Bruno Marchal wrote: > > On 17 Aug 2009, at 19:28, Flammarion wrote: > >> >> >> On 17 Aug, 11:17, Bruno Marchal <marc...@ulb.ac.be> wrote: >>> On 17 Aug 2009, at 11:11, 1Z wrote: >>> >>>> Without Platonism, there is no UD since it is not observable within >>>> physical space. So the UDA is based on Plat., not the other way >>>> round. >>> Are you saying that without platonism, the square root of 2 does not >>> exist? >> Yes, the square root of two has no ontological existence. > > > > All what matters with comp is that things like the square root of 2 > has a notion of existence independent of "me". > > > > >>> Prime number does not exist? >> Yes, prime numbers have no ontological existence > > I guess you make a "material" ontological commitment. One of my goal > is to explain, notably with the comp hyp, that a term like matter has > no referent. This would explain why physicist never use such > ontological commitment explicitly. > To say that matter exists simply is a non rational act of the type > "don't ask". UDA makes just this precise by reudcing the mind body > problem to a body problem. > > > >>> That mathematical existence is a >>> meaningless notion? >> Sense but no refence. Mathematical statements have >> truth values but do not refere to anything outside the >> formal system. > > Then they have no truth value. What you say is formalism, and this has > been explicitly refuted by mathematical logicians. > We know, mainly by the work of Gödel that the truth about numbers > extends what can be justified in ANY effective formal systems (and non > effective one are not really "formal"). > But I know that there are still some formalists in the neighborhood, > and that is why I make explicit the assumption of arithmetical > realism. It is the assumption that the structure (N, +, x) is well > defined, despite we can't define it effectively. > > >>> Mathematics would be a physical illusion? >> A referentless formal game, distinguished from fiction >> only by its rigour and generality > > You evacuate the whole approach of semantics by Tarski and Quine. I > will not insist on this because I will explain with some detail why > Church thesis necessitate arithmetical realism, and why this leads > directly to the incompleteness and the discovery that arithmetical > truth cannot be captured by any effective formal system. The formalist > position in math is no more tenable. > > >>> But physics use mathematics, would that not make physics illusory or >>> circular? >> No, because it uses mathematics empirically. The same >> language that can be used to write fiction can be used to >> write history. The difference is in how it used. not in the langauge >> itself > > I don't see any difference in the use of analytical tools in physics > and in number theory. The distribution of the prime numbers is > objective, and this is the only type of independent objectivity needed > in the reasoning. Nothing more. > > > >>>> It's a perfectly consistent assumption. THere is no >>>> disproof of materialism that doesn't beg the quesiton by >>>> assuming immaterialism >>> Well, I do believe in the natural numbers, and I do believe in their >>> immateriality (the number seven is not made of quantum field, or >>> waves, or particle). >> Then you are a Platonist, and you argument is based >> on Platonism. > > I believe that the truth of arithmetical statement having the shape > "ExP(x)" is independent of me, and you and the physical universe (if > that exists). > You can call that Platonism, if you want, but this is not obviously > "anti-physicalist". Non-physicalism is the conclusion of a reasoning > (UDA). > Given that Plato's conception of reality is closer to the conclusion, > I prefer to use the expression "Arithmetical realism" for this (banal) > assumption, and Platonism or non-physicalism for the conclusion. But > that is only a vocabulary problem. > > >>> So either you tell me that you don't believe in the number seven, or >>> that you have a theory in which the number seven is explained in >>> materialist term, without assuming numbers in that theory. >> The latter. > > Show it. I know an attempt toward "science without number" by Hartree > Field (wrong spelling?), but I found it poorly convincing. Most > physicists accept the objectivity of numbers. Even more so with the > attempt to marry GR and QM. > > > >>>>> This leads to major difficulties, even before approaching the >>>>> consciousness problem. >>>> Such as? >>> Explaining number with physical notions, >>> and explaining, even partially, physical notions with the use >>> numbers. >> That is just a repetition of the claim that there >> are problems. You have not in the least explained what >> the problems are. > > UDA is such an explanation. AUDA gives a constructive path toward a > solution. > > > >>>> You arguments here are based on the idea >>>> that primary matter needs to be given a >>>> purely mathematical expression. That in turn >>>> is based on an assumption of Platonism. If >>>> Platonism is false and materialism true, >>>> one would *expect* mathematical explanation >>>> to run out at some point. Your "difficulty" is a >>>> *prediction* of materialism , and therefore a >>>> successfor materailism >>> Not at all. Cf the "even partially" in my sentence just above. >> That sentence does not demonstate anything >> about anything. >> >>>>> and some physicists are already open, >>>>> independently of comp, to the idea that physical objects are >>>>> relative >>>>> mathematical (immaterial) objects. Which of course are "no >>>>> material". >>>>> Wheeler, Tegmark, for example. >>>> They have a consisent set of assumptions. So do >>>> their materialist oponents. You can't get an "is true" >>>> out of a "might be true" >>> Well the movie graph conclusion is that materialism is not >>> consistent, >>> unless it opt for eliminativism of persons and/or non >>> computationalism. >> Materialism=true and computationalism=false is a consistent >> set of assumptions. > > > I am not even sure of that, but given the fuzziness of the notion of > "primitive matter", why not. May be God created it in 6 days, or the > big bang in zero seconds. > I always felt that taking notion of matter, or consciousness, for > granted, is a creationist-like move on the type "don't ask". UDA shows > that we have to ask more precisely when we assume that personal > consciousness can be invariant