On 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, byusing onlyaddition 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 say above: "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 universal numbers`

`can do that. No need of first person notion. All this can be shown in`

`a 3p way. Indeed, in arithmetic. Even without the induction axioms, so`

`that we don't need 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. This was`

`shown mainly by Gödel in his 1931 paper (for rich Löbian theories).`

`It is called "arithmetization of meta-mathematics". I will try to`

`explain the salt of it without 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 a`

`positive answer.`

I think that the ascription of "self-interpretation" to a bare ontology is superficial; 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, we go at the meta-level and combine it with the notion of`

`arithmetical truth. 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 can`

`define a big part of that epistemology using only the elementary`

`ontology.`

`Let us agree on what we mean by defining something in arithmetic (or`

`in the arithmetical language).`

`The arithmetical language is the first order (predicate) logic with`

`equality(=), so that it has the usual logical connectives (&, V, ->, ~`

`(and, or, implies, not), and the quantifiers "E" and "A", (it exists`

`and for all), together with the special arithmetical symbols "0", "s"`

`"+" and "*".`

`To illustrate an arithmetical definition, let me give you some`

`definitions of simple concepts.`

`We can define the arithmetical relation " x =< y" (x is less than or`

`equal to 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, the notion`

`of universal number, computations, proofs, etc.`

`In particular any proposition of the form phi_i(j) = k can be`

`translated in arithmetic. A famous predicate due to Kleene is used for`

`that effect . A universal number u can be defined by the relation`

`AxAy(phi_u(<x,y>) = phi_x(y)), with <x,y> being a computable bijection`

`from NXN to N.`

`Like metamathematics can be arithmetized, theoretical computer science`

`can be arithmetized.`

`The interpretation is not done by me, but by the true relation between`

`the numbers. 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 and`

`now" is that your relative computational state exists, together with`

`the infinitely many 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, to`

`interpret some number relation as computations, because the numbers,`

`relatively to each other, already do that task. From their view, to`

`believe that we need some extra-interpreter, would be like to believe`

`that if your own brain is not observed by someone, it would not be`

`conscious.`

`Let me say two or three words on the SELF. Basically, it is very`

`simple. You don't need universal numbers, nor super rich environment.`

`You need an environment (machine, number) capable of duplicating, or`

`concatenating piece of code. I usually sing this: If D(x) gives the`

`description of x(x), then D(D) gives the description of DD. This`

`belongs to the diagonalization family, and can be used to proves the`

`existence of programs (relative numbers) capable of self-reproduction`

`and self-reference with respect to universal (or not) numbers. So,`

`some numbers can interpret by themselves some relative number`

`relations (relative to some probable local universal number) as a self-`

`referential statement (like "I have two hands"), or even "I am`

`hungry", making them hope some action in the environment will lead`

`them in most satisfying relation with that possible environment. Such`

`numbers can understand UDA like you and me, and realize that the only`

`way that is possible, is by its local reality being stable relatively`

`to the infinity of computations going through its computational states`

`at its correct comp level and below.`

Tell me if this helps. I use comp throughout, 'course. Bruno

DavidOn 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 interpretation isunavoidable. Now, my understanding of Bruno, after some fairlyclosequestioning (which may still leave me confused, of course) is thattheelements of his arithmetical ontology are strictly limited tonumbers(or their equivalent) + addition and multiplication. This emergedduring discussion of macroscopic compositional principles implicitinthe 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 further compositional principles and therefore appeals to some supplementary epistemological "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 "conscious merger" of these two polarities?Actually you can define computation, even universal machine, byusing onlyaddition 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 is Bp& 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 going outsideofarithmetic. It is here that we have to be careful of not doingSearle'serror of confusing levels, and that's why the epistemology internalinarithmetic can be bigger than arithmetic. Arithmetic itself does not"believe" in that epistemology, but it believes in numbersbelieving inthem. Whatever you believe in will not been automatically believedby God,but God will always believe that you do believe in them. BrunoDavidHi Bruno,You seem to not understand the role that the physical plays atall!Thisreminds me of an inversion of how most people cannot understandthe waythatmath is "abstract" and have to work very hard to understandnotions like"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 itseems tomakes PA unique and singular? In other words, how can multiplecopies ofPA 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 anapparent 3pworld. That 3p world may or may not be globally coherent (it ismostcertainly locally coherent), and may or may not be computable,typicallyIimagine it as being locally computed by an infinity of TMs, fromthe 1p.Atleast one coherent 3p foundation exists as the UD, but that'ssomethingverydifferent from the universe a structural realist would believe in(forexample, 'this universe', or the MWI multiverse). So a coherent 3pfoundation always exists, possibly an infinity of them. The parts(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 person living,relatively to you, that Sigma_1 truth, but the person itself isreallyrelated to all the proofs (in Platonia) of that sentences (roughly speaking). 