Re: why IMHO arithmetic is not a theory

Bruno Marchal Wed, 07 Nov 2012 08:07:34 -0800


On 07 Nov 2012, at 15:27, Richard Ruquist wrote:

So comp does not explain MWI, it just explains many dreams

It explain how the reality, both mental and physical, *emerge* fromthe relative number dreams.

It predicts that any machine looking at her bowy below itssubstitution level will see the "parallel computations". It does notexplain why such machine would necessarily extrapolate thosecomputation into world.

But my main point is that comp explains the very existence of physics,constructively. So we can test comp, and up to now, qualitatively (MW)and quantitatively (quantum logic) is already in the reach of comp.

Comp is just the most natural theory of consciousness, and the firstkey result is that physics, whatever it is, emerges from machinedreams. But none of those dreams is the physical world. The emergenceprocess is itself a complex partially arithmetical, partiallyanalytical phenomenon existing in the consciousness of the numbers.

Cautious: comp predicts that both consciousness and matter are *not*Turing emulable, at least not completely. It has nothing do to withdigital physics, which postulates that physics is the result of acomputation, and that the universe is a sort of computer. But withcomp, due to the first person indeterminacy, all computations and allcomputers (universal numbers) play some role.


Bruno

On Wed, Nov 7, 2012 at 9:01 AM, Bruno Marchal <[email protected]>wrote:


On 06 Nov 2012, at 15:02, Richard Ruquist wrote:



How has comp explained how there are Many Worlds?
I presume you mean MWI and many physical worlds, not just many dream
worlds..



Once comp is assumed, it is easy to prove that all dreams exists in
arithmetic.  But they obeys laws (relying on computer science or

arithmetic), and dreams can have coherent properties making themshared bypopulation of individuals, with reasonable relative proportionsgiving rise

to inferable "physical laws".
It is an open problem if this lead to "worlds", and in what sense.

If both comp and QM is correct, QM has to be derivable by onlycomp, andsome definition of knowledge. And up to now, this works well. Butit is hard(technically) to justify completely QM, and even harder to get theright

Hamiltonians, in case they are not purely geographical/contingent.

Bruno






Richard

On Tue, Nov 6, 2012 at 8:55 AM, Roger Clough <[email protected]>wrote:


Hi Bruno Marchal


OK.



Roger Clough, [email protected]

11/6/2012

"Forever is a long time, especially near the end." -Woody Allen



----- Receiving the following content -----

From: Bruno Marchal

Receiver: everything-list

Time: 2012-11-06, 07:21:19

Subject: Re: why IMHO arithmetic is not a theory



On 05 Nov 2012, at 13:19, Roger Clough wrote:


Hi Bruno Marchal


IMHO arithmetic, unlike theory, does not make predictions

in the real world,


?

It does, but we are blas?.


Let me give you example:


1) It predict that if I put two spoon of sugar in my tea, my tea will

have more sugar in it.


2) it predicts that some programs will not stop, and indeed we can

confirm this.


3) it predicts, together with string theory, that the mass of the

photon is zero. This uses the rather remarkable Ramanujan proposition

that the sum of all natural numbers 1+2+3+4+5+6+7+ ... is reasonably

equal to ... -1/12. So the apparant lack of mass of the photon

confirms this.


4) it predicts everything, with comp, although the math is hard to be

specific, but it has already explained why there is a quantization,

why there are many-worlds, and the whole of the theology of the L?ian

machines. This again is confirmed. of course here comp is used tomake

arithmetic the theory of everything, and in that setting manyproblems


are open.




so it has not contingency about it,

its truths are necessary, unchangeable. and always true.

That disqualifies arithmetic as a theory, which is man-made

(invented) and therefore contingent.


Theories are invented, but arithmetic is not,


You confuse a theory of arithmetic with the arithmetical truth.




arithmetic is discovered. It is most certainly a priori.


Indeed. For arithmetical truth. But arithmetical theories have take

time to be isolated or human-invented.


Bruno





On 03 Nov 2012, at 12:34, Roger Clough wrote:



Hi Bruno Marchal



All theories are based on the a priori but

can only give contingent results (this world

results).




Hmm.... OK.








However, arithmetic is not a theory,



Sorry, but it is. I mean there are even many theories. Two important

one in the comp setting is the "very elementary theory". Basically

just the four equalities:



x+0 = x

x+s(y) = s(x+y)



x*0=0

x*s(y)=(x*y)+x



This is already Turing universal.



A richer theory (PA), which is L bian (knows she is universal), is

the same four axioms +



0 ? s(x)

s(x) = s(y) -> x = y



and with the infinities of induction axioms, for all arithmetical

formula F(x) :



( F(0) & Ax(F(x) -> F(s(x)) ) -> AxF(x)



By G del 2, or by L b, Arithmetical Truth is far beyond *all*

theories and machines. "Arithmetical Truth" cannot be defined by

those machines, although they can build transfinite of

approximation, and handles pointer on the notion.









it is

arithmetical (permanent, necessary, logical) truth.