for the change of implementations done > below the substitution level. > > > >> Moreover, the movie graph doesn;t prove >> what you say it does since it involves an illegitimate move from >> "minimal physical basis" to "no physical basis". > > It goes explicitly to "no physical activity" in the MGA3 thread. But > MGA2 is enough, due to the "qua computatio" condition in the "yes > doctor" hypothesis. I guessed that your problem is in the > understanding of UDA step-8. > > >>>>> I tend to believe in many immaterial things. Some are absolutely >>>>> real >>>>> (I think) like the natural numbers. >>>> There's your Platonism again. Believe what you like, but don' >>>> call it proof. >>> Given that the theorem is "comp => platonism", and given that I am >>> open to the idea that comp could be correct, I am of course open to >>> the idea that Platonism may be correct. >> The theorem is platonism=>UD, UD=comp=>immaterialism > > I am glad you see this. All what I have to do is convince you that > formalism does not work for arithmetic and mathematical computer > science. > > > > >>> But again, I don't need platonism (non-physicalism) to be an >>> arithmetical realist, like all classical mathematicians. >> Yes you do. The UD doesn't exist physically. If it doesn't >> exist non-physically either, it doesn't exist, and I am not >> a programme running on it. > > > Because you don't believe in anything non physical. But this comes > from your "formalist" position which does no more make sense after > Gödel. Each formal system, and machine, miss almost all arithmetical > truth. > > > >>> This is >>> explicit in the assumption. The non physicalism and general >>> immaterialism is a consequence of the movie graph argument. What is >>> wrong with it? >> >> The movie graph doesn;t prove >> what you say it does since it involves an illegitimate move from >> "minimal physical basis" to "no physical basis". > > > See MGA3. Actually the contradiction appears, in the movie graph, even > when the whole physical activity is still there, but is no more > corresponding to any computation. This is a subtle point, no doubt, > and it asks for an understanding of the computational supervenience > thesis, which I am explaining in the "seven step series" thread. > > >>>> It changes everything. If the UD is a useful ficiton, I cannot be a >>>> programme running on it, any more than I can book a flight to >>>> Narnia. >>> Would you say that the 1000^1000th base ten decimal of PI is a >>> fiction? >> Yes. I don't beleive in *any* pixies, not a single one. > > All what I need is that the statement "the 1000^1000th base ten > decimal of PI is even" is true or false independently of the > existence of me, the planet earth or the physical universe (if that > exists). > > > >>>>> There is a sense to say those universal machines do not exist, >>>>> but it >>>>> happens that they don't have the cognitive abilities to know that, >>>>> and >>>>> for them, in-existence does not make sense. >>>> If they don't exist, they don't exist. You don't have the >>>> rigourous mathematical argument you think >>>> you have, you have some baroque Chuang-Tzu metaphysics. >>> I do like Chuang-tzu, and I can see the relation between comp and >>> Chuang-tzu, although it is more clear with Lao-Tzu, as you may see in >>> "Conscience et Mécanisme", where an explicit correspondence is >>> suggested. >>> So, what you tell me is that you don't believe in *any* form of >>> mathematical existence. >> Not in any, and not in any pixies either. >> >>> So you reject arithmetical realism, and thus you reject comp. >> The computaitonal Theory of Mind has no implications about Platonism. > > Comp is based on the notion of digitalness, which needs Church thesis. > I will explain in detail why Church thesis needs arithmetical realism. > I think that you are confusing everyone by switching "arithmetical > realism" with "Platonism". If you call "Platonism" what I call > "Arithmetical realism", I will put the result in the following way: > comp => non physicalism. It leads to a reduction of the mind-body > problem to the search of an explanation of stable beliefs in matter, > without matter. AUDA provides the explanation, yet not the physical > theory (but still the logic of physical propositions). It explains the > appearance of "many worlds" below the substitution level. > > > >> You may of course mean something else by "comp"..... >> >>> Arithmetical realism is needed to give a sense to Church thesis, >>> which >>> is part of comp. >> if AR is as claim abotu the immateial existence of numbers it does >> not. >> Not even remotely. > > AR is a claim that number exists independently of my body and soul. > Number are immaterial, by definition. You don't need a theory of > matter to explain what numbers are. On the contrary, all book which > talk on matter assumes them more or less explicitly. > > > >>> Some posts ago, you seem to accept arithmetical realism, so I am no >>> more sure of your position. >> I may have assented to the *truth* of some propositions... >> but truth is not existence. At least, the claim that >> truth=existence is extraordinary and metaphysical... > > Mathematical existence = truth of existential mathematical statement. > > The number seven exists independently of me, is equivalent with the > statement that the truth of the mathematical statement Ex(x = > s(s(s(s(s(s(s(0)))))))) is true independently of me.

The above of course is a set of tokens symbolizing a set of cardinality eight. The fact that it symbolizes something depends on humans interpreting it. This seems similar to the MGA and the idea that a rock computes every function. They depend on being interpreted in some context or environment. I'm happy to abstract them from their environment to get a manageable model. I'm not so comfortable to say that that abstraction doesn't need the environment and is what is really real. Brent > > If you really believe that the number 7 has no existence at all, then > the UDA reasoning does not go through, but then you are abandoning > comp because you can no more give sense to digitalness. You can still > say "yes" to a doctor, but you have to refer to some analog material > object, and not accept that you survive "qua computatio". This plays a > role in step-8. > > 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 -~----------~----~----~----~------~----~------~--~---