Kripke's Interpretation
In 1982 Saul Kripke published a new and innovative account of the argument in his book Wittgenstein on Rules and Private Language. Kripke takes the paradox discussed in ยง201 to be the central problem of the Philosophical Investigations. He develops the paradox into a Grue-like problem, arguing that it similarly results in skepticism, but about meaning rather than about induction. He proposes a new form of addition, which he calls quus, which is identical with plus in all cases except those in which either of the numbers to be added are greater than 57, thus:
He then asks if anyone could know that previously when I thought I had meant plus, I had not actually meant quus. He claims that his argument shows that "Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord, nor conflict".
Kripke's account is considered by some commentators to be unfaithful to Wittgenstein, and as a result has been referred to as "Kripkenstein".
Read more about this topic: Private Language Argument
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“Lets call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we dont require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)