Date: Apr 1, 2013 4:35 PM
Author: fom
Subject: Re: Mathematics and the Roots of Postmodern Thought
On 4/1/2013 2:25 PM, david petry wrote:

> On Monday, April 1, 2013 11:50:38 AM UTC-7, Jesse F. Hughes wrote:

>

>> I'm eager to believe you, oh, golly I am. But it feels like you're

>> making it up.

>

> You don't really seem to have the background needed to participate

> constructively in this discussion. The following is an actual

> quote from a serious and well-respected mathematician; I'm not just

> making it up:

>

> "The actual infinite is not required for the mathematics of the

> physical world"

>

> (Soloman Fefermanm, in an article titled "Is Cantor Necessary?")

>

Like any researcher in any field, Feferman has his own

pet theories. I already pointed out to you that his

version of predicativism is based upon a completed

infinity of the natural numbers ascending a predicative

type structure indexed by the transfinite numbers.

Feferman has also published papers complaining about the

syntax used for definitions in the calculus.

This is not surprising since the emphasis of his research

is precisely *constructive* mathematics.

http://math.stanford.edu/~feferman/

Let me observe that Feferman is not a "scientist" and,

therefore, is unlikely to convey the positions of

scientists in this matter.

David Tong was recently published in Scientific American

with an essay entitled "The Unquantum Quantum" which argued

for an "analog", or continuous, universe. It is likely

that his view is in a minority, but as one of the comments

on his article suggests, the majority view requires believing

in things not yet discovered.

Then there is the last comment on the page suggesting the

option of continuous, but not differentiable. This would

be a reference to Nottale's scale relativity.

http://www.damtp.cam.ac.uk/user/tong/

http://www.scientificamerican.com/article.cfm?id=is-quantum-reality-analog-after-all

http://en.wikipedia.org/wiki/Laurent_Nottale

http://en.wikipedia.org/wiki/Scale_relativity

The mathematics that physical scientists will require is

the mathematics that corresponds with how they understand

evidence in relation to their theories.

http://plato.stanford.edu/entries/evidence/