The Logic Off Topic list

Hendrik Jan wrote:

>[interesting stuff deleted for brevity]
>Didn't know this.  Interesting.  Thanks.
You're welcome. Glad you found it interesting. Not many people around here 
to talk that kind of stuff over with, so it's a pleasure.


>Uhm... are you implying that the fact that they didn't write about it
>must mean they thought about it differently than we do?
No must. Just a probably ... and enough of a doubt, when combined with the 
little we DO know to make the proposition basically one that should be 
doubted rather than (glibly) accepted.

>Because with
>that I wouldn't agree.  IMO there's no way we can figure out why they
>did or did not write about something.  But maybe I misunderstand what
>you're saying here.
I don't think you're exactly misunderstanding. I am saying that we can't 
KNOW, but we can conjecture from the fact that the famous Greek 
mathematicians we know about also did things like architecture, and in the 
record of the arts that we have regarding what they thought were sound 
principles for that, there is no record of the kind of abstractionist 
beautifying under debate. 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. Therefore, better to accord to 
them principles and thoughts we can be reasonably certain they did have -- 
from the evidence -- than attribute to them principles of our own and that 
we can't really be sure of.

I must repeat, though, that in my view GA Moore's argument about the 
Archimedes tomb is emotionally convincing and satisfying to me -- and 
therefore IMO likely to be correct -- about Archimedes at the very least, 
and therefore that it was also probably applicable to others of his ilk 
like Apollonius. I must still reluctantly say, though, that there's no 
EVIDENCE that would concord with the more general statement of this kind 
that is being made.

>Which is why I suggested to leave them out of the discussion.
I agree ... but in that case it calls into question the whole issue of what 
is meant by 'most mathematicians'. We are leaving out rather a lot of 
mathematicians over 'most' of the historical epochs in which mathematics 
has been done. Rather devalues the assertion IMO but that's probably just me.

[Regarding 'sorry']
>Ah, ok, that _is_ a misunderstanding then.  Probably to do with the
>"emotional charge" of some words.
Most likely.

>But I've come to understand that when a white man says
>"brother" to an Afro-American in the Bronx, he can get his butt
>kicked,
Could happen indeed.

>Apparently in certain contexts this simple word has far reaching
>connotations that I, as non-native, am not always aware of.
Yup.

>Oh man... maybe Af-Am is insulting too...  help...
I'm not sure about that. I'll have to check the latest reprint of the 
Politically Correct Dictionary.

> >Then there was all that mumbo jumbo he had about cosmic solids. He
> >really thought it beautiful. As a 'work of art'. maybe. But as a
> >mathematical demonstration? Yet ... there were people who thought, at the
> >time, that it was a demonstration of mathematics at its best.
>:-).  But then: what could be more beautiful than an abstract science
>being able to explain the entire cosmos with a basically simple
>model?  Isn't that every scientist's wet dream?
I would really like to believe that that is what Kepler intended. However, 
in Kepler's case it is really very doubtful. I honestly don't think, and 
nor do most of the people who write about him, think that this was Kepler's 
intent. He was filled through and through with Pythagorean mysticism and 
what pleased him was not the elegance of the pattern, or anything to do 
with it, but the simple fact that God had revealed the true meaning of 
number. God had done so in several other ways also, including by giving him 
visions. To Kepler, those other visions were all of a piece with his 
mystical cosmic solid system, and there doesn't seem to be any sign that 
the truly mathematical side of it evoked any more appreciation in him than 
the witchcraft that gave him the same kind of knowledge.His Mysterium 
Cosmographicum was certainly brilliant but in the same kind of way that a 
good theological book can be brilliant. It is also true that his 
presentation fused mathematics, imagination and aesthetics together, but 
this was done in a very Aristotelian rather than mathematical manner. 
That's to say, it was not mathematically logical, but simply 
philosophically or theologically logical.

>Sure I understand what you mean.  The essence of my reply was just
>that I thought you made things more complicated than they were ever
>intended.
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.

>:-)  So that's what you do when feeling stuck?  Keep saying sorry?
>Ahw, sorry, I shouldn't laugh about that, but I can't help it raises
>a kind of funny picture in my mind.
That's OK.

>Like someone bumping into a brick wall and then apologizing to the wall or so.
That's what I used to do, I guess, when I was given complex differential 
calculus stuff to do and I just couldn't get it right.

>OK, but then, to paraphrase what you said above: I'm not in the
>humiliate-others business.
Nicely put. And I never thought you were, or tried to imply that you were.

 >>Why you?
> >Because you are a very intelligent person,
>So are you...
Thanks.

> >and I agree with most of the things you say.
>You ought to. :-)
I keep trying to!!!!

> >Therefore, if you are saying something and I am not getting
> >it then chances are that it is my own position, and not yours, that need
> >re-evaluating.
>Mwah... I wouldn't disregard my own position so easily if I were you.
Re-valuating is not the same thing as disregarding.

