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 doctor, 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 convention." http://www.blacksacademy.net/content/2964.html >But > 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 irrelevant > >> 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. -- 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.
