On 09 Feb 2011, at 15:20, 1Z wrote:

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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 ofrealismwhich 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 couldthembelieve in Church thesis which is equivalent with the assertionthat auniversal 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 (typicallyanti-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 ordisagree on something. Or you might try to get my point, after all.Itonly 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 workon apurely 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/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.