# Re: Numbers in the Platonic Realm

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

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

On 30 Oct 2012, at 18:39, Stephen P. King wrote:

On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply only to the concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some machine/numbers. If not, comp does not even makes sense.

So your are agreeing? "Two" has no truth value, but "Two equals one plus one." does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that the truth of, say "Two equals one plus one." depend on some numbers or subject having to discover it, or prove it.

Bruno

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

Dear Bruno,

My point is that a number is not a capable of being an ontological primitive

Then I can stop reading as you need to assume the numbers (or anything Turing equivalent) to get them.

Dear Bruno,

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

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.

*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.

I can understand these symbols because there is at least a way to physically implement them.

Those notion have nothing to do with "physical implementation".
Implementation and physical will be explained from them. A natural thing as they are much more complex than the laws above.

In the absence of some common media, even if it is generated by sheaves of computations, there simply is no way to understand anything.

Why ?

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

1004.

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.

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.

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.

I actually agree, by accident, on this. But this is not relevant for my point. 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?

I believe that the totality of what exists is eternal, having no beginning and no end.

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).

What we infer from our observations of Hubble expansion is just an effect that follows, ultimately, from our finiteness.

Including time and space. So we do agree again.

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.

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.

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.

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.

We must us the principle to excluded middle [PEM] to reason, but this does not make the principle something external and independent of us.

1) the intuitionist can reason without them.
2) the PEM is a way to assert formally platonism, and I use it only in arithmetic. And it means that thetruth is independent of our reasons.

This is a red herring, Bruno. It is not addressing my claim at all.

Then you have to try to state it more clearly.

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...

This is too vague. 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 ยจ*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.

Even intuitionist (who are sort of mathematical solipsist) accept, for P arithmetical, the proposition ~ ~ (P v ~P), which makes them already realist in the sense used in comp.

Not relevant. Your intransigence in this debate only reinforces by suspicion that you are not interested in extending your result so that its open problem might be solved.

?
Please stop the ad hominem remarks, as they add nothing to the debate. You are the one who doesn't succeed to make clear your point, despite my generous willingness to bet there is one hidden in your post.

Bruno

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

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