Frank,
Thanks for pointing that out. I had not noticed that. I'm afraid that I
only know Reuben by reputation - mainly from you and Dean; so, no, I did
not send it to him; and I'm glad that you did.
Thx,
Grant
On 11/15/16 4:24 PM, Frank Wimberly wrote:
Have you sent this to Reuben Hersh? I just did so. Sine he is the
first mathematician referenced that seems appropriate.
Frank
Frank Wimberly
Phone (505) 670-9918
On Nov 15, 2016 4:12 PM, "Grant Holland" <[email protected]
<mailto:[email protected]>> wrote:
Thanks, Glenn. I appreciate your persistence in reading the whole
article.
I think this is an important and timely article, mainly, I must
admit, because it is in my current area of research. I'm working
on a different thread than Mumford but my intention is very
sympathetic to his. And I think you might agree that his main
points are that we are now in the "age of stochasticity" and that
we should now integrate "probability thinking" into the
foundations of mathematics.
To address your questions about the article, let me just suggest
to concentrate on his section 1, "Introduction", section 5,
"Putting random variables into the foundations" and section 7,
"Thinking as Bayesian inference". I think that unless one is a
mathematician, etc. the other sections can be skipped without too
much loss. And even within those sections, Mumford has pretty much
segregated math/logic-speak from plain English; and that one can
usually skip the insider stuff when you want to, and still get the
significance of the article.
Grant
On 11/15/16 1:11 PM, glen ep ropella wrote:
Very cool article, Grant! Thanks. I started to get lost on
page 11 with the meta-axioms that give the Bernoulli random
variables. *8^( It's interesting that the wikipedia page
(https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH
<https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH>)
mentions Feferman's semi-intuitionistic ideas in the same
context as Freiling's argument against the CH.
But I was irritated by his maps from the traditional
subdivisions of math to the primitive elements of human
experience. The geometry one seems right to me. But either
he didn't finish explaining the referents of analysis, or I
disagree. Analysis (to me, of course) is all about
_proximity_, the closeness of any bunch of things.
Differentiation being about the determination of a locality
and integration being about establishing totalities. Although
it's obvious (hindsight is 20/20) how to get to analysis from
the calculus and from forces. It doesn't strike me that
forces (and acceleration and oscillation) are the primitive
human experiences referred to by analysis, as a domain.
Also, I don't really agree with the map from algebra to
recipes of action. To me algebra is about the preservation of
some ... "substance" _through_ transformation. So, like with
forces giving us (well, Newton and Leibniz) a path into the
calculus, the composition of actions in algebra is a kind of
side effect. The core of it (to me, a non-mathematician!) is
about the preservation of some quality through equivalence
(and equivalence classes).
Obviously, it would be silly for me to argue with Mumford on
this sort of thing. But I'm wondering whether you (or anyone
on the list) see these experience correlations more as he sees
them?
As usual, I have no comment on the actual topic of the paper. 8^)
On 11/13/2016 10:21 AM, Grant Holland wrote:
http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf
<http://www.stat.uchicago.edu/%7Elekheng/courses/191f09/mumford-AMS.pdf>
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