# Re: arithmetic truth and 1p truth

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On 03 Nov 2012, at 11:58, Roger Clough wrote:```
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```Hi Bruno Marchal

I think in computationalism you only have to be able
to say that the result is arithmetically or algebraically
true. Arithmetic truth is what you seek.

However, I still have yet to know if  a particular
computation seems true to your 1p. That would be
1p truth. Does the arithmetic truth pass the 1p test ?
```
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Yes. Good question.
That's the purpose of AUDA. The arithmetical UDA.
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It is in the second part of sane04. The "interview of the universal machine". Up to now, thanks to the Everett/Feynman formulation of QM, comp succeeds the first tests.
```Arguably.

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: 2012-11-02, 13:23:36
Subject: Re: Numbers in the Platonic Realm

On 01 Nov 2012, at 22:50, Stephen P. King wrote:

On 11/1/2012 12:04 PM, Bruno Marchal wrote:

On 01 Nov 2012, at 01:18, Stephen P. King wrote:

On 10/31/2012 12:45 PM, Bruno Marchal wrote:

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can stop reading as you need to assume the numbers (or anything Turing equivalent) to get them.
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Dear Bruno,

So it is OK to assume that which I seek to explain?

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You can't explain the numbers without assuming the numbers. This has been foreseen by Dedekind, and vert well justified by many theorem in mathematical logic. Below the number, you are lead to version of ultrafinitism, which is senseless in the comp theory.
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Dear Bruno,

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I disagree with ultrafinitists, they seem to be the mathematical equivalent of "flat-earthers'.
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*and* having some particular set of values and meanings.

I just assume

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

And hope you understand.

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I can understand these symbols because there is at least a way to physically implement them.
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Those notion have nothing to do with "physical implementation".

So your thinking about them is not a physical act?

Too much ambiguous. Even staying in comp I can answer "yes" and "no".
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Yes, because my human thinking is locally supported by physical events. No, because the whole couple mind/physical events is supported by platonic arithmetical truth.
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Implementation and physical will be explained from them. A natural thing as they are much more complex than the laws above.
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Numbers are meaningless in the absence of a means to define them. Theories do not free-float.
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Truth is free floating, and theories lived through truth, they are truth floating, even when false.
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In the absence of some common media, even if it is generated by sheaves of computations, there simply is no way to understand anything.
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Why ?

Because there is not way to know of them otherwise.

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Our knowing as nothing to do with truth. If an asteroid would have destroy Earth before the Oresme bishop dicovered that the harmonic series diverge, she would have still diverge, despite no humans would know it.
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Unless you can communicate with me, I have no way of knowing anything about your ideas. Similarly if there is no physical implementation of a mathematical statement, there is no meaning to claims to "truth" of such statements.
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To claim, no. To be true is independent of the claim of the apes.

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You must accept non-well foundedness for your result to work, but you seem fixated against that.
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1004.

Pfft. Nice custom made quip.

