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On 18 Aug, 09:12, Bruno Marchal <marc...@ulb.ac.be> 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". that's what I meant. > >> 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. One of my goals is to explain that you cannot convince me tha matter doesn't exist without first convincing me that numbers do. You may be able to eliminate matter in favour of numbers, but that doesn;'t stop me douing the converse. >This would explain why physicist never use such > ontological commitment explicitly. Physicists write reams about matter. > 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. The UDA doesn't even start without Platonism > > >> 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. That statement requires some justification > What you say is formalism, and this has > been explicitly refuted by mathematical logicians. False. From previous conversations, you conflate fomalism with Hilbert's programme. I am not referring to the claim that there is a mechanical proof-porcedure for any theorem, I am referring to the claim that mathematics is a non-referential formal game. Note that Platonism vs. Formalism is an open quesiton in philosophy. > 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"). Irrelevant. Platonism vs. Formalism is a debate about *existence* not about truth. > 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. Maybe. Evidently I prefer Frege > 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. I've done both and I do. >The distribution of the prime numbers is > objective, and this is the only type of independent objectivity needed > in the reasoning. Nothing more. Truths about prime numbers are objective truths,. That says nothing about existence. > >>> 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). To get a claim of existence out of that claim of truth, you have to take the "exists" to have a single uniform meaning in all contexts,. This, we formalists dispute. > You can call that Platonism, if you want, but this is not obviously > "anti-physicalist". Show me where these numbers are phsycially, then >Non-physicalism is the conclusion of a reasoning > (UDA). Unfortunately, it is also the assumption > 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. I think AR conflates the objective truth claim with the ontological existence claim. > >> 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. 1. Numbers are (referentless) concepts 2. Concepts are mental 3. The mind is the activity of the brain 4. The brain is physical Both Platonism and Empriricism share the assumption that mathematical symbols refer to objects. An alternative to both is the theory that they do not refer at all: this theory is called formalism. For the formalist, mathematical truths are fixed by the rules of mathematics, not by external objects. But what fixes the rules of mathematics ? Formalism suggests that mathematics is a meaningless game, and the rules can be defined any way we like. Yet mathematicians in practice are careful about the selection of axioms, not arbitrary. So do the rules and axioms of mathematics mean anything or not ? The reader may or have noticed that I have been talking about mathematical symbols "referring" to things rather than "meaning" things. This eliptically refers to a distinction between two different kinds or shades of meaning made by Frege. "Reference" is the external- world object a symbol is "about". "Sense" is the kind of meaning a symbol has even if does not have a reference. Meaning is *not* the same thing as reference (Bedeutung). That is the box the anti-Platonist has climbed out of. Some terms have referents (non-linguistic items they denote), others have only "sense" (Sinn). Sense and reference are two dimensions aspects of meaning, but not every term has both. Sense is internal to langauge, it a relationship between a word/concept and others. It is like a dictionary definition, whereas reference is like defining a word by pointing and saying "it is one of those". But no-one has ever defined a unicorn that way, since there is no unicorn to be pointed to. Mathematical concepts are defined in terms of other mathematical concepts. Mathematical reference is impossible and unnecessary. In this way, statements about unicorns or the bald King of France have Sense but not Reference. Therfore, it is possible for mathematical statments to have a sense, and therefore a meaning, beyond the formal rules and defintions, but stopping short of external objects (referents), whether physical or Platonic. This position retains the negative claim of Formalism, that mathematical symbols don't refer to objects, and thus avoids the pitfalls of both Platonism and Empiricism. Howeverm it allows that mathematical symbols can have meanings of an in-the-head kind and thus explains the non-arbitrary nature of the choice of axioms; they are not arbitrary because they must correspond to the mathematician's intuition -- her "sense" -- of what a real number or a set is. So far we have been assuming that the same answer must apply uniformly to all mathematical statmentents and symbols: they all refer or none do. There is a fourth option: divide and conquer -- some refer and others don't. > >>>> 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. The UDA goes nowhere without Platonism > > >>> 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". Taking the immaterial existene of numbers for granted differs how? > 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). > No, because truth is no existence. There may be true facts about the UD, but if it doesn;t exist, it is not generating me. > >>>> 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 ... > > read more » --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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