Without the presupposition of 'absolute identity', therefore, the evident relativity of particular knowledge becomes inexplicable, since there would be no reason to claim that a revised judgement is predicated of the same world as the preceding — now false — judgement.
In this sense, the illusions that are attributed to the senses always involve false judgement.
The second proposal says that false judgement is believing or judging ta mê onta, "things that are not" or "what is not".
So we may suggest that the Second Puzzle is a mere sophistry for any decent account of false judgement, but a good argument against the empiricist account of false judgement that Plato is attacking.
So an explanation of false judgement that invoked entities called propositions would be unavailable to the sort of empiricist that Plato has in his sights.
Otherwise, there may be missed or false judgement.
Plato's question is not "How on earth can there be false judgement?" Rather it is "What sort of background assumptions about knowledge must Theaetetus be making, given that he is puzzled by the question how there can be false judgement?" Is it only false judgements of identity that are at issue in 187 201, or is it any false judgement?
A fortiori, then, x can make no false judgement about O1 either.
An indefinite proposition is said to be true if it yields a true proposition (Łukasiewicz says 'judgement' for a definite proposition) for all values of its variables, it is false if it yields a false judgement for all values, and is neither true nor false if it yields true judgements for some values and false judgements for others.
The old sophists took false belief as "judging what is not"; they then fallaciously slid from "judging what is not," to "judging nothing," to "not judging at all," and hence concluded that no judgement that was ever actually made was a false judgement.
