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Re: Bill Taylor's comments on uncomputable reals
Posted:
Apr 27, 1999 1:16 AM
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"Andrew Boucher" <Helene.Boucher@wanadoo.fr>
writes an article to which I am very sympathetic indeed!
|> Understandably you would like to try to render the
|> situation symmetric--whatever I say, you can say, etc. But
|> as you yourself acknowledge, there is an established
|> language ("mine"), and there is an alternative ("yours"), so
|> the situation is not symmetric.
Exactly! The very fact that it *is* established is a good reason for
using something a bit different.
Of course, the opposition might well say: "But you've chosen all the best
words for yourself, it's not fair, why can't we use them too!" One is
of course sympathetic to such a plaint, but someone's got to be first.
It's an area where clarity is greatly preferable to perfect justice, I feel.
|> Suppose someone says he has proved Cantor wrong,
A bit of a baby example, but still quite penetrating.
|> The fact that the constructivist feels compelled to use
|> (I would say abuse) terminology already in use rather than
|> new, explicit terminology is telling. It's a sign of weakness.
Indeed. It *may* be a sign of something rather worse. It often seems
to me that there is a little element of deliberate provocation, or even
dissembling. Not so very long ago I made this same point, saying
how there was an element of deliberate confusion, along the lines
of the radical deconstructionist's politically-based agenda of
deliberate deception by using familiar words in totally different
ways, and without saying so, in order to fool the unwary into agreeing
with things they actually disagree with somewhat. Of course, be
it noted that constructivists are nowhere near as revolting as
deconstructionists in this matter. Well, hardly anyone *could* be!
But still, there often seems to be this underlying tone.
I think Brouwer definitely had it, far more than those later.
|> Why not simply adapt different terms? Why not be clear? If
|> you want an alternative language, why not adapt alternative
|> terms (instead of using the same symbols and giving them a
|> different sense)?
Exactly! Why not? It would be honest and clear, even if perhaps
a little outre' or verbose.
Nice one, Andrew. No more Humpty-Dumptyism!
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Bill Taylor W.Taylor@math.canterbury.ac.nz
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Whatever you wish for me, may you get twice as much.
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