Date: Apr 7, 2013 9:20 PM
Author: David Petry
Subject: Recommended reading for WM Mueckenheim and others


The appendix to E. T. Jaynes' book "Probability Theory: The Logic Of Science" contains a lot of material relevant to Mueckenheim's discussion of infinity. I suspect that WM has already read this.

http://www-biba.inrialpes.fr/Jaynes/cappb8.pdf

Here's a quote:

"But the messages that Kronecker did communicate contained some very important truth; in particular he complained that much of set theory was fantasy because it was not algorithmic (that is, it contained no rule by which one could decide, in a nite number of operations, whether a given element did or did not belong to a given set). Today, with our computer mentalities, this seems such an obvious platitude that it is hard to imagine anyone ignoring it, much less denying
it; yet that is just what happened. We think that, had mathematicians paid more attention to this warning of Kronecker, mathematics might be in a more healthy state today."