FOM: Re: Berkeley and nonstandard analysis

Martin Davis martin at
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 Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at
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