Date: Apr 1, 2013 4:55 PM
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Apr 1, 11:43 pm, david petry <david_lawrence_pe...@yahoo.com>
> On Monday, April 1, 2013 1:26:45 PM UTC-7, Dan wrote:
> > I hold no liking for set theory , in its current form . CH may as well
> > be meaningless. However , the transfinite hierarchy , everything
> > including second order arithmetic and complex analysis are
> > unambiguous . I see no reason why we should give it up on a whim .
> Let me restate the basic point I've been making.
> Falsifiability is part of our natural thinking processes even if we don't always recognize it as such. It's already part of applied mathematics, even if applied mathematics has never been fully formalized. If the mathematicians involved in the debate over the foundations of mathematics that occurred in the early part of the twentieth century had taken the notion of falsifiability into consideration, it's very likely the debate would have been resolved in favor of falsifiability and against Cantorian set theory.
> The mathematicians chose to give up falsifiability on a whim. Nothing of value to society has come from that choice.
Have you paid no attention? Falsifiability was never a concern even
before Cantorian Set theory , nor can it ever be a concern outside the
scientist's modus operandi , into mathematics by itself, without the
Physical world on which to perform experiments . Going by your
'operational' usage of falsifiability, I would classify it as "not
even wrong" , to use an expression preferred by scientist .
Mathematics is about rational proof . Physics today is about disproof
of an endless stream of hypothesis .
"A fool sees not the same tree that a wise man sees."