From: Scott Roberts (jse885@cox.net)
Date: Mon Aug 01 2005 - 03:45:15 BST
Sam,
> Scott said:
> Still not convinced. Because they are fallible, mathematicians need peer
> review, that I don't deny. Further, there can be fashions in mathematics,
> in
> the sense of people working in one area rather than another, but that does
> not invalidate the unfashionable areas.
>
> In the case of 2+2=4, there is no alternative, if one accepts the Peano
> axioms of arithmetic. Compare it to moving a knight in chess.
<snip>
Sam said:
I agree with you on that, but I think what this points out is that, at this
stage, mathematics is a social practice, what Wittgenstein called a form of
life. Which is a thought that hadn't struck me before, but fits very closely
with how Wittgenstein viewed the foundations of mathematics - and to call
his views on that controversial would be an understatement. I'll have a
refresher on his remarks and see if I can integrate them.
Scott:
Well, of course mathematics is a social practice, in that
mathematicians meet in conferences, check each others' work, teach in
classrooms, and so on. But it is also the case that, assuming one has been
trained up to some level of competence, it is possible to do creative
mathematics after having been locked up in solitary confinement. One can of
course do other intellectual things as well, but I think there is a scale
over which various disciplines can be ranked according to how much
creativity can be done alone, and mathematics ranks at the top.
I'll take a look at Wittgenstein as well.
Scott said: > So there is a lot of mathematics of the form "if the Axiom of
> Choice, then ...". Since showing an error in the proof of FLT does not
> imply
> that the FLT is false (just unproven), all that stuff built on the FLT in
> the next fifty years just becomes "if FLT, then ...", and could still be
> interesting mathematics.
Sam said:
Absolutely. But I don't think that addresses my point. In the exploration of
interesting mathematics, ie which areas have high Quality, I think the
perception of the high quality is a function of the nature of the observer.
Scott:
I think I disagree, in spite of my mentioning fashions in my previous post.
Wouldn't it make more sense to say that the perception of high quality is
dependent on both the observer and the observed? Which in the case of
mathematics is complicated in that it isn't perception but thinking in which
there is no distinction between thinker and thought at the moment high
quality is experienced. (This is true outside of mathematics as well, though
in other areas it is possible to identify an observed other than the
observer after the fact.)
Sam continued:
Think of when Pirsig talks about receiving ideas, eg the little thought
which says 'what about me' - I can't remember the exact reference. Seems to
me that some of those little ideas are shunted out of consideration before
they clash with other presuppositions, and the clearing of presuppositions
is a necessary preliminary to gaining insight.
Scott:
Yes, but the point of Pirsig's remark was that the little thought was right:
it was the thought that is needed to fix the motorcycle. One does need to
have prepared oneself to be in the state in which its rightness will be
immediately appreciated at the moment of noticing it, but then it is seen
that the thought was always right. So what I am emphasizing is that, once
discovered, mathematics is eternal. To be able to discover is a matter of
culture and training, but the discovered is true in all cultures.
Sam said:
I've been thinking about what I mean by 'honesty', and I think the key for
me is one of the ones you refer to, viz 'self-deception', although I agree
with the others as well. So I think we're talking about the same thing.
Scott:
Yes, and self-deception is the biggie. Which is why I emphasize the logic of
contradictory identity: though it doesn't "get" one anywhere, it prevents
one from falling into one self-deceptive trap or other.
Sam continued:
But you say that increasing honesty/decreasing dishonesty is done through
intellect. If you spelt out -how- intellect does this, I'd probably be in a
complete agreement.
Scott:
Ceaseless self-observation and self-deconstruction, I suppose (N.b,
deconstruction is not destruction). Meditation, which, as Marsha just noted,
I see as purifying the intellect through fostering detachment.
Sam continued:
But I don't see the common understanding of intellect
(in this forum) being capable of it. In other words, if 'intellect' was
broadened out from what, for want of a better description, might be called
'SOM-intellect', ie "neutral" intellect, then I have no problem whatsoever
with using 'intellect' in that sense. But I think lots of people here would
disagree, because - from my point of view - they have an awful lot of ego
invested in the fruits of SOM intellect.
Scott:
I think that here is where we may be in disagreement, though how much that
is in form versus content I'm not sure. I agree that the MOQ view of
intellect is a bad one, but I see the cure as being more dispassionate, not
less. I agree with the MOQ that intellect needs to free itself from social
and biological influences, while I believe you hold it needs to be
integrated with them in some way. Correct me if I've misunderstood.
Sam continued:
But it strikes me that in so far as the MoQ incorporates insights from the
Buddhist tradition, how can it NOT involve this sort of understanding of
intellect? In other words, the 'detachment from desire' which I thought was
central to Buddhist spirituality seems to me to be exactly what I'm talking
about. You won't get enlightened until you have unearthed all your
attachments. But I'm happy to be corrected by you if that is a
misunderstanding of Buddhist teaching.
Scott:
You've got the Buddhism right. The problem is that Pirsig has it wrong, in
that he sees intellect as something to be transcended, rather than intellect
as that which transcends. I should admit, though, that many Buddhists will
agree with Pirsig, but I would argue that this is on account of
misunderstanding intellect, just as Pirsig has. The problem is that most of
the time in our current sorry state (that is, Original Sin, or as the
Buddhists call it, ignorance), intellect doesn't transcend squat, but is
largely used to justify our prejudices.
- Scott
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