Re: Why does Cantor a target for cranks?

Keith Ramsay wrote:

More simply, Wildberger is correct in saying that
one
doesn't need infinite sets to state the
completeness and
uncountability of the computable reals, in his
context,
because if one is assuming that all functions are
computable, which one can do, then all of the
objects being
discussed are computable functions of some kind,
and
representable in finite terms as algorithms. If one
uses the
usual definition of function, then of course these
functions
are all infinite sets already.

Isn't is simpler just to distinguish between
computable functions
and functions generally,
rather than trying to tell other people what they
should
or should not be doing?
If you don't want to repeat yourself,
why not just say at the beginning,
"The word function will always mean 'computable
function'
in this work", or something like that.

And if you don't like the law of the excluded middle,
why not just say, "I won't be using the law of the
excluded middle
in this work"?

I don't see why people get so worked up
about a personal choice like this.


--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College,
Dublin 2, Ireland



It's only important when one considers what constitutes
a convincing proof. If a proof of A relies on double
negation, such that A = ~~A (which in turn relies on
the principle of excluded middle), has one proven A?

Tom
.

Relevant Pages