On 2/3/2017 5:36 AM, Bruno Marchal wrote:
On 02 Feb 2017, at 20:38, Brent Meeker wrote:
On 2/2/2017 9:43 AM, Bruno Marchal wrote:
I do think the greek get the "correct" mystical insight, which is
that Truth is bigger than Reason.
It's also bigger than logic
Of course. Reason by itself is already bigger than logic. All theories
are bigger than (first order) logic.
- something which every scientist and engineer knows.
Engineers? I guess so. But scientists? Perhaps, but not so much the
Aristotelian believer, who are not aware that even just elementary
arithmetic is not unifiable in a complete theory. Many scientists are
just unaware of the impact of Gödel's discovery, and have sometimes a
reductionist conception of machine, numbers, and finite things in
general. It took Gödel's ingenuity to kill the the Leibniz-Hilbert
Dream of making the base of mathematics consistent and simple. For
many, when they understand this, they realize for the first time that
there is a mathematical reality beyond the theories which try to study
that reality.
It is only mathematicians and logicians who think all knowledge can
be reached by reasoning.
OK.
But you need to make such mistake to understand that they are
*scientific* mistake. Today, many scientists continue to do that
mistake with respect to arithmetic. That the arithmetical reality is
not even axiomatizable
You write that as though it was an important revelation - but no
Milesian philosopher (a term I will invent to describe those of
scientific mind, neither Platonic nor Aristotelian) would have even
entertained such an outlandish idea that reality might be
axiomatizable. However, arithmetic is axiomatizable and in fact that's
how it's defined - by a set of axioms such as Peano's.
(no complete theory) is quite very often badly understood. When
working in the interdisciplinary domain, it is better to assume that
nothing is obvious, and put all cards on the table. What is obvious
for some can be quite unbelievable for another. Sometimes obvious
thing are shown just wrong.
Which Leucippus and Democritus realized, e.g. the Earth is not flat.
Brent
Metaphysics is a restaurant where they give you a 30,000 page menu and
no food.
--- Robert Pirsig
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