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. Empirical
proofs can be ostensive. So I think the two kinds of 'proof' have little in common.
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.
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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