Bruno, are you familiar with the atheistic (so-called) theologies of Dr. Eric
Steinhart? He's a bright philosopher from William Patterson University, is the
US. He was originally a software engineer and is like yourself, a math guy. He
applies his experience to his philosophy, and after reading your writings here,
as well as Amoeba, his insights seem to parallel yours. Also, Clement Vidal's,
as well. Every heard of him? His papers focus on the origins of the universe(s)
Platonism, "Computationalism," and Digital Philosophy. It's not exactly like
your work, but it certainly parallels it. Ever heard of him? It sort of informs
this topic I think.
-----Original Message-----
From: Samiya Illias <samiyaill...@gmail.com>
To: everything-list <everything-list@googlegroups.com>
Sent: Sat, Feb 7, 2015 11:07 pm
Subject: Re: Why is there something rather than nothing? From quantum theory to
dialectics?
On Thu, Feb 5, 2015 at 8:27 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 04 Feb 2015, at 17:14, Samiya Illias wrote:
On Wed, Feb 4, 2015 at 5:49 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 04 Feb 2015, at 06:02, Samiya Illias wrote:
On 04-Feb-2015, at 12:01 am, Bruno Marchal <marc...@ulb.ac.be> 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).
I didn't use the axioms. I just substituted the axioms variables with the
natural numbers.
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?
Yes, thanks!
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.
1+8=9
Translating in successor terms:
s(0) + s(s(s(s(s(s(s(s(0)))))))) = s(s(s(s(s(s(s(s(s(0)))))))))
Applying Axiom 2 by substituting x=8 or s(s(s(s(s(s(s(s(0)))))))), and y=0,
s(s(s(s(s(s(s(s(0)))))))) + s(0) = s( s(s(s(s(s(s(s(s(0)))))))) + 0)
Applying axiom 1 to the right side:
s(0) + s(s(s(s(s(s(s(s(0)))))))) = s(s(s(s(s(s(s(s(s(0)))))))))
1+8=9
Is the above the correct method to arrive at the proof? I only used axiom 2
once. Am I missing some basic point?
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)
Yes, they hold true when substituted with natural numbers.
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).
I've tried two approaches, but I am getting stuck at the last step. Please see:
Approach 1:
Prove s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0))))))
for x=s(s(s(0))) and y=s(0)
Applying axiom 4
Step 1: s(s(s(0))) * s(s(0)) = s(s(s(0))) + (s(s(s(0))) * s(0))
Simplifying the bracket on the right side, again using axiom 4, assuming
x=s(s(s(0))) and y=0
x * s(y)= x + (x*y)
Step 2: s(s(s(0))) * s(0) = s(s(s(0))) + (s(s(s(0))) * 0)
Applying axiom 3
Step 3: s(s(s(0))) * s(0) = s(s(s(0)))
Replacing the value in Step 1:
s(s(s(0))) * s(s(0)) = s(s(s(0))) + s(s(s(0)))
In number terms, this translates to 3 * 2 = 3 + 3 which is correct but I do not
know how to proceed with the proof.
Approach 2:
Prove s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0))))))
for x=s(s(s(0))) and y=0
Using the distributive property of multiplication (or whatever is the correct
term for the following),
Step 1: s(s(s(0))) * s(s(0)) = {s(s(s(0))) * 0} + {s(s(s(0))) * s(0)} +
{s(s(s(0))) * s(0)}
Using axiom 3 to simplify the first {} on the right side,
Step 2: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) * s(0)} + {s(s(s(0))) * s(0)}
Using axiom 4 to simplify the second and third {} on the right side,
Step 3: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + [s(s(s(0))) * 0]} +
{s(s(s(0))) + [s(s(s(0))) * 0]}
Using axiom 3 to simplify the second and third {} on the right side,
Step 4: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + 0} + {s(s(s(0))) + 0}
Using axiom 1 to simplify the second and third {} on the right side,
Step 5: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + {s(s(s(0)))}
Removing {},
Step 6: s(s(s(0))) * s(s(0)) = s(s(s(0))) + s(s(s(0)))
which again translates to 3 * 2 = 3 + 3 which is correct but I do not know how
to proceed with the proof.
Samiya
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
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
