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.`

## Advertising

`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.`

`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.`

`If it is formal game playing, just play the game. The theory is enough`

`precise to allow that.`

`Do you have a definition of formalism which does not rely on`

`arithmetical realism. AR is the weakest assumption on which all`

`mathematician agree (except ulrafinitist). 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. 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).`

`Could you define *formally* 'real existence'? 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. 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). Adding`

`unnecessary metaphysics just add noise. Study the proof, and criticize`

`it. You might be adding an interpretative layer which exists only in`

`your mind, I'm afraid.`

Bruno On 07 Feb 2011, at 23:55, 1Z wrote:

On Feb 7, 4:06 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:On 06 Feb 2011, at 22:20, 1Z wrote:On Feb 5, 7:43 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:Computationalism needs Church thesis which needs AR (Arithmetical Realism).Nope, just AT (arithmetic truth).Actually, comp needs only, for the ontology, the quite tinycompleteSigma_1 truth.As I have stated many times, it doesn;t matter in the least how many or few immaterial objects you attribute existence to. It's like saying pixies exist, but only a fewWhat? It is always better to make a theory precise.The theory that some precise number of pixies exist is just as wrong as the theory that some indeterminate number exists. Mathematical anti realists hold that *no* mathematical objects exist. And they still accept CT and all the rest.Please don't put metaphysics where there is only religionBelieving in what is not proven is religion. I can argue for anti realism.I argue in favor of nothing.You argue that some subset of mathematics has immaterial existence.That's philosophy. You force me to be explicit on this; I do science. I am a logician, and I show that rational agent believing in comp believe that ... etc. I don't know about the truth.(saying yes to the admittedly betting doctor).Saying yes to the doctor will not guarantee your immaterial existence if there is no immaterial existence.But there is immaterial existence.To be fair, that's an unargued claim, not an argument.I recall you that I say in theontological context that something exist if Ex (bla-bla-bla x) istruein the standard model of arithmetic.Utterly wrong. In the *mathematical* context something exists if there is a true backwards-E statement asserting it, but the whole point of anti realism is that that is merely game playing and does NOT imply RITSIAR ontological existence.I use the standard meaning of existence of numbers, etc.As I have told you many times, there is no standard meaning. http://en.wikipedia.org/wiki/Philosophy_of_mathematicsAR/Platonism is a separate assumption to yes Dr.I have drop out AR. You need AR (in which everyone believes excepttheultrafinitists and the bad faith philosophers) to understand the term "digital" used by the doctor.No you don't. Mathematical anti realists can understand "digital computer"<And with comp,it is math, indeed, even (full, above Sigma_1 arithmetic.Arithmetical realism is what you need to apply the excludedmiddle incomputer science and in arithmetic.The excluded middle is a much of a formal rule as anthing else. Formalists can apply it, so it is compatible with anti realism.The theory admits a formal study. You don't act like a formalist at all. The term "Formalism" makes not an atom of sense without arithmetical realism.Formalism is a major variety kind of anti realism.In philosophy arithmetical realism is the weaker of all possible realism, except again for the ultrafinitists.The weakest kind is NONE WHATSOEVER....no pixies. Zip. Nada.If you are formalist and anti realist on the numbers you are in contradiction,What contradiction?or, once and for all, just replace numbers by thefollowing formal expression 0, s(0), s(s(0)), etc. + the axioms Ijustsent to Andrew, etc.Yep. Formalism says you have rules, and you manipulate them and certain things seem to move around a change, and we call those sets and numbers....and they don't really exist. When you switch off your PC there is no more Supermario, and when you stop doing maths there are no more numbers.AUDA provides more than a formalism,I don;t mean "a formalism"=" a mechanisable system for applying rules" I mean "formalism"="the claim that mathematics is a game played according to various sets of rules and is not 'about' any real entity". I have pointed out the distinction to you many timesit provides an arithmetisation, which is a *weakening* of formalism, made possible by AR. Gödel already exploited this.To understand the fundamental consequences of Church thesis you need to accept that some programcomputes function despite we have no means to know if it is totalorpartial, or that a program will stop or not.And I can accept that by positing LEM as a formal rule. I don;t