From: SQUONKSTAIL@aol.com
Date: Thu Aug 14 2003 - 01:27:22 BST
Squonk:
Hello Platt,
P
> Please explain "intellectual aesthetic of the geometric method of
> inference." If you can, please include some down to earth, plain
> English examples. Are you talking about good old Aristotelian logic, or
> something else?
S
> Take for example any triangle and then reproduce it twice the size.
> Place the two next to each other. The two triangles are identical apart
> from their scale - there is a ratio between them - one is twice the size
> of the other. No matter how the ratio varies - 2, 3, 4 times, the
> properties of the triangle remain the same - and this could be taken to
> be an eternal truth: Regardless of scale, triangles have certain
> properties. There are inferences that can be made regarding such taken
> to be eternal triangles, and it is these inferences that replace Gods.
> Who needs Gods when the internal angels of any triangle, regardless of
> scale, add up to 360*? Bertrand Russell suggests that for the next 2,000
> years after Euclid, many philosophers used the geometric method of
> inference to prove the existence of God. The geometric method basically
> starts with known assumptions, and then deduces results. And the basic
> assumptions are taken to be eternal, regardless of subjects and objects -
> the assumptions are super sensible, and perhaps the cause of subjects
> and objects. So, one may argue: God is the biggest. If God is the
> biggest, then it can be argued, in geometric fashion, that all big
> things are smaller than God and thus a part of God. Such reasoning -
> such ratio-analysing - may be highly dubious?
Dubious indeed because God is geometry, reasoning, ratio-analysing
and anything else we can imagine, including our assumptions. What
interests me is your glorification of the Plato's ideal forms, a view
shared by some mathematicians including the famous Roger Penrose.
Platt, Please? I am not glorifying Plato's forms. Plato, is glorifying
Plato's forms!
He
writes, "I believe consciousness to be closely associated with the
sensing of necessary truths--and thereby achieving a direct contact
with Plato's world of mathematical concepts." Moreover, Penrose is very
much attuned to your aesthetic idea, writing, "A beautiful idea has a
much greater chance of being correct than an ugly one."
Squonk: This may be, but i am not glorifying forms. I merely indicate that
Plato and geometric method are linked.
S
> The MoQ says that ratio - the proportion between two triangles - emerges
> from Quality. Therefore, ratio's are Quality relationships. Thus,
> geometry is intellectual quality. Its an aesthetic.
Since the MOQ says that everything emerges from Quality and thus
everything is in a Quality relationship to everything else, then
everything is aesthetic according to your reasoning. I'd agree that
everything is moral, but not aesthetic since morality includes the ugly
as well as the beautiful.
squonk: Ugliness is not aesthetic, would you agree?
> So, the inferences
> following from this aesthetic are based upon an aesthetic of Quality.
> All the centuries of trying to prove God's existence using geometry is
> intellectual quality - not of God, but of intellectual patterns
> themselves.
You lost me. How did proof of God's existence suddenly get into the
discussion?
squonk: This is the method many philosophers have used to prove the existence
of God. It's silly. But they did try!
> Aristotle used geometric methodology to try and show that 'things' in
> our experience - things we can point to as examples of things - can be
> proved to be certain in the same way that the properties of triangles
> can be certain. The flaw is that assumptions have to be made, and the
> assumptions can be the problem.
True. Philosophy is basically the study of assumptions.
Don't misunderstand me. I'm with you on most of this stuff. Maybe
because I flunked 11th grade algebra I find mathematical arguments
obtuse. I'm more the English major type. :-)
All the best,
Platt
squonk: I am not a mathematician myself. I am more in tune with you. I merely
indicate that early philosophy valued geometry a great deal - and made it the
super sensible realm - not that of subjects and objects.
All the best,
squonk
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