On 16 Jan 2012, at 20:42, David Nyman wrote:

On 16 January 2012 18:08, Bruno Marchal <marc...@ulb.ac.be> wrote:I do not need an extra God or observer of arithmetical truth, tointerpretsome number relation as computations, because the numbers,relatively toeach other, already do that task. From their view, to believe thatwe needsome extra-interpreter, would be like to believe that if your ownbrain isnot observed by someone, it would not be conscious.I'm unclear from the above - and indeed from the rest of your comments - whether you are defining interpretation in a purely 3p way, or whether you are implicitly placing it in a 1-p framework - e.g. where you say above "From their view". If you do indeed assume that numbers can have such views, then I see why you would say that they "interpret themselves", because adopting the 1p view is already to invoke a kind of "emergence" of number-epistemology. But such an emergence is still only a manner of speaking from OUR point of view, in that I can rephrase what you say above thus: "From their view, to believe that THEY need some extra-interpreter..." without taking such a point of view in any literal sense. Are you saying that consciousness somehow elevates number-epistemology into "strong emergence", such that their point of view and self-interpretation become indistinguishable from my own?

`It seems to me that this follows from UDA1-8. If not, then arithmetic`

`if full of immaterial zombies, given that those computations does`

`exist in arithmetic, in the usual sense of "17 is prime" independently`

`of me. Or you need to reify matter to singularize consciousness, but`

`this is shown by the movie graph (UDA-8, MGA) to be a red herring type`

`of move.`

`Number relations does implement computations, in the same sense that`

`brains' physics implement computations, by MGA.`

`Now the 1p are related, not on any particular computations in the UD`

`(or in arithmetic), but to all of them, making both matter and`

`consciousness not Turing emulable, but still recoverable from the`

`entire work of the UD (UD*) or from the whole arithmetical truth. The`

`point of view of some numbers will not differ from yours, given that`

`yours is given by infinitely many such numbers relations. OK?`

Bruno Bruno

DavidOn 16 Jan 2012, at 15:32, David Nyman wrote:On 16 January 2012 10:04, Bruno Marchal <marc...@ulb.ac.be> wrote:Actually you can define computation, even universal machine, byusingonlyaddition and multiplication. So universal machine exists inelementaryarithmetic in the same sense as in the existence of prime number.That may be, but we were discussing interpretation. As you sayabove:"YOU can define computation, even universal machine, by using only addition and multiplication" (my emphasis).Not just ME. A tiny part of arithmetic can too. All universalnumbers can dothat. No need of first person notion. All this can be shown in a 3pway.Indeed, in arithmetic. Even without the induction axioms, so thatwe don'tneed Löbian machine.The existence of the UD for example, is a theorem of (Robinson)arithmetic.Now, that kinds of truth are rather long and tedious to show. Thiswas shownmainly by Gödel in his 1931 paper (for rich Löbian theories). Itis called"arithmetization of meta-mathematics". I will try to explain thesalt of itwithout being too much technical below.But this is surely, as you are wont to say, too quick. Firstly, in what sense can numbers in simple arithmetical relation define THEMSELVES as computation, or indeed as anything else than what they simply are?Here you ask a more difficult question. Nevertheless it admits apositiveanswer.I think that theascription of "self-interpretation" to a bare ontology issuperficial;it conceals an implicit supplementary appeal to epistemology, and indeed to a self.But can define a notion of 3-self in arithmetic. Then to get the 1-self, wego at the meta-level and combine it with the notion of arithmeticaltruth.That notion is NOT definable in arithmetic, but that is a good thing, because it will explain why the notion of first person, and of consciousness, will not be definable by machine.Hence it appears that some perspectival union of epistemology and ontology is a prerequisite of interpretation.OK. But the whole force of comp comes from the fact that you candefine abig part of that epistemology using only the elementary ontology.Let us agree on what we mean by defining something in arithmetic(or in thearithmetical language). The arithmetical language is the first order (predicate) logic withequality(=), so that it has the usual logical connectives (&, V, ->, ~ (and,or, implies, not), and the quantifiers "E" and "A", (it exists andfor all),together with the special arithmetical symbols "0", "s" "+" and "*".To illustrate an arithmetical definition, let me give you somedefinitionsof simple