FOM: Re: Berkeley and nonstandard analysis
Martin Davis
martin at eipye.com
Fri Jan 28 12:28:24 EST 2000
At 08:57 AM 1/28/00 -0800, Charles Silver wrote:
> Let me try this out: Is it correct to say that Leibniz's infinitesimals
>should *not* have been rejected on the basis of Berkeley's complaint that
>they were "the ghosts of departed entities,"
Berkeley never asserted that what the mathematicians were doing was wrong.
Just that they had no business attacking theologians for their logic while
using methods just as dubious. His famous diatribe was addressed to "An
Infidel Matheamtician". So he was not "rejecting" infinitesimals, just
pointing out that there was no proper FOUNDATION for their use. He was
right. As you say, Robinson did provide such a foundation.
Incidentally, it was something like second order fluxions (not
infinitesimals as such) that Berkeley derided as "ghosts ...".
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
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http://www.eipye.com
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