Re: Bruno's argument
Bruno, \I don't see relevance in your example. I do not argue against singling out ONE number amongst all, I argue against singling out numbers amongst nuimbers AND non-numbers. In this sense numbers make sense only in relation with non-numbers. John - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: Sent: Tuesday, July 18, 2006 10:25 AM Subject: Re: Bruno's argument Le 17-juil.-06, à 20:54, John M a écrit : > In my 'wholistic' (not 'holistic!) 'taste' (<:I don't > call my narrative a worldview or hypo or theory:>) the > entire interconnection generates ANY further item > (step in any process) with no excludability of any. > One cannot pick ONE without tacitly including all > others. The same with numbers, I note in passing. You cannot believe in all numbers except this one. The number 17 exists only in relation with all the other numbers, in some sense. I would say the mathematical truth is wholistic. Perhaps even holistic ? Bruno http://iridia.ulb.ac.be/~marchal/ -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.394 / Virus Database: 268.10.1/390 - Release Date: 7/17/2006 --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: K the Master Set (+ partial answer to Tom's Diagonalization)
Hi Bruno Each one of us like to do what we do best and we apply our preferred techniques to the problem at hand. Thus a mechanic may solve the pollution problem by building electric cars, and the cook may solve the same problem by preparing vegetarian meals. As a mathematician you are trying to compose a theory of everything using mathematics, this is understandable, and you came up with COMP which is strongly rooted in mathematics and logic. I came up independently with my own concept involving a generalization of relativity to information theory ( my background is engineering/physics) and somehow we seem to agree on many points. Unfortunately I do not have the background and the time to give my ideas a formal background. It is just an engineering product and it feels right. I believe that what you are saying is right, however I am having some trouble following you, just like Norman Samish said. It would help if you outlined a roadmap. Then we would be able to follow the roadmap without having to stop and admire the mathematical scenery at every turn even though it is very beautiful to the initiated, I am sure. For example you could use several levels of explanation: a first level would be as if your were talking to your grandmother; a second level, talking to your kids (if they listen); a last level, talking to your colleagues. George --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only Existence is necessary?
Bruno and 1Z: both of you write extraordinary wise remarks in approx. 3-4 times as many words than I can attentively folloow. However - with mostly agreeing with the positions of BOTH OF YOU - I may remark (hopefully in less words??) * I consider the epistemic development of our experience about the world, from precaveman on, so I consider the figments of earlier explanations reflected in ongoing (scientific and common sense) thinking. Matter(ly?) is a primitive view physicists picked up centuries (25+?) ago and still ride it. I don't know better myself. Experimental (truth) is gathered by whatever constructs the appropriate epistemic level allowed for instrument design and for (sweatty) explanations on "readings". Math contributed always to the misunderstganding by equating the primitively cut model-views into soothing matchings: to satisfy the 'savants'. As long as we do abide by the past misunderstandings (and I mean EVERYTHING gotten from past wisdom) and do not regard them just as hints for a better thinking, we go in circles. Example the multiverse as a replications of this one we observe (as we can). I had no echo on 'my' multiverse: universes in "all possible" qualia and "all possible systems (some of them - maybe - CAPABLE OF CONTACTING US. That reaches into sci-fi, into the 'zookeeper' theory, even a rational foundation for many religious miracles and their systemic explanations. E.g. teleportation marvels and Q-suicide etc.) 1Z mentions 'mentality of matter' - of course, if we consider the m-word as ideational functioning, any following of 'rules' in the coexistence(?) simplified in our physics (and logical) reductionism as 'laws'. Matter is more difficult, we 'grew' into percepts over milennia to assign response to impact as 'hard', 'pain', 'warm', whatever. The "all possible" is a hard phrase, WE are not to tell what is (=we find) possible or not. Matter, particles are not possible, they are explanations for our age- long ignorance and so leveled explanations, which went as inherited memes into our basic 'mental' construction and gives foundation to the ways we think. I cannot elaborate on these features, cannot defend them in an argument, cannot even 'think' in them: I am (I hope) a human being with all the imperfections. And I may be wrong, just as any other thinking person. John Mikes --- 1Z <[EMAIL PROTECTED]> wrote: > > Bruno Marchal wrote: > > > Le 12-juil.