concepts.We can define the arithmetical relation " x =< y" (x is less thanor equalto y). Indeed x =< y if and only if Ez(x+z = y) We can define x < y (x is strictly less than y) by Ez((x+z) + s(0) = y) We can define (x divide y) by Ez(x*z = y) Now we can define (x is a prime number) by Az[ (x ≠ 1) and ((z divide x) -> ((z = 1) or (z = x))] Which should be seen as a "macro" abbreviation of Az(~(x = s(0)) & ((Ey(x*y = x) -> (z = 1) V (z = x)).Now I tell you that we can define, exactly in that manner, thenotion ofuniversal number, computations, proofs, etc.In particular any proposition of the form phi_i(j) = k can betranslated inarithmetic. A famous predicate due to Kleene is used for thateffect . Auniversal number u can be defined by the relationAxAy(phi_u(<x,y>) = phi_x(y)), with <x,y> being a computablebijection fromNXN to N.Like metamathematics can be arithmetized, theoretical computerscience canbe arithmetized.The interpretation is not done by me, but by the true relationbetween thenumbers. 4 < 6 because it is true that Ez(s(s(s(s(0))))+z + s(0) =s(s(s(s(s(s(0)))))) ). That is true. Such a z exists, notably z =s(0).Likewize, assuming comp, the reason why you are conscious "here andnow" isthat your relative computational state exists, together with theinfinitelymany computations going through it. Your consciousness is harder to tackle, because it will refer more explicitly on that truth, like in the Bp & p Theatetical trick.I do not need an extra God or observer of arithmetical truth, tointerpretsome number relation as computations, because the numbers,relatively toeach other, already do that task. From their view, to believe thatwe needsome extra-interpreter, would be like to believe that if your ownbrain isnot observed by someone, it would not be conscious.Let me say two or three words on the SELF. Basically, it is verysimple.You don't need universal numbers, nor super rich environment. Youneed anenvironment (machine, number) capable of duplicating, orconcatenating pieceof code. I usually sing this: If D(x) gives the description ofx(x), thenD(D) gives the description of DD. This belongs to the diagonalization family, and can be used to proves the existence of programs (relativenumbers) capable of self-reproduction and self-reference withrespect touniversal (or not) numbers. So, some numbers can interpret bythemselvessome relative number relations (relative to some probable localuniversalnumber) as a self-referential statement (like "I have two hands"),or even"I am hungry", making them hope some action in the environment willleadthem in most satisfying relation with that possible environment. Suchnumbers can understand UDA like you and me, and realize that theonly waythat is possible, is by its local reality being stable relativelyto theinfinity of computations going through its computational states atitscorrect comp level and below. Tell me if this helps. I use comp throughout, 'course. BrunoDavidOn 14 Jan 2012, at 18:51, David Nyman wrote:On 14 January 2012 16:50, Stephen P. King<stephe...@charter.net> wrote:The problem is that mathematics cannot represent matter otherthan byinvariance with respect to time, etc. absent an interpreter.Sure, but do you mean to say that the interpreter must bephysical? Idon't see why. And yet, as you say, the need for interpretationisunavoidable. Now, my understanding of Bruno, after some fairlyclosequestioning (which may still leave me confused, of course) isthat theelements of his arithmetical ontology are strictly limited tonumbers(or their equivalent) + addition and multiplication. This emergedduring discussion of macroscopic compositional principlesimplicit inthe interpretation of micro-physical schemas; principles which arerarely understood as being epistemological in nature. Hence,strictlyspeaking, even the ascription of the notion of computation to arrangements of these bare arithmetical elements assumes furthercompositional principles and therefore appeals to somesupplementaryepistemological "interpretation".In other words, any bare ontological schema, uninterpreted, isunable,from its own unsupplemented resources, to actualise whateverhigher-level emergents may be implicit within it. But what elsecoulddeliver that interpretation/actualisation? What could embody thecollapse of ontology and epistemology into a single actuality?Couldit be that interpretation is finally revealed only in the"consciousmerger" of these two polarities?Actually you can define computation, even universal machine, byusingonlyaddition and multiplication. So universal machine exists inelementaryarithmetic in the same sense as in the existence of prime number.All the"Bp " and "Dp" are pure arithmetical sentences. What cannot bedefined isBp & p, and we need to go out of the mind of the machine, and out ofarithmetic, to provide the meaning, and machines