Prev: Model != World?
Next: If Gauss Put His FFT On His Web Page It Wouldn't Have Had To Be Rediscovered In WWII
From: Robert on 6 Jan 2010 05:42
everyone knows archimedes invented calculus. almost.
From: chazwin on 6 Jan 2010 08:03
On Jan 5, 3:36 am, John Stafford <n...(a)droffats.ten> wrote:
> It matters not. The Calculus was not philosophically rationalized until
> quite recently. Regardless, it was perfectly useful until then, and
> remains useful today.
>
> For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
> out.
>
> Back to the subnect, it was found that Leibniz's approach was more
> useful, fewer hacks, more direct. Leibniz wins.

From: chazwin on 6 Jan 2010 08:05
On Jan 5, 3:36 am, John Stafford <n...(a)droffats.ten> wrote:
> It matters not. The Calculus was not philosophically rationalized until
> quite recently. Regardless, it was perfectly useful until then, and
> remains useful today.
>
> For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
> out.
>
> Back to the subnect, it was found that Leibniz's approach was more
> useful, fewer hacks, more direct. Leibniz wins.

Leibniz was a better publicist, whilst Newton was a loner and recluse.
That is why we tend to use his notation.
There is evidence that Leibniz stole the idea on a trip to England,
and Newton accused him of that.
But as it was useless in the 17th Century it hardly matters.
From: J. Clarke on 6 Jan 2010 08:21
John Stafford wrote:
> In article
> <80022c43-5c39-46ea-ab95-6ed4e668e906(a)q4g2000yqm.googlegroups.com>,
> M Purcell <sacscale1(a)aol.com> wrote:
>
>> On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote:
>>> It matters not. The Calculus was not philosophically rationalized
>>> until quite recently. Regardless, it was perfectly useful until
>>> then, and remains useful today.
>>
>> How was calculus recently philosophically rationalized?
>
> By recent, I mean after most philosophers were over dithering on the
> meaning of infinitesimals. The philosophers could not 'rationalize'
> the process, it seemed unnatural (another problem for the
> philosophers), but somehow calculus all worked very well regardless
> of objections. The first rationalization was when the Calculus turned
> to limits instead. I think it was the late 1800's. More recently, the
> 1960s's, Abraham Robinson returned to the interpretation of
> infinitesimal numbers apart from the philosophical, to mathematical
> theory - a stunning bit of reasoning, IMHO.
>
> I'm at a bit of a loss for precise description of the history - I no
> longer work at the university library (real bummer, but better pay
> here.)

If anyone is interested, Prof. H. Jerome Keisler at the University of
Wisconsin wrote an introductory calculus text based on this formulation.
It's out of print now but he has generously made it available under a
creative commons license and you can download it from his web site at
<http://www.math.wisc.edu/~keisler/>. The epilogue has some of the history.

<remainder trimmed>

From: John Stafford on 6 Jan 2010 08:52
In article <hi239002f5f(a)news2.newsguy.com>,
"J. Clarke" <jclarke.usenet(a)cox.net> wrote:

> John Stafford wrote:
> > In article
> > <80022c43-5c39-46ea-ab95-6ed4e668e906(a)q4g2000yqm.googlegroups.com>,
> > M Purcell <sacscale1(a)aol.com> wrote:
> >
> >> On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote:
> >>> It matters not. The Calculus was not philosophically rationalized
> >>> until quite recently. Regardless, it was perfectly useful until
> >>> then, and remains useful today.
> >>
> >> How was calculus recently philosophically rationalized?
> >
> > By recent, I mean after most philosophers were over dithering on the
> > meaning of infinitesimals. The philosophers could not 'rationalize'
> > the process, it seemed unnatural (another problem for the
> > philosophers), but somehow calculus all worked very well regardless
> > of objections. The first rationalization was when the Calculus turned
> > to limits instead. I think it was the late 1800's. More recently, the
> > 1960s's, Abraham Robinson returned to the interpretation of
> > infinitesimal numbers apart from the philosophical, to mathematical
> > theory - a stunning bit of reasoning, IMHO.
> >
> > I'm at a bit of a loss for precise description of the history - I no
> > longer work at the university library (real bummer, but better pay
> > here.)
>
> If anyone is interested, Prof. H. Jerome Keisler at the University of
> Wisconsin wrote an introductory calculus text based on this formulation.
> It's out of print now but he has generously made it available under a
> creative commons license and you can download it from his web site at
> <http://www.math.wisc.edu/~keisler/>. The epilogue has some of the history.
>
> <remainder trimmed>

That's it! I had forgotten Keisler's contribution. Wow. Thanks very much!
First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4 5 6 7 8 9
Prev: Model != World?
Next: If Gauss Put His FFT On His Web Page It Wouldn't Have Had To Be Rediscovered In WWII