[FOM] Hadamard's principle

Jeffery Zucker zucker at cas.mcmaster.ca
Wed Feb 9 21:05:03 EST 2005

In a paper I am now writing on analogue computation, I want
to make some remarks on the significance of continuity in
this connection, and I would like to refer, at least briefly,
to what is known as "Hadamard's principle".

Unfortunately I do not know of a succinct formulation of
this from a primary source, i.e. any of Hadamard's writings.

The only source I have is an article by Kreisel
["A notion of mechanistic theory", Synthese 29 (1974), 11-26]
in which he writes 

| [A] famous principle, due to Hadamard, which restricts the
| class of meaningful theories ... requires that theoretical
| relations corresponding to _functions_, mapping data to
| (other) observables, must be _continuous_ in the data.

[Emphasis in the original.  From the context in the article,
the word "theories" in the quotation seems to refer
specifically to physical theories.]

I have two questions:

(1) Is this a fair (albeit brief) summary of Hadamard's position?

(2) More generally: can anyone recommend a good general discussion 
    (in English) of issues related to this topic?

With thanks in advance,

Jeff Zucker

Dept of Computing & Software, McMaster Univ., Hamilton, Ont. L8S 4K1, Canada
zucker at mcmaster.ca        ||    http://www.cas.mcmaster.ca/~zucker
(905) 525-9140 x 23438    ||    fax  (905) 524-0340

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