can do that too.So, inarithmetic, you can find true statement about machine goingoutside ofarithmetic. It is here that we have to be careful of not doingSearle'serror of confusing levels, and that's why the epistemologyinternal inarithmetic can be bigger than arithmetic. Arithmetic itself doesnot"believe" in that epistemology, but it believes in numbersbelieving inthem. Whatever you believe in will not been automaticallybelieved byGod, but God will always believe that you do believe in them. BrunoDavidHi Bruno,You seem to not understand the role that the physical playsat all!Thisreminds me of an inversion of how most people cannot understandthe waythatmath is "abstract" and have to work very hard to understandnotionslike "in principle a coffee cup is the same as a doughnut". On 1/14/2012 6:58 AM, Bruno Marchal wrote: On 13 Jan 2012, at 18:24, Stephen P. King wrote: Hi Bruno, On 1/13/2012 4:38 AM, Bruno Marchal wrote: Hi Stephen, On 13 Jan 2012, at 00:58, Stephen P. King wrote: Hi Bruno, On 1/12/2012 1:01 PM, Bruno Marchal wrote: On 11 Jan 2012, at 19:35, acw wrote: On 1/11/2012 19:22, Stephen P. King wrote: Hi,I have a question. Does not the Tennenbaum Theorem prevent theconceptof first person plural from having a coherent meaning, since itseemstomakes PA unique and singular? In other words, how can multiplecopiesof PA generate a plurality of first person since they would be anequivalence class. It seems to me that the concept of pluralityof 1prequires a 3p to be coherent, but how does a 3p exist unless itis a 1pin the PA sense? Onward! StephenMy understanding of 1p plural is merely many 1p's sharing anapparent3pworld. That 3p world may or may not be globally coherent (it ismostcertainly locally coherent), and may or may not be computable, typically Iimagine it as being locally computed by an infinity of TMs,from the1p. Atleast one coherent 3p foundation exists as the UD, but that'ssomethingverydifferent from the universe a structural realist would believein (forexample, 'this universe', or the MWI multiverse). So a coherent3pfoundation always exists, possibly an infinity of them. Theparts (oreven the whole) of the 3p foundation should be found within the UD.As for PA's consciousness, I don't know, maybe Bruno can say alot moreabout this. My understanding of consciousness in Bruno's theoryis thatan OM(Observer Moment) corresponds to a Sigma-1 sentence.You can ascribe a sort of local consciousness to the personliving,relatively to you, that Sigma_1 truth, but the person itself isreallyrelated to all the proofs (in Platonia) of that sentences(roughlyspeaking). OK, but that requires that I have a justification for a belief in Platonia.The closest that I can get to Platonia is something like theclass ofallverified proofs (which supervenes on some form of physicalprocess.)You need just to believe that in the standard model of PA asentence istrueor false. I have not yet seen any book in math mentioninganythingphysical to define what that means. *All* math papers you cited assume no less.I cannot understand how such an obvious concept is notunderstood,eventhe notion of universality assumes it. The point is thatmathematicalstatements require some form of physicality to be known and communicated, OK. But they does not need phyicality to be just true. That's the point. Surely, but the truthfulness of a mathematical statement is meaninglesswithout the possibility of physical implementation. One cannotevenknow of it absent the possibility of the physical.it just is the case that the sentence, model, recursivealgorithm,whatever concept, etc. is independent of any particular form of physicalimplementation but is not independent of all physicalrepresentations.Of course it is. When you reason in PA you don't use any axiom referring tophysics. To say that you need a physical brain begs thequestion *and*is a level-of-reasoning error.PA does need to have any axioms that refer to physics. Thefact thatPAis inferred from patterns of chalk on a chalk board or patternsof inkon awhiteboard or patterns of pixels on a computer monitor orpatterns ofscratches in the dust or ... is sufficient to establish thetruth ofwhat Iam saying. If you remove the possibility of physicalimplementation youalso remove the possibility of meaningfulness.We cannot completely abstract away the role played by thephysicalworld. That's what we do in math.Yes, but all the while the physical world is the substratefor ourpatterns without which there is meaninglessness.I simply cannot see how Sigma_1 sentences can interface witheach othersuch that one can "know" anything about another absent some form of physicality.The "interfaces" and the relative implementations are definedusingadditionand multiplication only, like in Gödel's original paper. ThenUDA showswhyphysicality is an emergent pattern in the mind of