At 12:58 PM 21/12/1998 -0700, David Fowler wrote:
| ...
| I don't think that most historians now believe in a 'foundations crisis';
| I myself think that it may have been 19th century mathematicians blessing
| their own problems with number, irrationalities, the real line, the
| programme of the arithmetisation of lots of mathmatics, etc, back on the
| Greeks. (Most of our inventions are made from our own viewpoint, our own
| ways of thinking.) The first modern discussion of the issue was perhaps
|
| H Freudenthal, Y avait'il une crise des fondemennts des mathe/matiques dans
| l'antiquite/, Bulletin de la Societe/ Mathe/matiques de Belgique [and the
| journal also has more complicated name], 18 (1966) 43-55,
|
| and there are other subsequent ones: Burkert, Knorr, ...
|
| My own particular invention of why I don't think that the discovery was a
| crucial event is described in
|
| The story of the discovery of incommensurability, revisited, pp.221-235 in
| K. Gavroglu, J. Christianidis, & E. Nicoliaidis (eds.) Trends in the
| Historiography of Science, Boston Studies in the Philosophy of Science no.
| 151, Kluwer, 1994,
It might be useful to point out that this article is available on the Net:
*.ps format:
ftp://ftp.maths.warwick.ac.uk/pub/papers/dhf/incommensurability.ps
*.pdf format:
ftp://ftp.maths.warwick.ac.uk/pub/papers/dhf/incommensurability.pdf
| and this article has been recycled and adapted as the first section of the
| new Appendix of the 2nd ed of my book (for details, see my posting of
| December 10th), which I there recommend to readers as a new Introduction.
| The original text of the book itself doesn't raise the issue before the
| final section of the discussion of things Greek, where I present the
| evidence concerning the story and assert that it is so insubstantial that
| I haven't discussed it earlier, and haven't embroidered an interpretation
| out of it, since it would distract from my own particular invention which,
| this time, I am trying to broadcast.
|
|
| As you may see,the subtext of my message is that the 'history' of Greek
| mathematics is an arcane intellectual game played according to some
| collection of largely unspoken and continually changing rules. One of my
| main objectives is to introduce a new set of rules and try to persuade
| people to play the game my way. But beware: I've had a few year's practice
| at it, which is why I can volley back many of these queries and objections!
| All of them? - I just don't know, and I might have to refine some of my
| remarks here; they come off the top of my head.
|
|
| I also raise my glass this yuletide, in salutation of Julio, creator of
| this list, and to its members.
|
| David Fowler
Oh... Many thanks, David! Right now I'm raising my glass in salutation of
all members of this virtual (and very real) forum!
Cheers! ...
Julio Gonzalez Cabillon
--------------------------
Caminante, no hay camino,
se hace camino al andar.