From: Sam Norton (elizaphanian@kohath.wanadoo.co.uk)
Date: Sat Jul 30 2005 - 10:19:56 BST
Hi Scott,
> Sam said:
> My point is that the perception of the truth of, eg 2+2 = 4 is not
> independent of human character, eg honesty. I think we are too familiar
> with
> 2+2=4 and the like for the possibility of an alternative to be readily
> understandable. But consider Fermat's last theorem - there were a number
> of
> 'false starts' where people thought it had been solved, before Wiles
> actually did so (and even now people think that there must be a 'better'
> (ie
> simpler and more aesthetically pleasing) proof to be found). I think what
> seems to be 'independence' is simply a deeply embedded social level of
> agreement.
>
> Scott:
> 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>
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.
> 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.
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.
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.
> I also want to comment on your emphasis on honesty. As I see it, in this
> context, honesty is just the lack of dishonesty. By this I mean that
> intellect is hurt by dishonesty (hidden social and biological agendas,
> self-deceptions, unrecognized assumptions, and so on). Hence increasing
> honesty is a matter of decreasing dishonesty, which is done through
> intellect.
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.
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. 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.
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.
Cheers
Sam
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