Re: Why is there something rather than nothing? From quantum theory to dialectics?

2015-02-09 Thread Bruno Marchal


On 08 Feb 2015, at 13:30, spudboy100 via Everything List wrote:

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.



I don't think I know him although the name invke some familiarity. Did  
he got the first person indeterminacy, the mathematicalism or  
arithmeticallism?


The mean to test this. You might sum up the idea, if you have the time,

The problem with many scientists is that they stop doing science when  
doing philosophy. It is not a problem, but it can be confusing in that  
field.




Bruno










-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   truthGod
[]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 

Re: Why is there something rather than nothing? From quantum theory to dialectics?

2015-02-09 Thread Samiya Illias
On Tue, Feb 10, 2015 at 12:50 AM, Bruno Marchal marc...@ulb.ac.be wrote:


 On 08 Feb 2015, at 05:07, Samiya Illias wrote:



 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   truthGod
 []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.


 And use your common intuition. Good.

 The idea now will be to see if the axioms given capture that intuition,
 fully, or in part.






 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!


 You are welcome.




 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 see. Axiom 2 says:x + s(y)) = s(x + y). Well, if x = 8, and y =
 0, we get 8 + 1, and your computation/proofs is correct, in that case.

 So you would have been correct if I was asking you to prove/compute that 8
 + 1 = 9.

 Unfortunately I asked to prove/compute that 1 + 8 = 9.

 I think that you have (consciously?) use the fact that 1 + 8 = 8 + 1,
 which speeds the computation.

 Well, later I ill show you that the idea that for all x and y x + y = y +
 x, is NOT provable with the axioms given (despite that theorey will be
 shown to be already Turing Universal.

 No worry. Your move was clever, but you need to put yourself in the mind
 of a very stupid machine which understand only the axioms given.


I understand


 Can you show that 1 + 8 = 9. 

evangelizing robots

2015-02-09 Thread meekerdb


In two senses of that term! Or something.

http://bigthink.com/ideafeed/robot-religion-2

http://gizmodo.com/when-superintelligent-ai-arrives-will-religions-try-t-1682837922

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Re: Why is there something rather than nothing? From quantum theory to dialectics?

2015-02-09 Thread LizR
From Wikipedia I get the idea that he is interested in the technological
singularity, mind uploading and suchlike.

On 10 February 2015 at 09:16, Bruno Marchal marc...@ulb.ac.be wrote:


 On 08 Feb 2015, at 13:30, spudboy100 via Everything List wrote:

 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.



 I don't think I know him although the name invke some familiarity. Did he
 got the first person indeterminacy, the mathematicalism or
 arithmeticallism?

 The mean to test this. You might sum up the idea, if you have the time,

 The problem with many scientists is that they stop doing science when
 doing philosophy. It is not a problem, but it can be confusing in that
 field.



 Bruno









 -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   truthGod
 []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 

Re: Why is there something rather than nothing? From quantum theory to dialectics?

2015-02-09 Thread Platonist Guitar Cowboy
On Mon, Feb 9, 2015 at 9:16 PM, Bruno Marchal marc...@ulb.ac.be wrote:


 On 08 Feb 2015, at 13:30, spudboy100 via Everything List wrote:

 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.



 I don't think I know him although the name invke some familiarity. Did he
 got the first person indeterminacy, the mathematicalism or arithmeticallism?


The mean to test this. You might sum up the idea, if you have the time,

 The problem with many scientists is that they stop doing science when
 doing philosophy. It is not a problem, but it can be confusing in that
 field.


One of those names at least is familiar to the list because:


On Fri, Oct 3, 2014 at 12:25 AM, spudboy100 via Everything List 
everything-list@googlegroups.com wrote:


 To die for Allah is slay for Allah. The reward for the mujahedeen is
 enormous, for to sacrifice ones self, and the opponent of God, is to
 granted immediate entry into paradise (Janah) and its rewards are not
 unsubstantial. One way to change the Umah's mind (if such is even possible)
 would be to make widespread, *Clement Vidal*'s publications, especially,
 The Beginning and the End, The Meaning of Life in a Cosmological
 Perspective. Part of the book details with afterlife concepts in a rational
 sense, as well as much, more. *Vidal* is a colleague of Bruno Marchal at
 Free University, Brussels. * Vidal*'s influence may induce those looking
 for a heavenly, rewards, for head chopping unbelievers, a good think.

 It would also alter our own perspective as well. Make the world a bit more
 peaceful, and provide some reassurance for all.

 Honk! If you all agree ;-)





On Fri, Oct 3, 2014 at 11:52 PM, spudboy100 via Everything List 
everything-list@googlegroups.com wrote:

 Bruno might comment on his colleague, at university, *Clement Vidal*. The
 Evo-Devo approach, etc.





On Tue, Sep 30, 2014 at 3:46 AM, spudboy100 via Everything List 
everything-list@googlegroups.com wrote:



 Sent from AOL Mobile
  If We remain a sophisticated civilization, we should be able to leave
 space exploration for the robots, until such a time and and place where we
 uncover something dynamically interesting. But this is for another
 generation to decide, and not ours. Which makes things,  seem, our world,
 our times, our worries, seem so temporary. On the other hand I am now
 reading the work by *Clement Vidal*, of Free University, Brussels, a
 colleague, of Bruno Marchal, on the meaning and purpose of intelligence,
 life, and cosmology, leading to the far future-a very, different
 perspective indeed.




On Wed, Jun 25, 2014 at 5:55 PM, spudboy100 via Everything List 
everything-list@googlegroups.com wrote:

 Dr. Marchal, do you ever get in conversations with your fellow academician,*
 Clement Vidal*? He's a philosopher at your University? Do you ever get
 into the Evo-Devo view?


So that may be part of the reason the name is slowly becoming familiar
although I wouldn't know, as I can't search the list's archives completely,
nor do I receive/want all posts archived in my Inbox, therefore filtering
and/or ignoring a lot. PGC

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Re: Why is there something rather than nothing? From quantum theory to dialectics?

2015-02-09 Thread Bruno Marchal


On 08 Feb 2015, at 05:07, Samiya Illias wrote:




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   truthGod
[]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.


And use your common intuition. Good.

The idea now will be to see if the axioms given capture that  
intuition, fully, or in part.









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!


You are welcome.





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 see. Axiom 2 says:x + s(y)) = s(x + y). Well, if x = 8, and  
y = 0, we get 8 + 1, and your computation/proofs is correct, in that  
case.


So you would have been correct if I was asking you to prove/compute  
that 8 + 1 = 9.


Unfortunately I asked to prove/compute that 1 + 8 = 9.

I think that you have (consciously?) use the fact that 1 + 8 = 8 + 1,  
which speeds the computation.


Well, later I ill show you that the idea that for all x and y x + y =  
y + x, is NOT provable with the axioms given (despite that theorey  
will be shown to be already Turing Universal.


No worry. Your move was clever, but you need to put yourself in the  
mind of a very stupid machine which understand only the axioms given.


Can you show that 1 + 8 = 9. Better,  tell me how many times you will  
need to use the second axioms?









Let me ask you