13
$\begingroup$

A student recently asked me about the status of a 2001 arXiv post, Beware of the Gödel-Wette paradox!, by Alexander Yessenin-Volpin (aka Esenin-Volpin and several other transliterations) and Catherine Christer Hennix.

It claims to give a counter-example to Gödel’s second incompleteness theorem, which of course sets off the crackpot alarm. However, at least Yesenin-Volpin has done enough other serious and thought-provoking work (albeit more philosophy-of-maths than straight-up mathematics) that I am uncomfortable dismissing the paper without some consideration. I presume it either has an error, or works in a non-standard meta-mathematical setting, or in some other way does something weaker than it seems to claim; but it would be nice to substantiate this suspicion and find out which of these is the case.

Has anyone read this paper carefully, and discussed/debunked it?

Improve this question
$\endgroup$
12
  • 3
    $\begingroup$ Read 109 pages of known ultrafinitistic "disproving" a well-known theorem? Pass. $\endgroup$
    – Asaf Karagila ♦
    Commented Jan 5, 2015 at 10:31
  • 5
    $\begingroup$ The problem, and it applies more or less to that 300 pages long paper about why inaccessible cardinals are inconsistent, is that when a mathematician has to take several months of their time to read, analyze and understand something of this caliber, which clearly doesn't sit right with all previously known and thoroughly checked mathematics... it's impossible to persuade anyone to read it. Not to mention that you've never heard about an ultrafinitist going "Oh.... alright then, infinite set are consistent" after being explained their mistakes. So, again, why bother. $\endgroup$
    – Asaf Karagila ♦
    Commented Jan 5, 2015 at 11:44
  • 9
    $\begingroup$ @AsafKaragila It might not be so bad as that. Remember a few years ago when Nelson announced the inconsistency of PA? He was no crackpot either. I don't recall how long his official purported proof was -- it might have been comparable in length to this one -- but the error in his reasoning was sniffed out fairly quickly (by none other than Terence Tao). golem.ph.utexas.edu/category/2011/09/… The same could happen here. $\endgroup$
    – Todd Trimble
    Commented Jan 5, 2015 at 12:20
  • 6
    $\begingroup$ All I know is that I bought an experimental music album by Catherine Christer Hennix which had liner notes full of pseudo-mathematical jargon, so, perhaps unfairly, I'm slightly disinclined to take any purported mathematics by her too seriously. The music was pretty solid though. $\endgroup$
    – Jonathan Beardsley
    Commented Jan 5, 2015 at 16:32
  • 3
    $\begingroup$ @Peter and Asaf: "But when cranks accuse mathematicians of being hidebound reactionaries ignoring their work, we say that no, there are clear standards of correctness that they fail to live up to." "...when a mathematician has to take several months of their time to read, analyze and understand something of this caliber, which clearly doesn't sit right with all previously known and thoroughly checked mathematics... it's impossible to persuade anyone to read it." And yet - or perhaps for that very reason - one may still encounter demonstrably more cranky work in reputable journals. $\endgroup$
    – Adam Epstein
    Commented Jan 5, 2015 at 16:38

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .