Date: Apr 1, 2013 4:43 PM
Author: David Petry
Subject: Re: Mathematics and the Roots of Postmodern Thought
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.