On 03 Feb 2017, at 23:52, Brent Meeker wrote:
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.
Just to make things clear, I will use Arithmetic for Arithmetical
Truth, by which I mean the set of all true arithmetical propositions.
To be even more specific, I will identify the arithmeticl truth with
the set of Gödel numbers of the true arithmetical propositions. That
set is not axiomatisable. It is not recursively enumerable.
By arithmetic with a little "a", I mean either the set of G¨del number
of theorems of Robinson Arithmetic, or Peano Arithmetic. Those sets
are axiomatizable by construction, and that is what is denoited by the
"[]", in the case of Peano Arithmetic, or any "rational believer" (in
the mechanist theory).
I am not sure what you try to say. Could you elaborate on the
Milesian's conception of reality. As I (re)defined the Platonist and
Aristotelian view, I don't see how we can escape the alternative,
which is either the physical reality is the One ("Aristotle"), or
something else might be ("Plato").
(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
I tried to be less provocating using "metaphysics" instead of
theology, but I knew it will not make down the mockery :)
Bruno
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