number, andwhy ithas tobe like that if comp is true. AUDA shows how to make thederivation.No, you have only proven that the idea that the physicalistidea that"mind is an epiphenomena" is false,No. I show that the physical reality is not an ontologicalreality,once we assume we are (even material) machine. And I agree, the physical is not a primitive in the existential sense,but neither is the information. Idealism would have us believethatdifferences can somehow obtain without a means to make thedistinction.i.e. that material monism is false.I insist everywhere that this is not what I showed. I show thatallform ofweak materialism is incompatible with mechanism. All. Themonist one,the dualist one, etc.How weak does materialism get when its primary quality isremoved?Thisis a case of "vanishing in the limit", something similar tothe heapthat vanishes when we remove the last grain. A proof that I understand and agree with. Clearly you did not. You even miss the enunciation of the result. Mechanismis incompatible with WEAK materialism, that is the idea thatprimitivematter exist, or the idea that physics is the fundamentalscience.Can you not understand these words? How is materialism anyweakerthanthe case of no material at all? My argument is that thepossibility ofphysical implementation cannot be removed without removing the possibilityof meaningfulness. It is not an argument for a primitiveontologicalstatusfor matter. You even seem to follow this reasoning when I askyou wheredoesthe computation occur then there is not paper tape for the TMand yousay "on the walls of Platonia". Your arguments and discussions in support of ideal monism and,I prove that ideal monism is the only option, once you believethatconsciousness is invariant for digital functional substitutiondone atsome level. No, you did not. Your result cannot do such a thing because you cannot have your cake (a meaningful set of expressions) and eat it too. Digital functional substitution is the substitution of one physical implementationfor another, it shows that the fact of universality does notdepend onanyparticular physical implementation but DOES NOT eliminate theneed foratleast one form of physical implementation. Digitalsubstitutability isaninvariance over the class of physical implementations, but whathappensthen you remove all members of a class? It vanishes! like Berkeley's, still fail because while the physical is not primitive, it is not merely the epiphenomena of the mind either. It has to be by the UDA.And the UDA (like the UD) must have some implementation, eventhoughthe particulars of that implementation are irrelevant.You are perhaps confused by the fact that unlike the physical,ideascan represent themselves.I believe that comp makes the "physical" into an aspect ofnumber'sself-reference.There we agree but I would say that a number's self-referenceis itsconnection to some physical representation. My point is thattherecannot bea self-reference without an implementation even if theparticulars ofthe implementation do not matter.If I take away all forms of physical means of communicatingideas, nochalkboards, paper, computer screens, etc., how can ideas bepossiblycommunicated?Because arithmetical truth contains all machine 'dreams",includingdreams of chalkboards, papers, screens, etc. UDA has shown that a "real paper", or& "real screen" is an emergent stable pattern supervening oninfinitiesof computation, through a competition between all universal numbers occurringbelow our substitution level. You might try to tell me where intheproof you lost the arguement.When these "infinities of computations" are taken to havespecificproperties merely because of their existence. You are conflating existence with property definiteness. Most people have this problem.This does not make sense. I assume not just O, s(0), etc. Iassume alsoaddition and multiplication. That's enough to get the properties.There is an "I" in that statement! What is this "I"? What isitsfunction? What class is it an invariant upon? Exactly how is itthatyou know of these properties? Absent the possibility of some form ofimplementation in the physical, there is no distinction betweenyou andanything. Meaning requires distinction. Some even say thatmeaning *is*distinction. What other than the persistence of pattern that the physical offers acts to allow for the ability to know differences? Mere existence does not specify properties.That's not correct. We can explain the property "being prime"from themereexistence of 0, s(0), s(s(0)), ... and the recursive laws ofadditionand multiplication.No, existence does not specify anything, much less that "0,s(0),s(s(0)), ..." is distinct from any other string, nor does itspecifythelaws of addition or multiplication. Existence is not a propertythat anobject has. Exactly. that's the point. You seem to contradict