On 09 Feb 2011, at 15:20, 1Z wrote:
On Feb 8, 6:08 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
Peter,
you say that you are a formalist. I gave you the definition of
realism
which works for the understanding of the reasoning. It is the
acceptation of (P v ~P) when P is intended on the domain of the
natural numbers.
I can accept that as a *formal* rule that doens't mean anything
ontologically,
just like I can accept that some but not all Snarks are Boojums.
Yes, please, do that.
You
cannot come
to ontological conclusions just by writing down an axiom.
I don't do that. But I disagree with your point. here is a
counterexample:
Theory: God and Mary ontologically exist.
Conclusion: Mary ontologically exist.
Worse, the
decision
to use the Law of the Exclude Middle or not (it can of course be
dropped without
incurring a contradiction) is typically motivated by ontological
considerations.
We think LEM applies to past events because we think they either
happened
or they didn't. We doubt that it applies to future events.
I use LEM only in arithmetic.
That's all.
By standard use of numbers I mean the element (N, +, *) as
taught by mathematicians. I show that comp makes *some* theology as
part of the discourse of machine. This should not give any trouble,
*especially* to a formalist.
The idea that a hypothetical machine would give certain hypothetical
responses wouldn't, but of course, you are saying more than that:
you are saying that *I* am an immaterial machine. And that's an
ontological claim which cannot be supported by a merely formal
premise.
It is not more ontological that the premise that I could survive with
a digital brain. The rest is reasoning. It is up to you to find the
mistake, if you believe there is one. Please study the reasoning,
because it makes clear what is used and meant in the hypotheses. The
point is mainly "epistemological", although we might argue on this
too. The point is that physics is a branch of arithmetic, and that it
can be extracted (formally) from computability theory + the self-
reference logic (provability theory).
A mathematical anti-realist is an ambiguous expression. How could
them
believe in Church thesis which is equivalent with the assertion
that a
universal number exist in arithmetic.
In the way that I have explained to you a thousand times: the
assertion
that certain entities exist is just taken as part of the game.
No. You insist that there is primary matter. I am neutral on this. But
I do show we don't need that hypothesis to undersatnd why the
universal numbers develop beliefs and discourse on primary matters and
physical laws.
If it is formal game playing, just play the game.
If I just play the game I am never going to conclude that
I *am* a dreaming machine, any more than I am going to
conclude I am Supermario
You forget the "yes doctor" part of comp, which plays a crucial role
in the reasoning. I don't want to argue if it is ontological or not.
That is not needed to understand that physics is no more the
fundamental science once comp is assumed.
The theory is enough
precise to allow that.
Do you have a definition of formalism which does not rely on
arithmetical realism.
Yes: formalism is the claim that no mathematical
entities actually exist,
Well, that is you own physicalist definition. A general formalist
believes the same for any theory, and never assume things like primary
matter. You are not a formalist in math, but a conventionalist. But
then I think you have missed the failure of formalism and logicism in
math due to incompleteness.
that mathematics is just
the exploration of the consequences of various rules
and axioms, and that mathematical truth is contextual
to the system employed and has no wider significance.
That has been refuted by Gödel a long time ago, and is not what
mathematician call formalism, after Gödel.
AR is the weakest assumption on which all
mathematician agree (except ulrafinitist).
Formalists think it is true as well,,,but it is not a truth
about anything outside the game.
Then stay in the game. Of course, if you ever say "yes" to the digital
doctor, then the consequence are no more purely formal.
By works done by Glivenko,
Gödel and Heyting we know that intuitionist arithmetic (typically
anti-
realist) and classical arithmetic are essentially identical, and
process the same ontology.
You mean the same model. Ontology cannot be proven by
mathematical argument, it is meta-mathematical and metaphysical.
Yes the same model. It is OK to see it that way.
Real math (and formal) differences appears
only in analysis and set theory (on which I tend to be not realist,
although the work is neutral on this).
Formalists do not differ on which parts of maths are
true and false, they differ on its epistemology and
ontology.
OK. No problem.
Could you define *formally* 'real existence'?
There is no reason I should, and at least one reason I shouldn't:
I have stated that real existence cannot be established by formal
arguments.
Like non real existence. But then why do you keep insist that numbers
and math object have non real existence?
Formalists do not think everything is merely formal
game playing, they think maths is *as opposed to* other
things which are not.
Not true. That's the old conventionalism. All this has no relevance
for the reasoning.
Could you define
formally 'primitively material', so that we can continue to agree or
disagree on something. Or you might try to get my point, after all.
It
only shows the difficulty with such notions.
All philosophical problems are difficult, and that is no excuse
for pretending that there is nothing to a notion such a "real
existence"
You are the one using difficult concept with a tone that a reasoning
should be doubted, without providing any reason why. I was just asking
for clarification.
Obviously, as Chalmers
rightly insists, no formal characterization of consciousness can be
given. But comp makes it possible to retrieve formality as the meta-
level. That's the S4Grz1 formalism. It makes its possible to work
on a
purely formal account of what machine cannot formalize, and it shows
that machine can, like us, build meta-formal account of those things.
Once and for all, keep it mind that when I utter that a number exist,
I am just like PA proving a sentence of the form ExP(x), and
everything will flow easily (well with some effort).
Nope. The claim that I am, ontologically, an immaterial dreaming
machine
does not follow from PA.
It does from PA + comp (= CT+ YD).
Adding
unnecessary metaphysics just add noise.
The conclusion is metaphysical, therefore the argument
must be or the conclusion is a non-sequitur. Therefore
metaphysics is a necessity for you.
No the conclusion is scientific, in Popper's sense. Physics is given
by Bp & Dp (& p), with p sigma_1. This is 100% testable.
Without AUDA, you have also testable conclusion. It is that observable
reality appears as non local, indeterminist and that piece of matter
is non clonable, and that physics is given by a measure on the
computational histories (and that point is made formal with the Bp &
Dp (& p) stuff.
It is the main originality of the comp approach: it does science
(perhaps on the territory of philosophers, which would explain they
attempt to discard it, like the Church discarded earlier astronomers.
Study the proof, and criticize
it. You might be adding an interpretative layer which exists only in
your mind, I'm afraid.
OK?
Bruno
http://iridia.ulb.ac.be/~marchal/
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