Date: Apr 1, 2013 4:26 PM
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Apr 1, 10:59 pm, david petry <david_lawrence_pe...@yahoo.com>
> On Monday, April 1, 2013 12:17:22 PM UTC-7, Dan wrote:
> > On Apr 1, 9:58 pm, david petry <david_lawrence_pe...@yahoo.com> wrote:
> > > On Monday, April 1, 2013 11:38:05 AM UTC-7, Dan wrote:
> > > > Falsifiability only comes into consideration when you have something
> > > > apparently 'external' against which to test your mathematical models .
> > > Precisely. The "external" reality underlying mathematics is computation.
> > > A very good way of thinking about this stuff is to think of the computer as the mathematicians' microscope [...]
> > You've never actually seen a "real computer" , nor will you ever do
> > so . The Turing machine requires an infinite tape .
> That's what this "debate" is all about.
> I'm suggesting that mathematics should have meaning within the context of real-world computers which have arbitrarily large but finite memories, and you insist that "real" computers have an actually infinite memory capacity, and then (I think) you insist that mathematics itself deals with even larger infinities than that actually infinite memory of the "real" computer.
> I believe my view is superior for the mathematics of the real world.
> > "What Turing disregards completely is the fact that mind, in its use,
> > is not static, but constantly developing" -Godel
> Mind boggling.
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 .