[FOM] Is Godel's Theorem surprising?

[Henrik Nordmark]

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