Yes. But logically you have still to make your assumptions explicit

and clear, and then you see that arithmetical truth is bigger than

what we can conceive (provably so about the sound machines) and that

it will have many contingent internal aspects when seen from

"inside". Still both the necessary and the contingent obeys to

(meta) laws, in the computer science setting.



Bruno








Roger Clough, [email protected]

11/3/2012

"Forever is a long time, especially near the end." -Woody Allen



----- Receiving the following content -----

From: Bruno Marchal

Receiver: everything-list

Time: 2012-11-03, 05:59:33

Subject: Re: Against Mechanism





On 02 Nov 2012, at 22:02, John Clark wrote:



On Fri, Nov 2, 2012 Bruno Marchal wrote:





He believes he still exist, because he believes, or assumed, comp.



People believe they exist and in real life they don't have or need a

reason for doing so. And I no longer know what "comp" means.




Comp means that we can survive with a digital brain. Nothing else.

but it implies that Plato is correct and Aristotle is incorrect for

the global conception of reality.








Comp is that we can survive with a digital machine replacing the

brain.



I have no difficulty with that, but now you tell me that it means a

great many other things too,



Yes. It has concequences which contradict many point of Aristotle

metaphysics.







things that are clearly untrue; like consciousness was there before

Evolution produced brains or "the owner [of a brain] itself must

attach his consciousness to all states existing in arithmetic".




Let us go step by step.










you are stuck in step 3




And I will remain stuck there until you fix the blunders you made in

step 3;



Your "blunder" has been debunked by many people. Then you have

oscillate between contradictory statements. You are only confusing 1-

views with 3-views. Sometimes between 3-views on 1-views and the 1-

views on 1-views.

You are the one pretending being able to predict what happens after

pushing the button, but you have always given a list of what can

happen, which is not a prediction.









after that perhaps the additional steps that were built on that

fatally flawed foundation would be worth reading.




You did not show a flow, just a confusion between 1p and 3p.










the guy in W and the guy in M are both the guy in H



Yes.




by definition of comp.




I don't know what that is.




See above.










This is enough to get the 1_indeterminacy.




You don't know what your environment will be, what's new and

mysterious about that?





OK. Good. So you accept it. Please go to step 4 now, and tell me if

you agree. We have all the time to see where the reasoning will

eventually lead us.









I have no duplicating machine but I still don't know if my

environment will include rain tomorrow, but I can't find anything of

philosophical interest in that fact .




This is not the same form of indeterminacy. The impossibility of

predicting the weather is due to the deterministic chaos. This is

not used in the first person indeterminacy.










And the guy in Helsinki, if he can reason like any L?ian machine,




Like your other invention "comp" I don't know what a "L?ian

machine" is.




A universal machine capable of proving all sentence with the shape p

-> Bew('p'), with p being an arithmetical sentence with shape

ExP(x), and P decidable. Exemple: prover theorem for PA, ZF, etc.












What is the probability the Washington man will write in his diary

he sees Washington? 100%.





The question was asked to the Helsinki man.





But you said the Helsinki man was destroyed, if so then he's got a

rather severe case of writers block and is writing very little in

his diary.





The body of the guy in Helsinki is destroyed, but by comp, we have

already accept that the guy itself survives.



So when you say "The question was asked to the Helsinki man" you are

asking a question to a man who's body has been destroyed.



No, the question is asked before he pushes on the read/cut button.









Yes the Helsinki man is also the Washington man so you could say

there is a 100% chance the Helsinki man will write in his diary "I

see Washington".



No. the question is *about* a future 1-view. The guy knows that he

might very well be the guy in Moscow, so he cannot assert that he

will *feel* with 100% chance to be the one in Washington. Again you

confuse the 3-view and the 1-view.









Of course the Helsinki man is also the Moscow man so there is a 100%

chance the Helsinki man will write in his diary "I DO NOT see

Washington". There is no contradiction because you have been

duplicated.




Of course there is no contradiction. But the Helsinki man would find

to be contradict if he said I will find myself in W and I will find

myself in Washington, from the first person view, as he knows that

after pushing the button he will find himself being in only one

city, not in two cities simultaneously.








If Bruno Marchal's body is duplicated and sent to Washington and

Moscow but inside identical boxes then Bruno Marchal's consciousness

has not been duplicated and will not be until the boxes are opened

and different things are observed by the Brunos, at that point they

will no longer be each other but both will still be Bruno Marchal


Exactly. This contradict what you say above though.



I said a great deal above but I'll be damned if I see any

contradiction .




You did it again. You pretend that there is 100% chance that he will

feel to see Washington, and 100% chance he will feel to see Moscow,

and yet you agree that there is 100% chance he will see only one

city (and you forget that the question is which one, with what

chance).










It doesn't matter if Boltzman brains exist or not.





Of course it does matter. That the point of step 4, 5, 6, 7.



Which are useless because they were built on top of a step that does

not work.




... for someone unable to understand that the question is about the

future first person point of view, as seen by the future first

person point of view, and not about the 3-view on all future first

person points of view, as you keep giving.

Reading step 4 should help you to eventually grasp this key nuance.



Bruno





http://iridia.ulb.ac.be/~marchal/


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