-06, � 18:06, 1Z a �crit : > > > > > > > > I mean that is what material exists regardless > of any mathematical > > > justification. > > > > So this is your main hypothesis: what is material > exist. > > Now my problem is that a term like "material" is > very vague in physics, > > Huh ? Physics studies matter, energy, time and > space. Those > are its topics. Physics may not have a single neat > definition of > matter, but > that does not mean physicsts are a lot to know what > it is. > Arguably, the whole of economics is a definition of > "money", > Likewise for physics and matter. > > > > and I would say experimentally vague since the > birth of experimental > > quantum philosophy (EPR, Bell, Shimoni, Feynman, > Deutsch, Bennett ...). > > Huh Electrons and photons are still > matter...what *do* you mean ? > > (BTW, Deutsch uses the Johnsonian "if it kicks back" > appraoch > to reality). > > > > The big problem with the notion of *primary* > matter = how to relate > > "1-experiences" with "3-experiments". > > The mind-body prolbem boild down to qualia, and > the problem of qualia and physics boils down to > the problem of qualia and mathematical description > > > Consciousness is a problem for all forms of > materialism and physicalism > to some > extent, but it is possible to discern where the > problem is particularly > acute. > There is no great problem with the idea that matter > considered as a > bare substrate can > have mental properities. Any inability to have > mental proeprties would > itslef be a property and > therefore be inconsistent with the bareness of a > bare substrate. The > "subjectity" of > consciouss states, often treated as "inherent" boils > down to a problem > of communicating > one's qualia -- how one feesl, how things seem. Thus > it is not truly > inherent but > depends on the means of communication being used. > Feelings and seemings > can be more readily > communicated in artistic, poetice language, and > least readily in > scientifi technical > language. Since the harder, more technical a science > is, the more > mathematical it is, > the communication problem is at its most acute in a > purely mathematical > langauge. > Thus the problem with physicalism is not its posit > of matter (as a bare > substrate) > but its other posit, that all properties are > phycial. Since physics is > mathematical, > that amounts to the claim that all properties are > mathematical (or at > least mathematically > describable). In making the transition from a > physicalist world-view to > a
Re: SV: Only Existence is necessary?
Bruno Marchal wrote: > Le 12-juil.-06, à 18:06, 1Z a écrit : > > > > > I mean that is what material exists regardless of any mathematical > > justification. > > So this is your main hypothesis: what is material exist. > Now my problem is that a term like "material" is very vague in physics, Huh ? Physics studies matter, energy, time and space. Those are its topics. Physics may not have a single neat definition of matter, but that does not mean physicsts are a lot to know what it is. Arguably, the whole of economics is a definition of "money", Likewise for physics and matter. > and I would say experimentally vague since the birth of experimental > quantum philosophy (EPR, Bell, Shimoni, Feynman, Deutsch, Bennett ...). Huh Electrons and photons are still matter...what *do* you mean ? (BTW, Deutsch uses the Johnsonian "if it kicks back" appraoch to reality). > The big problem with the notion of *primary* matter = how to relate > "1-experiences" with "3-experiments". The mind-body prolbem boild down to qualia, and the problem of qualia and physics boils down to the problem of qualia and mathematical description Consciousness is a problem for all forms of materialism and physicalism to some extent, but it is possible to discern where the problem is particularly acute. There is no great problem with the idea that matter considered as a bare substrate can have mental properities. Any inability to have mental proeprties would itslef be a property and therefore be inconsistent with the bareness of a bare substrate. The "subjectity" of consciouss states, often treated as "inherent" boils down to a problem of communicating one's qualia -- how one feesl, how things seem. Thus it is not truly inherent but depends on the means of communication being used. Feelings and seemings can be more readily communicated in artistic, poetice language, and least readily in scientifi technical language. Since the harder, more technical a science is, the more mathematical it is, the communication problem is at its most acute in a purely mathematical langauge. Thus the problem with physicalism is not its posit of matter (as a bare substrate) but its other posit, that all properties are phycial. Since physics is mathematical, that amounts to the claim that all properties are mathematical (or at least mathematically describable). In making the transition from a physicalist world-view to a mathematical one, the concept of a material substrate is abandoned (although it was never a problem for consciousness) and the posit of mathematical properties becomes, which is a problem for consciousness becomes extreme. > The naïve idea of attaching consciousness to physical activity leads to > fatal difficulties. Do you mean the Maudlin/Olympia/Movie argument ? But that is very much phsyical activity as opposed to physical passivity. If you are the kind of physicalist who thinks counterfactuals and potentials are part of the total physical situation, the Maudlin argument has little impact. > >> Well, why not, if that is your definition. I understand better why you > >> say you could introduce "matter" in Platonia. Plato would have > >> disagree > >> in the sense that "matter" is the shadow of the ideal intelligible > >> reality. > > > > What is material exists. Whether Platonia exists > > is another matter. It is for Platonism to justify itslef > > in terms of the concrete reality we find oursleves in, > > not for concrete reality to be justify itself in terms > > of Platonia. > > It depends of the assumptions you start from. Of course. I start from the assumption that I exist, since I do. I don't start from the assumtion that numbers exist supernaturally , floating around in Plato's heaven. > > The "intelligible" is a quasi-empiricist mathematical epistemology. > > Mathematicians are supposed by Platonists to be able to "perceive" > > mathematical > > truth with some extra organ. > > > That is naïve platonism. Already condemned by Plato himself and most of > his followers. Read Plotinus for more on this (especially Ennead V). The question then is whether numbers have any role at all, if they have no epistemological role. > >> I don't understand what you mean by "numbers don't exist at all". > > > > Well, I've never seen one. > > > Again that would be a critics of naïve Platonism. As I have said: > "number n exists in Platonia" means just that the proposition "number n > exists" is true. For example I believe that the equation > x^2 - 61y^2 = 1 admits integers solutions independently of any things > related to me. If that is all it means, it cannot possibly support an argument whose conclusion is that something really exists. The conclusion of a deductive argument has to be implicit in its premisses. > >> Numbers exists in Platonia in the sense that the classical proposition > >> "4356667654090987890111 is prime or 4356667654090987890111 is not > >> prime" is true there. > > > > It's true here. why bring Platonia into
Re: SV: Only Existence is necessary?
Bruno Marchal wrote: > Le 18-juil.-06, à 16:37, 1Z a écrit : > > > > A computer simulation is obviously computable. > > > Not necessarily from the first person povs. It is far from obvious that a simulation even contains 1stP POV's. In any case that doesn't effect the logic: simulations *might* be detectable, so they are not necessarily indetectable. > No. But what actually *seems* to exist, could emerge from mathematical > truth. No, same problem. There's no more any phenomenality to be found in maths than any substantiallity. --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only Existence is necessary?
Le 18-juil.-06, à 16:37, 1Z a écrit : > A computer simulation is obviously computable. Not necessarily from the first person povs. > The word "emerge" is often used to hide magic. I agree with you. Often, but not necessarily always. > What actually exists cannot emerge from mere truths. No. But what actually *seems* to exist, could emerge from mathematical truth. Sometimes I feel we agree on everything except the theory we play with. 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only Existence is necessary?
