# Re: why IMHO arithmetic is not a theory

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On 05 Nov 2012, at 13:19, Roger Clough wrote:```
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```Hi Bruno Marchal

IMHO arithmetic, unlike theory, does not make predictions
in the real world,
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?
It does, but we are blasé.

Let me give you example:

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1) It predict that if I put two spoon of sugar in my tea, my tea will have more sugar in it.
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2) it predicts that some programs will not stop, and indeed we can confirm this.
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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.
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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 Löbian machines. This again is confirmed. of course here comp is used to make arithmetic the theory of everything, and in that setting many problems are open.
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```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,
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You confuse a theory of arithmetic with the arithmetical truth.

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```arithmetic is discovered. It is most certainly a priori.
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Indeed. For arithmetical truth. But arithmetical theories have take time to be isolated or human-invented.
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Bruno

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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,

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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

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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

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and with the infinities of induction axioms, for all arithmetical formula F(x) :
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(  F(0)   &   Ax(F(x) -> F(s(x))  )     ->      AxF(x)

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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.
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it is
arithmetical (permanent, necessary, logical) truth.

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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, rclo...@verizon.net
11/3/2012
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content -----
From: Bruno Marchal
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.

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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.
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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.
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Comp is that we can survive with a digital machine replacing the brain.
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I have no difficulty with that, but now you tell me that it means a great many other things too,
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Yes. It has concequences which contradict many point of Aristotle metaphysics.
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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".
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Let us go step by step.

you are stuck in step 3

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And I will remain stuck there until you fix the blunders you made in step 3;
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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.
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after that perhaps the additional steps that were built on that fatally flawed foundation would be worth reading.
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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.

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You don't know what your environment will be, what's new and mysterious about that?
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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.
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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 .
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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.
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And the guy in Helsinki, if he can reason like any L?ian machine,

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Like your other invention "comp" I don't know what a "L?ian machine" is.
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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.
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What is the probability the Washington man will write in his diary he sees Washington? 100%.
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The question was asked to the Helsinki man.

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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.
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The body of the guy in Helsinki is destroyed, but by comp, we have already accept that the guy itself survives.
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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.
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No, the question is asked before he pushes on the read/cut button.

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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".
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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.
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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.
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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.
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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
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Exactly. This contradict what you say above though.

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I said a great deal above but I'll be damned if I see any contradiction .
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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).
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It doesn't matter if Boltzman brains exist or not.

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

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Which are useless because they were built on top of a step that does not work.
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... 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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