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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