fom
Posts:
1,968
Registered:
12/4/12


Re: Mathematics and the Roots of Postmodern Thought
Posted:
Apr 1, 2013 4:35 PM


On 4/1/2013 2:25 PM, david petry wrote: > On Monday, April 1, 2013 11:50:38 AM UTC7, 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 wellrespected 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=isquantumrealityanalogafterall
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/