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You are often escaping answers by inappropriate mathematical precision, which meaning contradicts your mathematical super- relativism. It is really 1004+contradiction.
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A statement, such as 2 = 1+1 or two equals one plus one, are said truthfully to have the same meaning because there are multiple and separable entities that can have the agreement on the truth value. In the absence of the ability to judge a statement independently of any particular entity capable of "understanding" the statement, there is no meaning to the concept that the statement is true or false. To insist that a statement has a meaning and is true (or false) in an ontological condition where no entities capable of judging the meaning, begs the question of meaningfulness!
```  You are taking for granted some things that your arguments disallow.

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Do you agree that during the five seconds just after the Big Bang (assuming that theory) there might not have been any possible observers. But then the Big Bang has no more sense.
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No, I don't. Why? Because that concept of "the five seconds just after the Big Bang" is an assumption of a special case or pleading. I might as well postulate the existence of Raindow Dash to act as the entity to whom the Truth of mathematical statements have absolute meaning. To be frank, I thing that the Big Bang theory, as usually explained is a steaming pile of rubbish, as it asks us to believe that the totality of all that exists sprang into being from Nothing.
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I actually agree, by accident, on this. But this is not relevant for my point.
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It is very relevant to mine.

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Imagine that we can show that some solution to GR equantion have universe so poor that life cannot exist in there, would you say that such universe cannot exist?
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If there does not exist a means to "show the solution" there is no solution.
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Mathematical solipsism.

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I believe that the totality of what exists is eternal, having no beginning and no end.
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I am OK with that. It is close to Platonism. But with comp we can restrict this to the arithmetical truth (a highly non computable structure, but still conceivable by universal numbers, relatively).
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Well, can we work with that agreement?

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Come on, you say that you can escape the consequence of comp, you have to find the flaw, or to be more cautious in your judgment. There is no one statement I made on this list which I have not published before, and there have been a lot of peer-review (especially that many philosophers hate that work, but they try to defend the philosophy curriculum against a possible invasion of science: that is usual and normal).
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What we infer from our observations of Hubble expansion is just an effect that follows, ultimately, from our finiteness.
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Including time and space. So we do agree again.

Good!

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I think Brent is right, and Quentin. You confuse 1+1=2 with human expression for pointing on that proposition. You obviously needs human to understand those " "1+1=2" ", but the content of "1+1=2" has simply no relation at all with the human, or with a physical universe.
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No, none of you have yet to be able to understand my counter- argument. It is not complicated. We cannot assume to have something when the means for its existence is not allowed. My claim is that meaningfulness supervenes on the possibility of interaction of *many* entities and is independent of any *one* (or some lesser finite subset) of that Many.
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But arithmetical truth is full of entities, even full of galaxies themselves full of self-aware being. That is a fact. But with comp (and UDA), those entities are saved from zombieness.
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Yes, and bundles of arithmetic statements generate many individual observers that in turn "interact" (which I model via a combination of cyclic gossiping on graphs and bisimulations) with each other to define a common physical world which in turn acts to "implement" the arithmetic. It is a loop, an eternal cyclical process that never exactly repeats. It is in this infinite loop that I see your UD.
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It is not a loop. It is more like a recurring abyss, like the Mandelbrot set.
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I asked you some time ago if you agree with the use of the excluded middle in arithmetic. It asserts that for any arithmetical proposition P, even highly non computably verifiable, you can accept as new arithmetical truth the proposition asserting that P v ~P. Which intuitive meaning that the proposition is unambiguously either true, or false, despite you have no idea if it is P or ~P which is the true one. To accept this means that you accept that such truth are independent of the means to prove or verify them.
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We must us the principle to excluded middle [PEM] to reason, but this does not make the principle something external and independent of us.
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1) the intuitionist can reason without them.

Yes, but their reasonings are severely limited.

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You are the one saying that truth is limited to the means of knowing!!!
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2) the PEM is a way to assert formally platonism, and I use it only in arithmetic. And it means that the truth is independent of our reasons.
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Truth is independent of any particular reasoning, but it is NOT independent of the reasoning of all entities.
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Ambiguous. trivially true with comp as the reasoning of all entities belongs to the (tiny part of) arithmetical reality.
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This is a red herring, Bruno. It is not addressing my claim at all.

Then you have to try to state it more clearly.

I am trying. ;-)

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You seem to be stuck on the idea that only one entity can have or not have some property or power and cannot reason about the possibility that *many* may be required to solve some problems. A plurality is not a multiplicity...
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This is too vague.

OK, I will try again.

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I don't see that one one entity can have or not have some property or power, nor why I can't reason on the possibility that ?*many* might be required (on the contrary, there are many notion of many playing in comp and the emergence of physics. No clue what you mean here.
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Are you familiar with Jaakko Hintikka's ideas? I am using his concept of game theoretic semantics to derive truth valuations.
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I read this. yes. I don't see relevant at all.
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I do appreciate his linking of intention and intension, but it is a bit trivial in the comp theory.
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Bruno

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

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