From: Scott Roberts (jse885@earthlink.net)
Date: Wed Nov 17 2004 - 20:25:47 GMT
Mark SH,
[MSH:] > I think I would say that mathematics is rooted in empiricism and
> blossoms through reason, and thus cuddles snugly with my rational-
> empiricist interpretation of the MOQ. I've forgotten more set
> theory than I remember, but I'm pretty sure that our conception of
> numbers derives from our sense experience of collections. We see a
> box containing a turnip, a radish and a carrot, and another box with
> an orange, an orange, and an orange, and abstract the commonality as
> the number three. Similarly the other base 10 digits, including,
> maybe, an empty box for zero. We then start combining the elements
> of the various boxes in various ways, and suddenly we have an
> abstract "sense" of addition and subtraction, and are well on our way
> to deriving a base-10 mathematics.
[Scott:] I don't deny that mathematics prior to Pythagoras, and the way we
learn arithmetic is with the help of the senses. But proving that the
square root of two is not a ratio of two integers is a whole new ballgame.
You cannot sense the difference between a rational and irrational number.
(A side note: in the West arithmetic went on for over a thousand years
without the number zero, but that's not really germane.)
The key thing your analysis overlooks is that abstraction is, from an
empirical point of view, a totally mysterious process. Overlooking its
eldritch nature is what allows nominalism to flourish -- and this debate is
really over that age-old question. N.b., DMB claims that Pirsig is not a
nominalist, since he says that ideas are as real as rocks and trees. Hence,
I am using "nominalism" to mean the denial that rocks and trees embody, or
manifest, ideas. In contrast, my position is that ideas were around from
the beginning, and are not dependent on the existence of humanity. To me,
this is a consequence from the concept of SQ -- a static pattern of value.
As a pattern, it can be abstracted by us as an idea. As having value, it
must be treated as an idea in itself, that is, without needing a human
observer, and so we are not just making up an idea, as nominalism holds,
but reproducing in our minds the ideas that produced the rock or tree.
[MSH:] > If this doesn't convince you, then I think another way to arrive
at
> the fundamental empirical nature of mathematics is to try to imagine
> what sort of numeric reasoning a person who is sense-deprived from
> birth might develop. In fact, it's difficult to understand how ANY
> kind of sustained thought process might occur under such
> circumstances.
[Scott:] No doubt. But what our senses perceive is a consequence of at
least two levels of processing that are better described as unconscious
thinking than as mechanical. First there is the transformation of
who-knows-what (though physics has it currently as electrons and photons)
into colored blotches and movement in space (for vision), then the
coalescing into things like trees and rocks. Hence what we call reasoning
about these things is a partial rediscovery of this unconscious, highly
static rationality. (This really requires more extensive argumentation, or
at least quotes from Barfield's Saving the Appearances, but I'm not up to
that right now.)
[MSH:] So what on earth can we mean by the phrase non-
> empirical consciousness?
[Scott:] My position is that the rational/empirical distinction is another
SOM platypus.
> >dmb:
> > In any case, to take your counter-example for example, its clear
> > that you have not noticed what this expanded empiricism means. As
> > MSH has pointed out, mental experience counts as experience within
> > rational empiricism. Unlike the most narrow kind of empiricism,
> > where only sensory exprience counts, rational empiricism would most
> > definately say that mathematical is an entirely empirical reality.
>
> scott:
> That's not what Pirsig said. He said "The MOQ denies this. (That
> Reason perceives truths which are incapable of verification in
> sense-experience."
>
> msh says:
> Can you provide a page or chapter reference for this? We might need
> to see it in context.
[Scott:] It's from the Copleston Annotations on Ant's web site. Search for
Coleridge. Copleston just gives a quick overview of Coleridge's
metaphysics, and Pirsig's notes are based just on this overview. For a more
comprehensive understanding of Coleridge, I recommend Owen Barfield's What
Coleridge Thought.
>
>
> scott:
> Mathematical truths are not verified in sense-experience. They are
> verified through reason,
>
> msh says:
> But they are rooted in sense-experience; the verification is the
> rational blossom... see above.
[Scott:] But Pirsig said: "The MOQ denies this. (That Reason perceives
truths which are incapable of verification in sense-experience." So are you
disagreeing with Pirsig? No sense experience can tell you that no ratio of
integers is the square root of 2.
>
> scott:
> so if you now say that the rational verification process is itself
> experience,
>
> msh:
> The rational verification process is secondary to experience...
[Scott:] Here you are disagreeing with DMB (as do I but for different
reasons). Pirsig does wax lyrical about the role of value in mathematical
experience in ZAMM, in his discussion of Poincare. The trouble is that in
Lila, he keeps stressing how intellect hides, or detracts from "pure
experience", and doesn't say anything about how an intellectual experience
should be treated *as* a pure experience. My impression is that he just
didn't get around to addressing this problem, having other things (i.e.,
morality) as his main focus. So my position is that when one does get to
these problems, some stuff at the start, such as touting empiricism, needs
re-examination.
The problem with saying that the rational verification process is secondary
to experience, is that the verification process *is* the mathematical
experience. That's the point that George Spencer Brown makes, that DMB
quoted Wilber (who sort of misses the point, at least about mathematics.)
Recall the Coleridge quote: that mathematical "objects" are "acts of the
imagination that are one with the product of those acts"
>
> scott:
> in order to keep with the next sentence: "Reason grows out of
> experience and is never independent from it."
>
> msh says:
> I would say reason without experience is impossible...
>
> scott:
> ... then you are saying that, in the case of mathematics, reason
> grows out of reason.
>
> msh says:
> I don't follow your reasoning here, empirical or otherwise.
[Scott:] I'm just combining Pirsig's definition of the relation of reason
to experience with DMB's claim that mathematics is just another empirical
process.
[MSH:] I would
> say what I said in the beginning: math is rooted in experience and
> flowers through reason. No roots, no reason.
[Scott:] While I'm saying that the roots are reason as well.
>
> scott:
> What is clear from this is that the way you want to extend
> "empirical" to include reason makes the word "empirical" lose any
> distinctive value it might have.
>
> msh says:
> I'm not sure what DMB would say here, but I'm not extending
> "empirical" to include reason. I'm saying that any sentient deprived
> of sensual input from birth will, upon emerging from his SD
> environment, be INCAPABLE of reasoning for a mensurable amount of
> time.
[Scott:] Then, I would say, you haven't escaped SOM. As for DMB's position,
that adds up to denying any distinctive value to "empirical".
I agree that no human could be rational without sense experience. My
position, though, is that physical phenomena serves Reason in general in
the same way that a mathematician uses pencil and paper to keep his or her
thoughts straight. That is, as Intellect (or Reason, I'm using the words
interchangeably) is fundamental, it expresses itself as what we call
reality, which serves as feedback for further creativity and further
expression. It shouldn't be too hard to see this as an alternative
formulation of Quality/DQ/SQ, though of course it is anathema to the
modernist, nominalist, viewpoint.
- Scott
MOQ.ORG - http://www.moq.org
Mail Archives:
Aug '98 - Oct '02 - http://alt.venus.co.uk/hypermail/moq_discuss/
Nov '02 Onward - http://www.venus.co.uk/hypermail/moq_discuss/summary.html
MD Queries - horse@darkstar.uk.net
To unsubscribe from moq_discuss follow the instructions at:
http://www.moq.org/md/subscribe.html
This archive was generated by hypermail 2.1.5 : Wed Nov 17 2004 - 20:28:26 GMT