[FOM] The Lure of the Infinite

[Matthew E. Moore]

Greetings,

Having been apprised of Gabriel Stolzenberg's comment about Berkeley and
his intentions in The Analyst, I would like to contribute my two cents.  Actually,
they're not my two cents, but are shamelessly lifted from Douglas Jesseph's
excellent book Berkeley's Philosophy of Mathematics.  My immediate reaction to
Stolzenberg's remark was that Berkeley did not take so irenic a view of infinitesimals,
though he was keen to conserve the new physical results that had been obtained with
their aid.  The following passage from Jesseph (p. 183) puts it nicely:

"Beyond [its] theological and philosophical concerns, the Analyst advances a number 
of important mathematical claims: First, that, contrary to the pronouncements of Newton 
and some of his followers, the Newtonian calculus of fluxions does indeed require the 
postulation of infinitesimal quantities.  Second, that the proofs of even the most basic 
results in the calculus are fallacious and sophistical.  Third, that the success of the 
calculus can be explained by a 'compensation of errors' which arises whenever 
infinitesimal differences or evanescent increments are used in a calculation but dismissed 
from the result."

Hope this is useful.

Matthew Moore