Date: Sep 24, 2017 12:06 PM
Author: Dan Christensen
Subject: Re: 0 = 1
On Sunday, September 24, 2017 at 8:19:14 AM UTC-4, Peter Percival wrote:
> Dan Christensen wrote:
> > On Saturday, September 23, 2017 at 12:41:43 PM UTC-4, FredJeffries
> > wrote:
> >> On Saturday, September 23, 2017 at 9:10:59 AM UTC-7, Dan
> >> Christensen laid down the law:
> >>> If you cannot formally define these concepts of yours purely in
> >>> terms of the symbols of logic and set theory (or some
> >>> equivalent), it isn't mathematics.
> >> That's ridiculous. You have just chauvinistically declared the
> >> mathematics of thousands of years and hundreds of cultures to be
> >> "n[o]t mathematics"; not to mention all of the experimental and
> >> not-yet-formalized current research; not to mention all of the
> >> checkbook balancing done by millions of people who never saw a
> >> "symbol of logic" in their lives.
> > Ordinary arithmetic (2+2=4, etc.) was formalized some time ago. So
> > too has algebra, calculus, differential equations, etc. As for
> Where have differential equations (a hell of a big subject!) been
Don't know a good reference off hand.
> > "experimental" research, it will always be just a preliminary work
> > until it can be axiomatized.
> ... in the sense of axiomatized? Indeed, what would it mean "to
> formalize" differential equations? That an equation and some axioms are
> put into a box, shaken well, and out pop the solutions?
If "shake well" includes repeatedly invoking specific rules of logic and axioms of set theory, then yes.
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com