[FOM] A Reductio of Witt.
Charlie
silver_1 at mindspring.com
Tue Feb 21 14:22:53 EST 2017
Before we get too involved in accepting problems with carrying out a rule, note that Kripke, in his book on Wittgenstein, supposes he’s only previously added numbers smaller than 57. Then, attempting to follow Wittgenstein, he formulates a rule for adding two numbers — i.e., quussing two numbers..
Again, here’s Kripke’s definition of “quus”:
x ⊕ y = x + y, if x, y < 57
= 5 otherwise.
Kripke asks “Who is to say that this is not the function I previously meant by ‘+’ “?
Note that Kripke isn’t being himself here, he’s trying to *interpret* Wittgenstein, and it may well be — Kripke is coy about this — that Kripke is providing us with a *Reductio* of Wittgenstein. (Please note that we *can* give a precise, rule-governed definition of “plus” [in terms of specifying the “addition” of any two one-digit numbers, and then “carrying” when the sum exceeds nine].)
This is different from “continuing (a finite sequence) in the same way”, since “same way” is unclear. “Addition" is not.
Charlie
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