Date: Apr 1, 2013 4:35 PM
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.
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.
The mathematics that physical scientists will require is
the mathematics that corresponds with how they understand
evidence in relation to their theories.