On 4/7/2013 8:20 PM, david petry wrote: > > 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." >
It was a surprise to see a call for civility in the paper at your link.
I did not spend much time looking at the "relevant" sections. But, then, I am not so greatly interested in delineating good math from bad math. I am sure the definitions are reasonable for the purposes for which they are developed.
Some of the revisited historical account was good. Because so much presentation attempts to be formal, often without motivation, the history of the subject is obscured and sometimes skewed with later retellings.
WM has been asked to provide reasonable definitions of his own or to use standard terms according to standard usage.
None of it has been forthcoming.
Notice how much of the material in your link is presented in reasonable fashion.