On Feb 9, 4:35 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> 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.

I already am

> > 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.

Sigh...You cannot come to ontological conclusions just by writing down
a logical or mathematical axiom.

> > 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.

Pure arithmetic cannot reach ontological conclusions

> >> 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.

What does "digital" mean here? Made of silicon.... or made of numbers?

There is a bait and switch going on here. The guy goes into the
agrees to the digital brain, and walks out thinking the doctor is
going to
laboriously build a machine or write a programme. Instead, the doctor
sits back confident that a digital brain already exists as an
immaterial number

>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,

If there is no reality to numbers, arithmetic cannot even produce the
appearance of physics. Illusions have a real basis. Again, you need
an ontological premise.

>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.

Whether I do or not has no bearing on how formalists interpret
mathematical existence postulates.

> 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.

We  need the postulate that numbers exist, because non existing
things have existing beliefs.

> >> 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.  

Well, you should.

> That is not needed to understand that physics is no more the  
> fundamental science once comp is assumed

Comp alone does not do it.

> >> 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.

"Conventionalism: This is also called formalism. In Kantian terms this
is the view that mathematics is analytical a priori. In other words,
that all mathematical statements are true by definition or


> then I think you have missed the failure of formalism and logicism in  
> math due to incompleteness.

Sigghh..no that's the failure of Hilbertian formalism, not of
game-playing formalism.

> > 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,

I disagree.

> 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.

Is the doctor promissing me a brain made of silicon or of numbers?

> >> 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?

I am not claiming to have proven mathematically. I am arguing it
how it should be argued, as an explicitly metaphysical claim.

> > 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.

They are synonyms.

> All this has no relevance  
> for the reasoning.

> >> 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).

No, because those are not sufficient to show that there
are any immaterial machines in the first place --  the "I am"
therefore being

> >> 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.

It is perfectly possible to be both scientific and metaphysical.

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