On 09 Jan 2013, at 18:56, Richard Ruquist wrote:
On Wed, Jan 9, 2013 at 12:01 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 09 Jan 2013, at 16:17, Richard Ruquist wrote:
On Wed, Jan 9, 2013 at 10:05 AM, Bruno Marchal <marc...@ulb.ac.be>
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!
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.
Agreed, and I hope that truth is true .
Lol.
Can we say that physical particles are often localised volumes
that are full of "infinities of discrete number relations"
Sounds to much physicalist for me (or comp).
and that a "flux density of infinities" can flow between them.
Or is that overboard?
If not taken literally, it can perhaps help. But there is a risk of
reifying
the particles, or of interpreting the "flux densities of
infinities" in a
too much materialist sense.
But Bruno, you just said that matter came from
"infinities of discrete number relations"
The appearance of matter comes from infinities of discrete number
relations.
Those appearances themselves are like continuous dream.
If you compensate with "matrix-" or "simulacron"-like illustration,
that
will be OK. You need to get the familiarity with the idea that those
infinities of computations exists in arithmetic, and that it
becomes "matter
appearances" only from the "number's pov" as distributed on the
whole UD* or
(sigma_1) arithmetical truth.
I can find that rather weird too. In the beginning I thought that
this was
just some steps toward a refutation of comp, but like with the
Gödelian
argument against mechanism, when made precise enough, the machine
turns such
argument in favor of comp.
I would never have found comp plausible if there were not the strong
evidence given by Gödel's theorem, Church thesis and QM. And of
course,
*many* problem are far from being solved (to say the least), but at
least we
have the tools to formulate them precisely.
Bruno
Are you granting that QM laws are
arithmetic theorems on the level
as those of Godel and Church?
Yes. (I will be explicit on FOAR, on this). But everything is
explained on the sane04 paper.
The arithmetical quantization is given by []<>p , with []p = Bp & Dt,
with D = ~B~, and B = Gödel's *arithmetical* beweisbar (provability)
predicate.
An arithmetical version of a Bell inequality is
[]<>([]<>A & []<>B) ->[]<>([]<>A v []<>B) & ([]<>A v []<>C)
So you can argue from them
like they were axioms?
Yes. All formula are theorem in Löbian (enough rich, like PA or ZF)
arithmetic, from the classical definition of knowledge, that we
recover by using Theatetus'definition of knowledge in the arithmetical
setting (with believable = provable, which makes sense for the ideally
correct machine that we have decided to "interview").
Bruno
Richard
Richard
points and lines
word geometry?
Richard
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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