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From: Pollux on 10 Jun 2010 21:53
(6/10/10 4:56 PM), Barb Knox wrote:
> In article
> <00537029-ea1e-4c83-a597-998c26607676(a)o30g2000yqb.googlegroups.com>,
> Transfer Principle<lwalke3(a)lausd.net> wrote:
> [SNIP]
>
>> And so this gives us another generalization about the difference
>> between standard theorists and "cranks" (which maight be viewed as a
>> "lie"): standard theorists believe that the provability of
>> counterintuitive results is a _good_ thing, since a theory that
>> doesn't prove any counterintuitive results can't possibly be that
>> "powerful," while "cranks" believe that the provability of
>> counterintuitive results is a _bad_ thing, since they want more
>> control over what can be proved in their theory.
>
> Many authors of fiction have noted that characters often seem to take on
> a life of their own and push the story in a direction different from
> what the author originally planned.
>
> This happens even more so in mathematics. Starting with intuitively
> unobjectionable axioms one comes up with some unintuitive and even
> counterintuitive results. This is a Good Thing; it shows where our
> intuitions need adjustment.
>
> I think your characterisation of cranks is reasonable -- they believe
> that their personal intuitions should be the measure of all things,
> rather than accepting the fact that their intuitions are limited to
> familiar experience, and once they journey outside those borders they
> will surely encounter strange and wonderful things.
>
> [snip]
>
It seems to me that a good part of the history of science is about
establishing on more reliable grounds than intuition. I am very
skeptical of intuition as a reliable means of acquiring definite knowledge.

Pollux

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