[FOM] reply to S.S. Kutateladze (19 Mar)

[joeshipman@aol.com]

One clarification -- I did not mean to imply that Leibniz thought 
infinitesimals SHOULD be eliminated or that they were ONLY a manner of 
speaking, just that he knew how to eliminate them and knew that 
infinitesimals COULD be regarded as a manner of speaking.

-- JS

-----Original Message-----
From: joeshipman at aol.com
To: sskut at math.nsc.ru; fom at cs.nyu.edu
Sent: Fri, 23 Mar 2007 11:12 AM
Subject: Re: [FOM] reply to S.S. Kutateladze (19 Mar)

   Calculus CAN indeed be purified from the concept of an infinitesimal; 
not merely formally, but conceptually too. (We know that Archimedes did 
not need infinitesimals in his proofs though using the concept helped 
him find his results; we know that Leibniz understood how to eliminate 
infinitesimals though he found them useful as a manner of speaking; and 
mathematicians since Cauchy have used Calculus without needing 
infinitesimals even conceptually).
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