# why IMHO arithmetic is not a theory

```Hi Bruno Marchal

IMHO arithmetic, unlike theory, does not make predictions
in the real world, 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,
arithmetic is discovered. It is most certainly a priori.

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

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, 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.

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

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.

Bruno

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

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