The Logic Off Topic list

HJ wrote:

>Yes, this is an extremely interesting and subtle topic when studying
>anything that has to do with ancient Greece culture and value
>judgements.

And ... the fact that the original statement was in fact a value judgement 
and not the definitive statement of fact that it purported to be was 
exactly one of the points I was trying to make. I simply felt that since it 
was nothing more than a value judgement it should have been -- and was not 
-- labelled as such. And ... then granted that as a statement of fact it 
seemed to me to be clearly untrue when taken generally -- which was the 
overall tenor it seemed to have --  then at the very least it was in need 
of extreme qualification so that its limited parameters of relevance were 
somewhat clearer.

>Art could have "arete", and a warrior could.  Probably a
>mathematical proof could also have "arete".
I would tend to agree with you.

>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.
And I would again agree with you by saying that a statement gains in a very 
great deal of arete once it has been taken through the process of proof and 
so becomes a theorem. That's a view that I'm quite sure you share. I am not 
for a moment pretending to speak for what them guys back then actually did 
have in their heads. I am just agreeing with you that that's also how I 
feel about these things.

>  Lots of confusion can rise
>from an improper understanding of such pivotal concepts.
Ain't that the truth/


>Geesh, apparently my years at the philosophy department haven't all
>been wasted :-).
"Apparently". (!!!)


>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?

Yes it would.


> >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".
That is true. However, the original assertion was presented as -- and was 
also initially defended as -- a statement of fact. And in the area of 
things asserted as facts, faultiness is sometimes possible.

>And neither is there the need to re-evaluate your
>viewpoint or whatever.  Both interpretations are equally valid.
Yes. And as for the interpretation, I think we all three agree that 
Archimedes and those others, by any reasonable standard we have today given 
how WE understand those words, was most probably in touch with how we view 
things. These are still not matters of fact, though. Just a way to get a 
warm fuzzy feeling about Archimedes. Which I don't object to in the least. 
Go Archimedes.

>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.
And ... the interpretation of 'most' is exactly what I addressed.

When I tried to say that IF by 'most' he/you meant 'all those after Gauss 
then fine'; and that if he/you meant 'most of history' then not fine; I 
still met with strenuous objections -- including statements that I didn't 
properly understand what was going on and that I had misunderstood and so 
forth.

> >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.
Well ... I do try very hard not to use bluster and slipshod arguments, but 
that's what I've been accused of in the past. Not by you. When I say 
something, I try to base it on solid facts and my experience and knowledge. 
If I don't have the grounds and backings for such things, I try very hard 
not to pretend that I have it.


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

OK. You reach out for that credit card ... and help yourself to another whisky.

Kool Musick
Keep Musick Kool


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