[FOM] A Reductio of Witt.

[tchow]

Charlie Silver wrote:

> 	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.

As I said before, I'm wary of trying to argue for ChowKripkenstein over
SilverKripkenstein, but I really think it cannot be correct to assert
baldly, in the context of Kripkenstein, that "we *can* give a precise,
rule-governed definition of 'plus.'"  If we could, then the answer to
Kripke would be simple: *Anyone* can say this is not the function, 
because
they would just have to point to the numerous textbook discussions that
"give a precise, rule-governed definition of 'plus,'" which would
exclude the possibility that "quus" was intended instead.  It would also
be entirely irrelevant that only numbers smaller than 57 had been added
before.

If specifying a rule for an operation like addition is entirely
unproblematic, then it's hard to see why Kripke would be so deeply
impressed with the originality and power of this skeptical argument,
and write such a huge long essay about it.

Tim Chow