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
.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... that there are no infinite sets at all. ... Robinson knows about what he talks. ... takes place in a greater context of classical mathematical logic and ... misunderstood by you) for your continual harrumping that set theory is ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... that there are no infinite sets at all. ... Robinson knows about what he talks. ... Why don't you think about Robinson's mathematics and philosophy a bit ... Such distortions of context and misrpresentation of what the writers ...
    (sci.math)
  • Re: Cantor Confusion
    ... Albrecht wrote: ... Any progress on the definition of complete ... Your repeated claim is that infinite sets cannot be complete. ... you never give a context. ...
    (sci.math)
Quantcast