Re: Cantorian pseudomathematics

david petry wrote:
Achava Nakhash, the Loving Snake wrote:
david petry wrote: 

What I have been advocating is that the right way to develop the real
numbers is to first introduce probabilistic notions into the
foundations of mathematics, and then develop a notion of
"finite-precision real number" as a rational number plus an estimate of
the uncertainty to be attached to the number.  Then real numbers are
the limiting case of finite precision real numbers as the uncertainty
goes to zero. The key idea is that a finite precision real number
includes an estimate of its own uncertainty (imprecision), and thus it
is not the same as a floating point number.  And note that when we do
calculations, we must keep track of the uncertainties.  Also note that
this is not the same as standard constructivism.

If you wish to be taken seriously, then you should develop the real
numbers in the way you are advocating.  If you can do it, it sounds
interesting, although it is not clear to me that it would be taken
seriously in any event, but that is true of much research.  At least
that way you would not be taken as a cheerleader for a team that
someone is just thinking about forming.


If you had read the article that started this thread, you would realize
that I wanted to develop this theory when I was in graduate school, but
I got discouraged by the reaction of the mathematics community to my
ideas. Now I have nothing to do with the mathematics community, but I
still think there is some point to spending some of my free time in
this newsgroup, and trying to debunk the pseudoscience which is
infecting and corrupting modern mathematics.

So you spent quite a lot of time over the past years posting to sci.math. And if you continue to do so, the world will still be no smarter in 2020 than it is now.
Perhaps it makes more sense to spend all those hours in the coming years on elaborating your ideas into a concrete formalism? Or at least in a large collection of concrete examples, completely worked out?

--
Cheers,
Herman Jurjus






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