On 09 Jan 2013, at 21:55, meekerdb wrote:
On 1/9/2013 7:05 AM, Bruno Marchal wrote:
On 09 Jan 2013, at 12:35, Richard Ruquist wrote:
On Wed, Jan 9, 2013 at 5:09 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 08 Jan 2013, at 15:59, Roger Clough wrote:
Hi Bruno Marchal
Whoever invented the word "God" invented atheism.
Not necessarily. The modern notion of God comes with the
platonist, and was
almost a synonym with "truth". There was an implicit, but
reasonable
assumption, that humans search truth. Atheism has arised by
reaction to
*imposed* notion of God, and, unfortunately, throws the
"theology" baby with
the clerical bath water.
Before, God was a scientific hypothesis, more or less equivalent
with the
idea that there is a reality which transcend us.
Agreed but your next statement is too restrictive in my opinion
unless
you mean experimental proof. For sure there is arithmetic proof that
goes beyond experimental proof in scope.
I prefer to keep the term "proof" in the strong logician's sense
(formal or informal).
I would talk only on experimental *evidence*.
You are right that proof usually can go much farer than any
evidence. We know that there is a prime number bigger than
10^10000, but have no
experimental evidences at all for that!
And we know that the Earth orbits the Sun - but there is no
mathematical proof of that. Mathematical proofs are always relative
to axioms and rules of inference.
OK.
Empirical proofs can be ostensive.
But I prefer not using "proof" for that. It can only be misleading
when we do applied logic. I prefer to call that "empirical evidences".
So I think the two kinds of 'proof' have little in common.
Almost nothing indeed.
Mathematical proofs are about transforming one set of propositions
into others. They are relevant to empirical propositions only
insofar as there is an interpretation that maps the axioms to facts.
I agree. Axioms comes from empirical evidences. The consequences of
the axioms can be used to test the theory, and refute it, but will
never prove it to be true.
Bruno
Brent
But I am saying something stronger: that many arithmetical truth
are just beyond proof (not just beyond experimental evidence). The
simplest one is the consistency of PA, which is true but impossible
to be proven by PA. Note that by the *completeness theorem* (Gödel
1930),
consistency is equivalent with "having a model", or having a
(mathematical) reality satisfying the axioms. Self-consistency is
already an assertion, made by some machine, that there is a
transcendental (with respect to that machine) reality.
Bruno
Richard
By definition it cannot be
proved to exist, not even named. Exactly like "arithmetical
truth" has to
appear for any sound machine.
Bruno
[Roger Clough], [rclo...@verizon.net]
1/8/2013
"Forever is a long time, especially near the end." - Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2013-01-08, 09:52:18
Subject: Re: Science is a religion by itself.
On 07 Jan 2013, at 19:47, John Clark wrote:
On Mon, Jan 7, 2013 wrote:
Consider God, a word for Mind
OK, I have a mind therefore I am God.
I said it before I'll say it again, for some strange reason that
is
unknown to me many people are willing to abandon the idea of God
but not the
word G-O-D. Those letters and in that sequence (DOG just will
not do) MUST
be preserved and it doesn't matter what it means.
GOD means the reality in which you believe. It is, imo, a bit
more neutral
than "Universe", which is the third Aristotelian God, and which
does not
belong to what constitutes the "being" for the Platonist. Since
about 1500
years, the term "God" has acquired many christian cultural
colors, but there
is no reason to identify God with the God-father of Christian
"theory". God
has no name, in many theologies, so all terms to designate it
can only be a
fuzzy pointer. Tao is not bad, as it has many similar qualities
than the
abramanic god, but with a less "person" feature. I use the term
God to
designate whatever transcend us and is responsible for our
existence. With
comp, I am open to the idea that (arithmetical) truth can play
that role,
and this is exploited in the arithmetical interpretation of
Plotinus
'neoplatonism'.
Bruno
http://iridia.ulb.ac.be/~marchal/
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