have to posit an immaterial Plato's heavenI make clear that the immaterial Plato Heaven for the machine is just the truth of arithmletical proposition.Truth is not existence.It is an non arithmetical notion, union of the entire Kleene-Mostowki arithmetical hierarchy, and well know non controversal mathematical object in the field of logic.Sighh.to anti-realists, all immaterial existence is controversialI use the "immaterial Plato heaven" terminology, either as poetical shortcut,Well, it isn;t material since matter is some sort of iluusion within it, according to youor as a point in the arithmetical representation of some term in Plotinus theory. I explained this already to you, but you keep adding metaphysical stuff which don't exist.It's metaphyscial already. I exist , and you say I am a programme that is not running on a physcial platform. That adds up to a statement about existence. You are making a statement about me, so you are making a statement about existence. You conclusion is ontological, so it either comes from an ontological premise or it is a non sequitur.Only ultrafinitist denies AR.Wrong. Anti realists deny it. I have pointed this out many times. You think the only debate is about the minimal set of mathematical objects, and that is not the only debate. Anti realists can accept a maximal set of objects, with the proviso that their existence is fictive and not real existenceI am agnostic on all notion of existence.All, except my own consciousness here and now.You keep insisting that some subset of arithmetic exists!!!!I suggest a theory, and derive consequences in that theory.AR+, the idea that we don't need more than AR, in this setting,is aconsequence of the math. From 'outside' the tiny effectiveuniversalsigma_1 complete set is enough. from inside, even mathematicalismisnot enough (it is more 'theologicalism').The ontological status of mathematical objects is a area of contention in metaphysics, and not straightforwardly proven by mathematics itself.With comp, you don't need more than the part on which almost everybody agrees: arithmetical realism.Anti realists do not agee on the real existence of any part. There are no pixies at all, not just a few pixies.If you believe in prime numbers,I don't. No pixies means no pixies.and if you are patient and good willing, I can explain that there are all universal numbers, and why assuming comp that's enough and that's necessary to solve the white rabbit problem. And that postulating physical laws miss the epistemological existence of the qualia.The basic ontology is not important. If you take less than auniversalsystem (like numbers, combinators, ...) you don't have enough for comp, if you take more you miss the qualia.No problem with a formalist interpretation of all this. ActuallyS4Grzformalize at the meta-level what the machine can uderstand to be non formalisable (like consciousness).The engineers, the scientists, most philosophers. Except for Thorgny Tholerus I never met an ultrafinitist. You don't have to decide if numbers are idea of the mind or sort of angel in Plato Heaven. With comp the very idea of number will itself be a number, a sort of second order number, relative to universes (universal numbers).ULtrafinitism has nothing to do with it. For formalists no number exists. They have no prejudice about any kind,If comp is false because, according to you 7 does not exist, then it is your problem.I never said that. The whole point is that comp and AR are *separate* assumptions. The one is *not* a corollary of the otherI told you that I am working in a theory, which is neutral on those question. Formalist have normally less problem with a tiny sigma_1 arithmetic than with the real or complex numbers.Anti realist formalists, and any other kind of anti realists DO NOT ACCEPT THE REAL EXISTENCE OF ANY MATHS AT ALL. *****Nooooooooo******* pixies!I just don't believe you don't believe in seven.Well, I don't. And I have been having the same argument with you for years, and you really need to stop thinking in your box.You confuse 'immaterial' with 'inexistent'. If you don't believe in seven, do you still believe in the formal expression s(s(s(s(s(s(s(0))))))) ?I believe in the pixels I am looking at..which are material. But that is the existence of pixels, not of numbers or sets.http://en.wikipedia.org/wiki/Philosophy_of_mathematicsAnd you cannot refute an argument by anticipating a refutation. So if you have a refutation of MGA you should present it.See Colin Klein;s refutation of Maudlin's Olympia.We have already discussed this and Colin Klein does not touch the movie graph argument.Then you had better stop saying the MGA and Olympia are equivalentThe movie graph *argument*, is not attacked by Klein. Klein attacks the Olympia *argument*.When I say that Olympia and MGA are equivalent, I am talking abouttheconclusion, not about the arguments leading to the conclusion. Bruno http://iridia.ulb.ac.be/~marchal/--You received this message because you are subscribed to the GoogleGroups "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.

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