[FOM] Is Godel's Theorem surprising?
Henrik Nordmark
henriknordmark at mac.com
Thu Dec 7 17:11:54 EST 2006
Dear Charles,
I think your psychological question regarding why Godel's Theorem
seems or seemed surprising is very interesting.
And I think it would be a great idea to collect some empirical data
on this.
> I'm also wondering, though this is a separate point, whether today
> the theorem is not only not surprising, but perhaps even intuitively
> obvious.
I don't think it is intuitively obvious.
This is only anecdotal evidence, but I have met a fair amount of
mathematicians working outside foundations who find the
incompleteness of PA very counter-intuitive and they react similarly
with regards to independence results such as CH.
This is only speculation on my part, but I think there are good
reasons to believe that ordinary mathematicians simply equate truth
and provability because this is what they are used to in their
everyday lives.
Kind regards,
Henrik Nordmark.
Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam
www.henriknordmark.com
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