Hi John,
On 06 Sep 2009, at 18:03, John Mikes wrote:
> Bruno,
> there is a lot of wisdom in your post. Your last sentence, however,
> may apply to that wisdom as well I am afraid.
>
> "...I have to assume that [such] truth are not dependent of me,..." -
> nor on anything else we may know of. I stay clear of 'truth' which
> is applied in whoever's theory - as 'his' truth.
I think you are perhaps confusing provable (in a theory), and truth
(of possible statements assertable in the theory). A theory does not
known "his" complete truth.
Being realist on the arithmetical statement is an admission of
ignorance in arithmetic. We accept that truth extends the mean of our
brains, theories, systems, etc.
I hope I can clarify this later for you. It is weird, and not easy to
explain without providing details.
Reality is beyond fiction and when you make attempt to be just honest
(and may be false), then "reality looks crackpot" ...
> I am in trouble with the "Church Thesis", it seems to be anchored in
> the math of functions and applied to comp.science. (BTW "recursive
> functions" pointing back to themselves? a restriction into what has
> been known (already)? I may have the wrong idea (if any) about the
> Ch-Th of course.)
> It may be 'fundamental' in - what I consider - a segment of the
> totality.
For mathematical reasons, assuming comp, we will have the choice
between a non completely knowable totality, or on some necessarily
partial, but complete in their domain, "totality", or sequence of
totalities.
Self-extending totalities are akin to the notion of first person.
With machines incompleteness makes room for the others (the second and
third persons)
>
> I can accept the 'universal machine' as not restricted to
> mathematical comp,
This is unclear. Universal machine appears only in that 'apparently
restricted digital world'. remember that after Gödel, we can no more
be sure that digitality is a restriction. Gödel signed the
reductionist conception of numbers. Assuming comp, we know that we are
either insane or very limited. And then UDA shows that the physical
worlds arise 'logically' from our limitations (where "us" = the Lobian
machine/entity, not the humans).
> it definitely should not apply those binary-slanted algorithms. I
> consider it as
> some analogue 'think-tank' beyond our present terms.
That is the case for all theory. Science is modest.
(and in AUDA all 8 hypostases are derivable from the Löb 'modesty'
formula B(Bp->p)->Bp, I say this for those who have follows some post,
or read Smullyan's or Boolos (or Smorynski) book on the logic of
provability/consistency.
> Whatever I would try to characterize it with, is MY restriction to
> its unlimited capabilites. So I don't.
You are a universal machine, John. I can prove it, and I can even show
that, as far as you are sound, you are Löbian. This means you can know
that your are, at least, a universal machine. And this will be used
negatively, in some way. Because Universal machine are very limited.
They are under the jug of many limitation theorems.
In the arithmetical interpretation of Plotinus theology. Universal
machine corresponds to what Plotinus call "man", 'or reasoner".
>
> Bruno, is your own restriction concentrated to 'physics' with
> 'math' as in:
> ("All theories in physics use at least that arithmetical
> fragment....")?
Not here. I am just making the quasi obvious remark that physicist
needs the concept of number, or anything equivalent (like real numbers
+ trigonometry) in their theory.
> I love your extension of 'metaphors' (bosons) into galaxies and
> brains. They certainly are, included into our presently valid
> "perceived reality" of figments.
Yes. With comp, brains, galaxies, atoms, still exists, but not as
first order citizens. This is not obvious, and is the conclusion of
UDA. This is so counter-intuitive that I have no problem with those
who takes this as a reason to doubt comp. Without the Everett-QM
confirmation, I would have believed that this is close to a refutation
of comp.
>
> "Scientists do not commit themselves ontologically...."
> Most - (especially the conventional ones) do.
This is due to the abandon of theology (the fundamental science) by
academy to temporal political power. Atheists and Christians are ally
against the reintroduction of non confessional theology in the
academy. This explains why there is a still widespread belief that
science can do ontological commitment. But then it is no more science
but "religion".
> I find it a restriction of the total into the so far experienced
> portion - even to the adjusted format of those - serving as the
> 'entirety this 'ontology' is based on. I would love to device an
> ontology for the 'totality' - that would explain lots of
> questionmarks we still have in our ignorance (the how-s, why-s, and
> the other 1000 to be modest).