it. But existence is thus independent of properties and thus distinctions.So your claim that " "being prime" from the mere existence of0, s(0),s(s(0)), ... and the recursive laws of addition andmultiplication"requires a substrate that allows form representative patterns to obtain. Universalityallows us to substitute one form of substrate for another solong asthe function is the same. But universality and existence alone are insufficientfor your claim that "I prove that ideal monism is the onlyoption". Youalsohave to show how the properties are both definite andinvariant. Thisrequires implementation in a form that is invariant (to somedegree)withrespect to time. There is not time in Platonia therefore therein noinvariance with respect to time for the patterns of differenceto occurfor implementation to be said to obtain.You need to study the "problem of universals" in philosophy, itis wellknown and has been debated for even thousands of years. Forexample see1 or 2. This is a red herring.In a way, surely, but the essence of the problem is not. Thepaperthat is reference 1 explains this well. I go so far as considering that the wavefunction and its unitary evolution exists and it is a sufficiently universal "physical" process to implementthe UD, but the UD as just the equivalent to Integers, nay,that Icannotbelieve in. “One cannot speak about whatever one cannottalk.” ~Maturana (1978, p. 49)I think Maturana was alluding to Wittgenstein, and thatsentence isalmostas ridiculous as Damascius saying "one sentence about theineffable isonesentence too much". But it is a deep meta-truth playing somerole innumber's theology.OK, I deeply appreciate your erudition, you are much moreeducatedthanI am, but nevertheless, I submit to you that you cannot justignore theuniversals vs. nominal problem and posit by fiat that justbecause onecan proof the truth of some statement that that statement's existence determinesits properties. Our ability to communicate ideas follows fromtheiruniversality, that they do not require *some particular* physicalimplementation, but that is not the same as requiring *no*physicalimplementation. You argue that *no* physical implementation is necessary; I disagree.It is the result of the proof. It is up to you to show theflaw, or toabandon comp.The problem is that mathematics cannot represent matter otherthan byinvariance with respect to time, etc. absent an interpreter.What youseemto think is that mathematics can prove things to itself in amannerconsistent with how I might be able to write out a set ofsymbols onyourchalkboard that represent a proof of some theorem. You rejectDavidDeutsch's discussion of how this is wrongheaded out of hand,that isunfortunate since it would greatly strengthen your case if youcouldshow exactly where Deutsch is going wrong, if he is... But I think that you cannot define the universal wave without postulatingarithmetical realism. In fact real number+trigonometricalfunction is astronger form of realism than arithmetical realism. Adding"physical"infront of it adds nothing but a magical notion of primarysubstance.Epistemologically it is a form of treachery, by UDA, it singlesout auniversal number and postulate it is real, when comp explainspreciselythat such a move cannot work.I am allowing for realism, it is a belief that may be true,but it isnot a unique singleton in the universe of models. I am arguingagainsttheidea that the physical is primitive, against substantivalismespeciallyas it is occurring in physics, for example see: www.dur.ac.uk/nick.zangwill/Haeccieties.doc or 4.In physics there is a huge debate over the haecceity of space-timeandyour result is important in this, but your attempt to arguefrom theother side is as treacherous because it ignores the necessity of the physical.Comp makes necessary that there is no *primitive* physicalness.But asDavidpoints in his reply, you cannot say that I ignore the physical.Thewholework is an explanation of why we believe in the physical, whyand howsuchbelief emerges and are persistent, etc. Physics is entirelygiven bythematerial hypostases, which are defined by number's self-reference, asUDA shows it to be the case necessarily so.This is insufficient. Merely postulating a property does notmake itso.You continued intransigence on the non-existence of thephysical worldwithstatements that is shown to not be primitive is an avoidance oftheproblemby ignoring it, not a solution to it. The fact that is removingallpossibility of physical implementation by a theory ofEverything makesitworse than mute, it eliminates itself as a meaningful theorysimplybecause, to be consistent, it cannot be communicated. Onward! Stephen --You received this message because you are subscribed to theGroups "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. 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