> >And ... what's wrong with adjusting my understanding of affairs after
> >interacting with two people? No word has an absolute meaning.
>Exactly: this holds for interpretations or meanings given by me or GA
>or whoever else as well.
True. 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. At the very least, surely, next time either the one of 
you makes a similar remark and someone else disagrees, you might have some 
idea why. That's all I can hope. But ... I can only HOPE in your cases. For 
myself, I can make sure that it is definitely the case that I consider 
other issues than the ones first come to my mind.


>Yes, it _can_ mean something different.  But what you previously said
>(or what I thought you said) was that you'll accept that from now it
>it _does_ mean something different.  Simply because I and/or GA says
>so.  And that, of course, makes no sense.
I agree it makes no sense. I meant 'can' and not 'does'.

> >>As far as I'm concerned, I have a problem with people adjusting
> >>themselves to me "in modesty".
> >I think my life will be easier if I leave this as your problem and do not
> >take it on myself.
>Very wise :-).  Every man's got to deal with his own shortcomings in
>the end, hasn't he?
Yes.

> >>Remember, this stuff
> >>is quite subtle and requires accurate phrasing,
> >I tried that.
>
>I was referring to my own troubles with accurate phrasing, enlarged
>by the fact that I;m no native English speaker.
I accept that ... but ... I was also remembering that GAM was reading ... 
and he has a very sharp eye for spotting the hole in an argument. I think 
he reads too much theology, to be honest (just a joke!!!!). So ... I was 
trying to anticipate and plug those holes so that I wouldn't have to do so 
later. 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? 
I.e. my position was faulty, then it could not really be salvaged by any 
number of facts. However, since I did not feel my position to be faulty but 
rather a subtle one that might not have been considered due to a certain 
lack of information regarding the historiography of mathematical reasoning, 
I tried to defend my position by presenting those facts but in a close knit 
way that left no holes in it for people as well versed in dialectical 
argumentation as you and GAM. 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!! I was just trying to cover my bases and make my position look not 
only reasonable, but well-thought out and justified. The only way to do 
that was present evidence in the form of information that you might not 
have known and that you might not therefore have considered.

That's all, really. What GAM at first said had a great deal of plausible 
face value, and in order to explain why I did not accept it a great deal of 
underground stuff seemed to me to be required.

>:-)  Again: maybe it's just my non-nativeness that gives me trouble
>reading such long posts.  To me, it feels as if the real meaning gets
>somewhat lost in the large amount of words.  But again, that's
>probably me.
Not entirely you, I think. Like I said, you two are not easy people to 
debate anything with and I was doing my best to present a thorough and 
convincing argument. Since you fiercely believed what you were saying, you 
were making it very hard work for me to present the alternative case. Very 
hard work indeed. I am still not entirely certain I have succeeded, but I 
don't think it matters any more because I think we've all learned a great 
deal we didn't know before to carry forwards with us ... which I think is 
good thing.

>Leaving out "most" would yield a statement like "mathematicians
>appreciate the beauty of abstractions", which is far _more_
>generalising than inserting "most" before "mathematicians".
Yes. But another statement would be 'I think' or 'in my opinion, most 
mathematicians in history have appreciated the beauty of abstractions'. 
Those conditionals turn it into a very different kind of statement. There 
were no conditionals of any kind in the original assertion, and a 
conviction seemed to be apparent there that something truthful and 
revealing had been said about all mathematicians in history. That simply 
was not so IMO and that's all I have tried to point out.

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

> >  >As for respect: I've come to respect you at least as much as you've
> >>come to respect me.
> >That's nice. You must have been on the same neurolinguistic programming
> >course!! (Sorry Tony if you're reading ... just a little joke there!!!)
>
>No, this has nothing to do with 60ies cuddly fuzzy feelie stuff.  I
>was just being honest and straightforward.
Oh dear. I _knew_ you were being serious. I, on the other hand, was trying 
to make a joke.

>... that way the others in this group would see, time and time
>again, what a wonderful sort of person I really am.  And what's good
>for my reputation is good for me, isn't it?  :-))
That's indeed so. I'll give some thought to the matter. (Another joke!!!)

>But seriously, if anything, I think that an attitude of a kind of
>friendship (or whatever you want to call our "relationship") would be
>more appropriate.  I think you're on OK-guy, and so when you have a
>problem I try to help you out.  I suppose you'd do the same for me.
>Gratitude does have its place there but, imo, shouldn't be the
>dominant feeling.  More like "[HJ|Kool] is an OK-kind-of-guy".
Gratitude is not the dominant feeling. But it is there. I weigh it in my 
way. You weigh it in yours.

>Oh well, what are we talking about...?  this does start sounding like
>fuzzy feelie etc.
It's all that neurolinguistic programming you've been doing.

> >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!!).

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com