| Esenin-Volpin was mentally counting to the desired power of 2, to verify that it really exists |
[Oct. 5th, 2011|12:25 am] |
![[info]](http://lj.rossia.org/img/userinfo.gif) maxmornev навёл на крутое (http://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html):
Ultrafinitists don’t believe that really large natural numbers exist. The hard part is getting them to name the first one that doesn’t.
Richard Elwes replied, pointing out a conversation between the ultrafinitist Alexander Esenin-Volpin and the master of large infinities, Harvey Friedman. Friedman challenged Esenin-Volpin to name the first number that doesn’t exist:
I raised just this objection with the (extreme) ultrafinitist Esenin-Volpin during a lecture of his. He asked me to be more specific. I then proceeded to start with 2^1 and asked him whether this is “real” or something to that effect. He virtually immediately said yes. Then I asked about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2^100 times as long to answer yes to 2^100 then he would to answering 2^1. There is no way that I could get very far with this.
I believe that after each question Esenin-Volpin was mentally counting to the desired power of 2, to verify that it really exists. |
|
|