Recommended reading for WM Mueckenheim and others

david petry

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Apr 7, 2013, 9:20:37 PM4/7/13

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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."

fom

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Apr 8, 2013, 12:05:31 AM4/8/13

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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.

AMiews

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Apr 8, 2013, 1:21:15 PM4/8/13

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"david petry" <david_lawr...@yahoo.com> wrote in message
news:1a6e7c17-a39c-436c...@googlegroups.com...

>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

Silly, set theory is not algebra, and algebra is not set theory, they are
two different fields of math.

So why are you quoting a SILLY source ?

david petry

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Apr 8, 2013, 9:54:43 PM4/8/13

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On Monday, April 8, 2013 10:21:15 AM UTC-7, AMiews wrote:

> So why are you quoting a SILLY source ?

That "silly" source (E. T. Jaynes) did some rather important work in probability theory and applied mathematics. Maybe he's not so silly.

fom

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Apr 9, 2013, 1:49:21 AM4/9/13

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https://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes

You are right.

And, he is cited in

http://plato.stanford.edu/entries/epistemology-bayesian/

http://plato.stanford.edu/entries/logic-inductive

so that his ideas have extended beyond the technical
sphere.

apoorv

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Apr 9, 2013, 3:14:14 PM4/9/13

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Thanks for sharing that interesting link.
Apoorv

Robin Chapman

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Apr 15, 2013, 8:22:21 AM4/15/13

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On 08/04/2013 18:21, AMiews wrote:
> "david petry" <david_lawr...@yahoo.com> wrote in message
> news:1a6e7c17-a39c-436c...@googlegroups.com...
>

> So why are you quoting a SILLY source ?
>

maybe 'cos it reinforces his prejudices?

david petry

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Apr 16, 2013, 12:15:02 AM4/16/13

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I feel like I have some obligation, as a friend, to point out to you that no one looks at that remark of yours and says, "now there's an insightful man".

FredJeffries

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Apr 16, 2013, 12:37:01 PM4/16/13

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On Apr 7, 6:20 pm, david petry <david_lawrence_pe...@yahoo.com> 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.
>

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

The entire book contains much that might be relevant. The work quoted
is full of examples (especially chapter 15) of calculation involving
"actually" (Jaynes's term) infinite sets. This book is a laying down
of the "really trustworthy standards of rigor" (Jaynes's phrase) for
certain calculations involving infinite sets.

See the comments to Matheology § 042

More of Jaynes's book can be found at:
http://omega.albany.edu:8008/JaynesBook.html
http://books.google.com/books?id=tTN4HuUNXjgC