On 04 Feb 2015, at 17:14, Samiya Illias wrote:
On Wed, Feb 4, 2015 at 5:49 PM, Bruno Marchal <[email protected]>
wrote:
On 04 Feb 2015, at 06:02, Samiya Illias wrote:
On 04-Feb-2015, at 12:01 am, Bruno Marchal <[email protected]> wrote:
Then reason shows that arithmetic is already full of life, indeed
full of an infinity of universal machines competing to provide
your infinitely many relatively consistent continuations.
Incompleteness imposes, at least formally, a soul (a first
person), an observer (a first person plural), a "god" (an
independent simple but deep truth) to any machine believing in
the RA axioms together with enough induction axioms. I know you
believe in them.
The lexicon is
p truth God
[]p provable Intelligible (modal logic, G and G*)
[]p & p the soul (modal logic, S4Grz)
[]p & <>t intelligible matter (with p sigma_1) (modal logic,
Z1, Z1*)
[]p & sensible matter (with p sigma_1) (modal logic, X1, X1*)
You need to study some math,
I have been wanting to but it seems such an uphill task. Yet, its
a mountain I would like to climb :)
7 + 0 = 7. You are OK with this? Tell me.
OK
Are you OK with the generalisation? For all numbers n, n + 0 = n.
Right?
Right :)
You suggest I begin with Set Theory?
No need of set theory, as I have never been able to really prefer
one theory or another. It is too much powerful, not fundamental. At
some point naive set theory will be used, but just for making thing
easier: it will never be part of the fundamental assumptions.
I use only elementary arithmetic, so you need only to understand the
following statements (and some other later):
Please see if my assumptions/interpretations below are correct:
x + 0 = x
if x=1, then
1+0=1
x + successor(y) = successor(x + y)
1 + 2 = (1+2) = 3
I agree, but you don't show the use of the axiom: x + successor(y) =
successor(x + y), or x +s(y) = s(x + y).
Are you OK? To avoid notational difficulties, I represent the
numbers by their degree of parenthood (so to speak) with 0.
Abbreviating s for successor:
0, s(0), s(s(0)), s(s(s(0))), ...
If the sequence represents 0, 1, 2, 3, ...
We can use 0, 1, 2, 3, ... as abbreviation for 0, s(0), s(s(0)),
s(s(s(0))), ...
Can you derive that s(s(0)) + s(0) = s(s(s(0))) with the statements
just above?
then 2 + 1 = 3
Hmm... s(s(0)) + s(0) = s(s(s(0))) is another writing for 2 + 1 = 3,
but it is not clear if you proved it using the two axioms:
1) x + 0 = x
2) x + s(y)) = s(x + y)
Let me show you:
We must compute:
s(s(0)) + s(0)
The axiom "2)" says that x + s(y) = s(x + y), for all x and y.
We see that s(s(0)) + s(0) matches x + s(y), with x = s(s(0)), and y =
0. OK?
So we can apply the axiom 2, and we get, by replacing x (= s(s(0)))
and y (= 0) in the axiom "2)". This gives
s(s(0)) + s(0) = s( s(s(0)) + 0 ) OK? (this is a simple
substitution, suggested by the axiom 2)
But then by axiom 1, we know that s(s(0)) + 0 = s(s(0)), so the right
side becomes s( s(s(0)) +0 ) = s( s(s(0)) )
So we have proved s(s(0)) + s(0) = s(s(s(0)))
OK?
Can you guess how many times you need to use the axiom "2)" in case I
would ask you to prove 1 + 8 = 9. You might do it for training purpose.
Let me ask you this. Are you OK with the two following multiplicative
axioms:
3) x * 0 = 0
4) x * s(y) = x + (x * y)
Can you prove that s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0)))))) ? This
is of course much longer, and you need all axioms 1), 2), 3) and 4).
If you can do this, Allah already knows that you are Turing universal
(in some large sense). You can know that too, once we have a
definition of Turing universal.
With computationalism, except for some purely logical axioms, we have
already the "theory of everything". You can see that it has very few
assumptions. It does not assume matter or god, nor consciousness. The
link with consciousness, and Allah, can be made at some metalevel, by
accepting the idea that the brain or the body is Turing emulable. But
for this we need to work a little bit more.
Bruno
Samiya
Bruno
Samiya
to see that this give eight quite different view the universal
machines develop on themselves.
Reminds me of this verse [http://quran.com/69/17 ]:
And the angels are at its edges. And there will bear the Throne
of your Lord above them, that Day, eight [of them].
It is like that: The four first (plotinian) hypostases live
harmonically in the arithmetical heaven:
God
Terrestrial Intelligible Divine
Intelligible
Universal Soul
But then the Universal Soul falls, and you get the (four) matters,
and the "bastard calculus":
Intelligible terrestrial matter Intelligible
Divine matter
Sensible terrestrial matter Sensible Divine
matter
Here divine means mainly what is true about the machine/number and
not justifiable by the numbers.
It provides a universal person, with a soul, consistent
extensions, beliefs, and some proximity (or not) to God (which is
the "ultimate" semantic that the machine cannot entirely figure
out by herself (hence the faith).
Interesting!
All universal machine looking inward discover an inexhaustible
reality, with absolute and relative aspects.
Babbage discovered the universal machine, (and understood its
universality). The universal machine, the mathematical concept,
will be (re)discovered and made more precise by a bunch of
mathematical logicians, like Turing, Post, Church, Kleene.
You are using such a universal system right now, even plausibly
two of them: your brain and your computer. They are a key concept
in computer science. They suffer a big prize for their
universality, as it makes them possible to crash, be lied, be
lost, be deluded. They can know that they are universal, and so
they can know the consequences.
The religion which recognizes the universal machine and her
classical theology might be the one which will spread easily in
the galaxy in the forthcoming millenaries. (Independently of being
true or false, actually).
Bruno
Samiya
If you want to convince me, you have to first convince the
universal person associated to the Löbian machine, I'm afraid.
I am not pretending that the machine theology applies to us, but
it is a good etalon to compare the theologies/religions/reality-
conceptions. The problem is that we have to backtrack to Plato,
where what we see is only the border of something, that we can't
see, but yet can intuit and talk about (a bit like mathematics or
music)
Bruno
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