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 of allverified proofs (which supervenes on some form of physicalprocess.)You need just to believe that in the standard model of PA asentence istrue or false. I have not yet seen any book in math mentioning anything physical 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 andcommunicated,OK. But they does not need phyicality to be just true. That's thepoint.Surely, but the truthfulness of a mathematical statement is meaninglesswithout the possibility of physical implementation. One cannoteven knowof it absent the possibility of the physical. it just is the case that the sentence, model, recursive algorithm, 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 axiomreferringtophysics. To say that you need a physical brain begs the question*and* isa 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 ink onawhiteboard or patterns of pixels on a computer monitor orpatterns ofscratches in the dust or ... is sufficient to establish the truthof whatIam saying. If you remove the possibility of physicalimplementation youalso remove the possibility of meaningfulness.We cannot completely abstract away the role played by thephysical world.That's what we do in math.Yes, but all the while the physical world is the substrate forourpatterns without which there is meaninglessness.I simply cannot see how Sigma_1 sentences can interface with eachothersuch that one can "know" anything about another absent some form of physicality. The "interfaces" and the relative implementations are defined using additionand multiplication only, like in Gödel's original paper. Then UDAshowswhyphysicality is an emergent pattern in the mind of number, and whyit hastobe 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, oncewe assume we are (even material) machine.And I agree, the physical is not a primitive in theexistential sense,but neither is the information. Idealism would have us believe thatdifferences 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 thatall formofweak materialism is incompatible with mechanism. All. The monistone, thedualist one, etc.How weak does materialism get when its primary quality isremoved?Thisis a case of "vanishing in the limit", something similar to theheapthat 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 fundamental science.Can you not understand these words? How is materialism anyweaker thanthe 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 ask youwheredoesthe computation occur then there is not paper tape for the TM andyou say"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 believe thatconsciousness is invariant for digital functional substitutiondone atsome level.No, you did not. Your result cannot do such a thing becauseyou cannothave your cake (a meaningful set of expressions) and eat it too.Digitalfunctional 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 for atleast one form of physical implementation. Digitalsubstitutability is aninvariance 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 notprimitive,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,ideas canrepresent themselves. I believe that comp makes the "physical" into an aspect of number's self-reference.There we agree but I would say that a number's self-referenceis itsconnection to some physical representation. My point is thatthere cannotbea self-reference without an implementation even if theparticulars of theimplementation 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", including dreamsof chalkboards, papers, screens, etc. UDA has shown that a "realpaper",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 inthe proofyou 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 is itsfunction? What class is it an invariant upon? Exactly how is itthat youknow 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 thephysicaloffers 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 ofaddition andmultiplication.No, existence does not specify anything, much less that "0,s(0),s(s(0)), ..." is distinct from any other string, nor does itspecify thelaws 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 thusdistinctions.So your claim that " "being prime" from the mere existence of 0,s(0),s(s(0)), ... and the recursive laws of addition and multiplication" requires a substrate that allows form representative patterns to obtain. Universalityallows us to substitute one form of substrate for another so longas thefunction 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 and invariant.Thisrequires implementation in a form that is invariant (to somedegree) withrespect to time. There is not time in Platonia therefore there innoinvariance with respect to time for the patterns of difference tooccurfor 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 see 1or 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 evolutionexists and it is a sufficiently universal "physical" process toimplementthe UD, but the UD as just the equivalent to Integers, nay, thatI cannotbelieve in. “One cannot speak about whatever one cannot talk.”~ Maturana(1978, p. 49) I think Maturana was alluding to Wittgenstein, and that sentence is almostas ridiculous as Damascius saying "one sentence about theineffable isonesentence too much". But it is a deep meta-truth playing some roleinnumber'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 determines its properties. Our ability to communicate ideas follows from their universality, that they do not require *some particular* physical implementation, but that is not the same as requiring *no* physicalimplementation. You argue that *no* physical implementation isnecessary;I disagree.It is the result of the proof. It is up to you to show the flaw,or toabandon comp.The problem is that mathematics cannot represent matter otherthan byinvariance with respect to time, etc. absent an interpreter. Whatyouseem to think is that mathematics can prove things to itself in a mannerconsistent with how I might be able to write out a set of symbolson yourchalkboard that represent a proof of some theorem. You reject DavidDeutsch's discussion of how this is wrongheaded out of hand, thatisunfortunate since it would greatly strengthen your case if youcould showexactly 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 primary substance.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-time andyour result is important in this, but your attempt to argue fromtheotherside is as treacherous because it ignores the necessity of thephysical.Comp makes necessary that there is no *primitive* physicalness.But asDavidpoints in his reply, you cannot say that I ignore the physical.The wholework is an explanation of why we believe in the physical, why andhowsuchbelief emerges and are persistent, etc. Physics is entirely givenby thematerial hypostases, which are defined by number's self-reference, as UDAshows 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 the physicalworldwith statements that is shown to not be primitive is an avoidance of the problem by ignoring it, not a solution to it. The fact that is removing allpossibility of physical implementation by a theory of Everythingmakes itworse than mute, it eliminates itself as a meaningful theory simply because, to be consistent, it cannot be communicated. Onward! Stephen --You received this message because you are subscribed to theGoogle 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. 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