open exactly which assumption is the cause of the contradiction.

This is the case in the PLA: The reasoning of the PLA depends on certain grammatical observations, which form hidden premises in the argument. (For example, “Any ostensive definition must introduce a sample”, and “A sample can function only within a practice”.) For the reductio to successfully show that a logically private language is impossible, these hidden premises must be beyond doubt – yet they can be challenged!

So does Wittgenstein’s reasoning commit the fallacy of petito principi?

He holds that the main problem with the private linguists explanation of the sign ‘S’ is the failure to specify criteria in virtue of which he can distinguish correct from incorrect applications of S. In other words, he lacks the criteria for judging whether his later application of S exhibits understanding or misunderstanding of the sign.

But it might just be denied that it’ necessary to provide public criteria for understanding symbols – why can’t these criteria also be private? (A consistent Cartesian would surely do this.)

Thanks for all of the help

Answer 1

Firstly, the private language argument (PLA) isn't a single argument in the normal sense of a logical argument. There is disagreement among commentators on which sections of the Philosophical Investigations constitute the private language argument, probably better described as the private language arguments as there is more than one thread of thought.

You're saying it's possible that the criteria could be private (hence the language would be private). Isn't this what Wittgenstein is arguing against in his PLA? He doesn't like the idea of private criteria being grounds for understanding. He is not against the idea of someone inventing their own language (e.g. a Robinson Crusoe, lone man on an island, inventing his own language). Wittgenstein is saying that the idea of an essentially private language is incoherent.

I think you might be misinterpreting the emphasis of Wittgenstein's points. I don't think he's taking public criteria to be a premise to prove no language is private. Instead he directly tries to argue against private criteria to show private language is incoherent. Wittgenstein believes the Cartesian is mistaken.