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
> formalized...
>


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.

Dan

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