[FOM] Infinitesimals

[Antonino Drago]

A my previous post remarked that infinitesimals cannot change calculations 
on experimental facts.
The question arises when we deal with theoretical principles and 
definitions. For instance the third principle of thermodynamics (the value S 
= 0 is unattainable by physical tools) cannot be expressed by means of 
infinitesimals.
In the history of science, in 17th Century classical chemistry born 
according to the heuristic principle that the matter cannot be divisible in 
an infinitesimal way (see: H. Guerlac: "Quantification in Chemistry",  ISIS, 
52 (1961) 194-214) and Leibniz avoided infinitesimals in the foundations of 
his theoretical physics (a "reform" of dynamics) since "the facts have to 
explained by facts" , without introducing idealizations (letter to H. Fabri 
1677).
Best regards
Antonino Drago

----- Original Message ----- 
From: "Sam Sanders" <sasander at cage.ugent.be>
To: "Foundations of Mathematics" <fom at cs.nyu.edu>
Sent: Thursday, July 12, 2012 10:32 AM
Subject: [FOM] Infinitesimals


> Dear members of the FOM list,
>
> I would like your opinion on the following statements (Please declare them 
> true/false, with a possible explanation why).
>
> 1) infinitesimals are used throughout physics and engineering (in some 
> informal way, formalizable in Nonstandard Analysis).
>
> 2) when infinitesimals are used in physics and engineering, the choice of 
> infinitesimal does not matter
> (i.e. a calculation involving an infinitesimal \e remains valid if \e is 
> replaced with any other infinitesimal \e' .)
>
> 3) The aforementioned independence (of the choice of infinitesimal) in 
> physics and engineering has been observed before by X (Please fill in X).
>
> With kindest regards,
>
> Sam
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