On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote:
> What is the point? Do we have experimental procedure to validate
> the opposite of the fanciful scenario? Giving that we were talking about

I see, we're at the "prove that the Moon is not made from green cheese when
nobody is looking" stage.

I thought this list wasn't about ghosties'n'goblins.
Allright, I seem to have been mistaken about that.

> first person scenario, in any case it is senseless to ask for
> experimental procedure. (experience = first person view; experiment =
> third person view).

So the multiverse is not a falsifyable theory?

> Don't tell me you were believing I was arguing.

You were asserting a lot of stuff. That's commonly considered arguing, except
you weren't providing any evidence so far. So, maybe you weren't. 

> About logic, it is a branch of mathematics. Like topology, algebra, analysis
> it can be *applied* to some problem, which, through some hypothesis,
> can bear on some problem. With the comp hyp mathematical logic makes
> it possible to derive what consistent and platonist machine can prove about
> themselves and their consistent extension.

Except that machine doesn't exist in absence of implementations, be it
people, machines, or aliens. 

> >My point is that formal systems are a very powerful tool with very small 
> >reach,
> >unfortunately.
> But I never use formal system. I "modelise" a particular sort of machine by
> formal system, so I prove things *about* machines, by using works
> *about* formal system. I don't use formal systems. I prove things in 
> informal
> ways like all mathematicians.

Above passage is 100% content-free.

> >Because we know that QM is not a TOE. You haven't heard?
> How could be *know* QM is not a TOE?  (I ask this independently of
> the fact that I find plausible QM is not a *primitive* TOE).

Because general relativity and quantum theory are mutually incompatible. So
both TOE aren't. We have several TOE candidates, and an increased number of
blips heralding new physics, but no heir apparent yet. 

> You believe that the theorem "there is an infinity of primes" is a human
> invention?  (as opposed to "a human discovery").

Of course. Not necessarily human; there might be other production systems
which invented them. Then, maybe there aren't.

Infinity is something unphysical, btw. You can't represent arbitrary values
within a finite physical system -- all infoprocessing systems are that.
You'll also notice that imperfect theories are riddled with infinities; they
tend to go away with the next design iteration. So infinities is something
even more primatish than enumerable natural numbers.

> >I do not see how arithmetic realism (a special case of Platonic realism, is
> >that correct?) is an axiom. I agree with the rest of
> >your list.
> Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical
> Truth is independent of me, you, and the rest of humanity. There exist

Oh, I disagree with that allright. Nonliving systems don't have an
evolutionary pressure to develop enumerable quantities representation.

> weaker form of that axiom and stronger form. Tegmark for instance
> defends a much larger mathematical realism (so large that I am not sure
> what it could mean). As I said some ultrafinitist defends strictly
> weaker form of mathematical realism.
> The more quoted argument in favour of arithmetical realism is the one based
> on Godel's theorem, and presented by him too) which is that any formal
> systems (and so any ideally consistent machines) can prove, even in 
> principle,
> that is with infinite time and space, all the true proposition of 
> arithmetic.

Sure. Notice that infinite time and space is unphysical, and of course a
machine which doesn't exist doesn't produce anything.

I was hoping for a falsifyable argument, showing that this spacetime is an
operation artifact of some finite production system.

> But look also to the site of Watkins
> http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm

Oh, basically you're arguing that the unreasonable applicability of
mathematics in physics is anything but unreasonable, and that a TOE arisen
from a formal system is in fact the universe itself?

> for a lot of evidence for it (evidence which are a priori not related to
> my more theoretical computer science approach).
> Now my goal (here) is not really to defend AR as true, but as sufficiently 
> plausible
> that it is interesting to look at the consequences. You can read some

I do not deny that a TOE can be immensely useful (but not necessarily so,
higher levels of theory tend to require increasing amounts of crunch to
predict anything useful), but that TOE has anything to do with the metalayer,
or that in fact that distinction is meaningful.

You don't seem to disagree, so we're not actually arguing.

> main post I send to this list where I present the argument according to
> which if we take comp seriously (comp = AR + TC + "yes doctor") then
> physics is eventually a branch of machine's psychology (itself a branch
> of computer science" itself a branch of number theory.

Ah, some severe leap of faith required here.

> If you find an error, or an imprecision, please show them.

I'm experiencing a severe cognitive dissonance, trying to understand why you
think formal systems do exist in absence of their production systems. 

> Or, if there is a point you don't understand, it will be a pleasure for me
> to provide more explanations.
> Also, I thought you were postulating an universe, aren't you? (I just try

Sure, we're having a conversation (albeit a bit surreal one), so we seem to exist.

> to figure out your philosophical basic hypothesis).
> Regards,
> Bruno
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