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]> 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) 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 >>> >> >> > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