Comp provides a vast range of acceptable and equivalent *hypothetical*
ontology.
The hypothetical ontology of comp is a subset of all scientific
theories today.
This has nothing to do with the fact that comp entails that we can
stop speculating on matter. Even if matter exists, it would be an
epiphenomenon, or better, an epinoumenon. Almost exactly like
invisible horses driving the cars. But this should not be considered
as obvious. It is a consequence of comp which needs some reasoning.
> I am not sure about the 'excluded middle' since that is excluded
> from a mere segment we consider 'them all' while the entire set may
> include quite another middle. (My usual objection against
> statistical conclusions and probabilities of course, that are mere
> illusions of our human ways of anticipatory thinking).
>
> I intended this reflection to be 'positive' to your ideas, as
> considered them in more ways than just 'arithmetically
> based' (numbers?).
I will try to reassure you about the idea that "arithmetically based"
could be a reductionism, or a restriction. On the contrary, this idea
leads to the idea that universal machine should have the right to vote
(to put the things in this way). With the discovery of the universal
machine, there is a sense to say that now we really have a better view
on our ignorance, which appears to be larger than what we could ever
have conceived before the work of Cantor, Kleene, etc.
The universal machine is not the solution of our problems. The
universal machine *is* our problem. (Assuming comp/CTM).
I think that I will have to make a little detour into other
"impossibility theorem". I can already hear you saying that an
impossibility theorem is impossible, because impossible could be a
relative notion. But this is not the case, mathematics kicks back, and
many things are just impossible, sometimes absolutely impossible, and
sometimes we can prove it to ourself (assuming our consistency).
You cannot prove that an impossibility theorem is not possible,
because if you prove that, you are proving an impossibility theorem!
Of course we need some faith, that 0 is different from 1, for example,
but not much more. I intend to show that the principle of excluded
middle can be seen as a tolerance-of-ignorance principle. As I said to
Brent a long time ago, the excluded middle principle is more a rule of
politeness among persons than a platonic reality. With comp, it
reveals, in 'Arithmetica', incredible and innumerous unknown forms of
'living entities', and some incredible mess, too. The Mandelbrot set
provides some partial illustration of that phenomenon(*).
Bruno
(*) You may enjoy this interpenetration of two parts of the M set. M
invades itself, as you can see when zooming on the border of a little
Mandelbrot. As in this "dezoom":
http://www.youtube.com/watch?v=KnJLcyHOUHc&feature=channel_page
>
> On Fri, Sep 4, 2009 at 5:12 PM, Bruno Marchal <marc...@ulb.ac.be>
> wrote:
>
>
> On 04 Sep 2009, at 19:21, Flammarion wrote:
>
> > ... Bruno has been arguign that numbers
> > exist because there are true mathematical statements asserting their
> > existence. The counterargument is that "existence" in mathematical
> > statements is merely metaphorical. That is what is being argued
> > backwards
>
>
>
> I have never said that numbers exists because there are true
> mathematical statements asserting their existence.
>
> I am just saying that in the comp theory, I have to assume that such
> truth are not dependent of me, or of anything else. It is necessary to
> even just enunciate Church thesis. A weakening of Church thesis is 'a
> universal machine exists". In the usual mathematical sense, like with
> the theorem asserting that 'prime numbers exists.
>
> I just make explicit that elementary true arithmetical statements are
> part of the theory. You are free to interpret them in a formlaistic
> way, or in some realist way, or metaphorically. The reasoning does not
> depend on the intepretation, except that locally you bet you can 'save
> your relative state' in a digital backup, for UDA. And you don't need
> really that for the 'interview' of the universal machine.
>
> All theories in physics uses at least that arithmetical fragment. But
> fermions and bosons becomes metaphor, with comp. May be very fertile
> one. Like galaxies and brains.
>
> Scientist does not commit themselves ontologically. They postulate
> basic entities and relations in theories which are always
> hypothetical. I am just honest making explicit my use of the non
> constructive excluded middle in the arithmetical realm.
>
> You get stuck at step zero by a bullet you are ntroducing yourself, I
> 'm afraid.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
>
> >
http://iridia.ulb.ac.be/~marchal/
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