Posted by
glen ep ropella on
URL: http://friam.383.s1.nabble.com/Wittgenstein-tp1133169p1304368.html
Thus spake John F. Kennison circa 10/07/2008 10:53 AM:
> Okay, suppose someone else simply entered some numbers in a Suduko
> grid and said, "I wonder whether there is any solution that
> incorporates these numbers, and, if there is a solution, is it
> unique?" I concede that the person who did this invented the problem.
> But if I prove that there is a solution and that it is unique, I
> haven't invented that fact as that fact was implicit in the original
> question, but I have discovered that the fact was implicit, have I
> not?
Well, what you're saying depends on your usage of your words,
particularly the words "fact", "implicit", and "discover".
But to answer as directly as possible, all you did was transform
something some other person invented. So, yes, you invented the first
sentence (the solution to the puzzle). And you invented the second
sentence (the statement that the solution is unique). And you invented
the string of sentences that "proves" the two previous sentences. The
puzzle creator did not explicitly invent those two sentences or the
string of sentences that constructs the proof.
It's just like folding a piece of paper. Someone hands you a piece of
paper and you fold it into an origami swan. Did you _discover_ the
swan? Or did you invent the swan?
I don't intend to play around with the definitions of words. But
playing around with words is a _great_ demonstration of Wittgenstein's
beef with platonic mathematicians. All they're doing is playing around
with symbols. It's not science. It's symbol manipulation. There is no
discovery in the same sense that scientists mean. It is invention.
--
glen e. p. ropella, 971-219-3846,
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