Bruno Marchal wrote: > Le 18-juil.-06, à 12:30, 1Z a écrit : > > >> Quentin Anciaux: Because if you were in a "simulation" and you have > >> managed to get out of it, > >> how can you know you have reach the bottom level of reality (ie: the > >> material > >> world then) ? How can you know the new real world you are now in is > >> the real > >> world and not another simulation ? > > > > 1Z: e.g it has some non-computable physics. > > > But comp and platonism already predict some non computable physics. You > said it yourself by pointing correctly that platonism leads to the > apparent possibility of HP universe (Harry Potter Universe, or flying > pigs, or random noise, ...). Platonism obviously implies non-computability, since non-computable functions mathematically exist. However, the claim was that we are in a computer simulation. A computer simulation is obviously computable. >The mystery with "naive comp" is that it > remains something apparently computable in our neighborhood. > And that "mystery" cannot be used as a straightforward refutation of > comp, once we look at the non trivialities of computer science and of > consistent self-referential discourses. > > If we bet on comp, then we can already bet we already live in a > simulation, the natural one which emerges from the "creative nature" of > the relations between numbers. The word "emerge" is often used to hide magic. What actually exists cannot emerge from mere truths. --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Bruno's argument
Le 17-juil.-06, à 20:54, John M a écrit : > In my 'wholistic' (not 'holistic!) 'taste' (<:I don't > call my narrative a worldview or hypo or theory:>) the > entire interconnection generates ANY further item > (step in any process) with no excludability of any. > One cannot pick ONE without tacitly including all > others. The same with numbers, I note in passing. You cannot believe in all numbers except this one. The number 17 exists only in relation with all the other numbers, in some sense. I would say the mathematical truth is wholistic. Perhaps even holistic ? 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only Existence is necessary?
Le 18-juil.-06, à 12:30, 1Z a écrit : >> Quentin Anciaux: Because if you were in a "simulation" and you have >> managed to get out of it, >> how can you know you have reach the bottom level of reality (ie: the >> material >> world then) ? How can you know the new real world you are now in is >> the real >> world and not another simulation ? > > 1Z: e.g it has some non-computable physics. But comp and platonism already predict some non computable physics. You said it yourself by pointing correctly that platonism leads to the apparent possibility of HP universe (Harry Potter Universe, or flying pigs, or random noise, ...). The mystery with "naive comp" is that it remains something apparently computable in our neighborhood. And that "mystery" cannot be used as a straightforward refutation of comp, once we look at the non trivialities of computer science and of consistent self-referential discourses. If we bet on comp, then we can already bet we already live in a simulation, the natural one which emerges from the "creative nature" of the relations between numbers. 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
K the Master Set (+ partial answer to Tom's Diagonalization)
Hi Tom, Hi George, George, and others, you can skip the "partial answer to Tom", and go directly to "K, the master set" below. Tom seems to propose an alternate proof, which does not convince me, although I cannot right now provide a full counter-example. Note that the section "K, the Master Set" could already put some light on that matter. 1) Partial answer to Tom: Le 17-juil.-06, 22:42, Tom Caylor a crit : >> Now *your* G is just defined by G(n) = GEN2(n). > > But doesn't G output the range of one of the set of *all* partial > recursive functions, whereas GEN2 outputs the code of a *fortran* > program? So shouldn't it be the following, where execute() actually > executes the fortran program generated by GEN2(n)? > > G(n) = execute(GEN2(n)) I should have written G(n) = Gen2(n) (n) (= execute Pn on n) >> Tell me if you are convince that "your" and "my" G are programmable. >> > > They are both programmable, but I think they are both non-*executable* > on "k" (if G=Fk), for the same reason, self-reference. Let me give you a counterexample with a sequence of total functions. Let Hi be a RE sequence of (codes) of total functions. (so the seq. Hi is from the seq. Fi) Let GBruno be defined by GBruno(n) = Hn(n) +1 Let GTom be defined by GTom(n) = Hn(n) Could GBruno belongs to the sequence Hi? If GBruno belongs to the Hi, it means there is a number kbr such that GBruno = Hkbr, thus GBruno(kbr) = Hkbr(kbr) = Hkbr(kbr)+1. So I can be sure that GBruno does not belong to the sequence Hi. OK? (the usual simple subtraction would lead to 0 = 1) Does GTom belongs to Hi? If