The Logic Off Topic list

Thoughts from the mind of Kool Musick, 11-11-2001:
>It's a hotly debated topic for example whether
>thinkers of that era distinguished between 'good' and 'beautiful' and
>'well-made' (i.e. does the job it's intended to do well) in the easy kind
>of way we do. Thus it could be that to them a 'beautiful proof' was 'good'
>in the sense that it was moral; or that it was 'beautiful' in the sense of
>concise ... the possibilities are endless.

Yes, this is an extremely interesting and subtle topic when studying 
anything that has to do with ancient Greece culture and value 
judgements.  One of the dominant words in Greek thinking was "arete", 
which nowadays often gets translated as "virtue" -- i.e. with a kind 
of ethical connotation.  However, it covered much more than virtue 
alone.  Art could have "arete", and a warrior could.  Probably a 
mathematical proof could also have "arete".  A more proper 
translation would probably be something like "excellence", in a 
rather broad sense.  The tale of Ulysses is one about a man "gaining 
arete" -- i.e. proving his excellence.  Some one with arete was a 
good fighter but at the same time a good scholar, a thinker, 
craftsman, father and husband.  It was someone who excelled at as 
many things as possible.
So yes, indeed, terms like good, beautiful, moral, just, high-quality 
nowadays all have different meanings or nuances, whereas in the old 
days, it all was part of "excellence".  Lots of confusion can rise 
from an improper understanding of such pivotal concepts.

Geesh, apparently my years at the philosophy department haven't all 
been wasted :-).

>I only tried to explain the basis for my disagreement. I guess that would
>inevitably complicate things, because on the face of it GAM's original
>assertion does on the face of it seem very simple. Since I wasn't prepared
>to take it at face value, I guess inevitably I was making it complicated.

It's a pity this whole discussion apparently couldn't have been as 
simple as this:
---
GA: most mathematicians appreciate pure abstract beauty.

Kool: if that's supposed to hold for all mathematicians past and 
present, I don't think that's true.  There are arguments suggesting 
that the beauty of abstraction was only appreciated relatively 
recently, and that in "the old times" much (or all?) of the beauty of 
mathematics was found in its applicability to (sometimes) urgent and 
practical problems.

GA: Oh yes, sure.  I just meant to talk about living mathematicians. 
or at least about recent (few centuries) mathematics.

HJ: Agreed too (if I had said anything at all in such a clear and 
simple exchange of thoughts)
---
That would have spared all of us an awful lot of typing, wouldn't it?

>But ... I simply can't do anything about whether or not you are
>prepared to re-evalute YOUR understandings and meanings of 'most
>mathematicians' etc. I can only work on whether or not I am prepared to
>re-evaluate mine.

See directly above.

>Of course, if the whole position is faulty then no amount of detail
>can cover it up, which might be basically what you were criticizing me for?

No.  When talking about different _interpretations_ there's no such 
thing as "faulty".  And neither is there the need to re-evaluate your 
viewpoint or whatever.  Both interpretations are equally valid.  When 
talking about "all mathematicians past and present" you made a valid 
point.  When talking about "all living or 'recently' living 
mathematicians", GA had a valid point.  The difference is only in the 
interpretation of the word "most", and no value judgement can be 
attached to such interpretations.

>The two of you just don't make it easy for those of us who tend to 
>get by with bluster and slipshod arguments, you know!!

You, of all people, are certainly _not_ in the category of "those of 
us... slipshod arguments", so I don't see how the above applies to 
you.

>  >And yes, I know this is a lousy rethoric remark.  It's not to be
>>taken seriously.
>Should have read this first, I guess.

Yeah. That's one of the things I try to teach my students: first read 
the question very carefully before attempting to give any answers :-).

>  > >Here's to many years of successfully sorting little 
>communication problems.
>>
>>I'll have a whiskey to that.  Cheers.
>Make it a good expensive whiskey. (On your own credit card, though!!).

Lagavullin.  16 years old, wonderful single malt Scottish whiskey. 
Anything cheaper than that I find undrinkable.  I'm a snob, 
sometimes...


cheers,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html