GTom belongs to the Hi, it means there is a number kto such Gtom = Hkto, thus Gtom(kto) = Hkto(kto), which is the case by definition of "your" Gtom. No contradiction occurs, so in principle the total function Gtom could belongs to the list, and indeed is equal to the sequence Hi, despite self-reference. The same could be true for the partial recursive Fi. I don't see any reason why, if G(n) is defined by Fn(n), G should be necessarily undefined on its own index. Your argument could rely on the way you implement G. Actually I could perhaps build an ad hoc counterexample working for some particular enumeration of the Fi, but I need some time to do it, if it is possible So I propose we come back on this after a while. Probably you will figure out what is happening by yourself. Actually your intuition is right: something happens with self-application (see below). If I try to explain all of it here, this could be a little confusing. What you need to be sure of is the fact that when G(n) is defined by Fn(n)+1, then G(k) will be necessarily undefined on all k such that G = Fk. (Independently of the fact that you could be right that G'(k') is also undefined when G' (n) is defined by Fn(n), and k' is a code or index of G'; but your argument is not a proof because it depends on the precise way G is implemented). I must think ... 2) K, the Master set Emil Post, the founder of Recursion Theory, introduced the following set (of numbers) which will appears to be fundamental. It will correspond, in term of set, to the universal machine. K will be an universal RE set, capable of "generating" all RE sets. I recall the code of the RE sets are generable, and the RE sets are the domain Wi of the Fi. Definition: K is the set of numbers x such that Fx(x) is defined. So K is the set of natural number x such that the xth programs in the enumeration of the codes of all programs does stop when apply on itself. I prefer to talk about self-application instead of self-reference (to follow standard terminology). I give exercises (if only because my office is an oven and my brain is boiling hot): 1) Is K an RE set? Answer: yes (why?) 2) Is N \ K an RE set? Answer: no (why? Hint: diagonalization) 3) From this conclude that the halting problem is insoluble. 4) try to justify that someone having an algorithm for generating K will be able to generate any Wi. Put in another way, from a mechanical solution to the problem "does Fx(x) stop" we can construct an algorithm solving the apparent more general problem "does Fx(y)" stop. 5) From "2)" show that N \ K is productive (like the set of codes of the computable growing functions). That is N \ K is not only not-RE, but is constructively not-RE. You need to find an algorithm A such that for any Wi included in N \ K, A(i) will give an element in N \ K which is not in Wi. If you look at that Wi as an attempt to enumerate all N \ K, you can see the algorithm A as providing a counter-example. Conclude that N \ K can be better and better approximated by iterations in the constructive transfinite (like we done with the fairy). MAIN DEFINITION (Emil Post): A set E (of numbers) is called CREATIVE if 1) E is RE 2) N \ E is productive So the exercise can be sum up into: show that K is a creative set. There are deep relations between creative se
Re: SV: Only Existence is necessary?
Quentin Anciaux wrote: > Le Mercredi 12 Juillet 2006 23:54, 1Z a écrit : > > Bruno-computationalism is standard computationalism+platonism. > > Since I reject platomnism, I reject Bruno-computationalism > > (whilst having rather less problem with the standard computational > > thesis, that "cognition is computation"). > > If computationalism is true then platonism must also be true. > > Because if you were in a "simulation" and you have managed to get out of it, > how can you know you have reach the bottom level of reality (ie: the material > world then) ? How can you know the new real world you are now in is the real > world and not another simulation ? e.g it has some non-computable physics. > It is the turtle on the turtle on the > turtle... Even if you take "standard computational thesis", then by the > reasoning upper you must reject a bottom level real... ie: a material world, > a stuffy world... every reality is stuffy and real (from the inside). "(seemingly) real (from the inside" just doesn't add up to "really real". Your argument only works if you adopt solipsistic premises to start with -- if you just want to have your sensations explained. All you are saying is that if you don't care about what is ultimately true, you do need to bother with what is ultimately real. Equally, if you are interested in ultimate truth, you will need ultimate reality. It has no impact on a realist at all. (BTW, the same arguments that say you don't need matter mean you don't need Other Minds, so solipsism is very much the word!) --~--~-~--~~~---~--~~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
