On 05 Aug 2012, at 19:18, Stephen P. King wrote:

On 8/5/2012 4:01 AM, Bruno Marchal wrote:On 04 Aug 2012, at 17:19, Stephen P. King wrote:Hi Bruno,There was a typing error in what I wrote originally. Pleasetry it again.On 8/4/2012 7:50 AM, Bruno Marchal wrote:[SPK]Yes, and that is exactly why I am asking you to reconsiderthe idea that "arithmetic is ontologically primitive"! When wereduce a class to the ontological primitive level (meaning thatall else supervenes upon that class or some subclass thereof),then we make the relational structure of that class degenerate.We literally eliminate the meaningfulness of the class if wemake it uniquely primitive. This is why a primitive class isdenoted as "neutral". It cannot be "any particular thing", it iseither "Everything" or "Nothing" or both simultaneously(depending on your pedagogical stance).I cannot give sense to that paragraph.Are you familiar with the concept of degeneracy?Yes.Explain why assuming addition and multiplication makes arithmeticor reality degenerate.Dear Bruno,Addition and multiplication, as the operators alone, do notcause degeneracy and that is not what I am claiming. It is the actof taking Godel numberings of arithmetic strings that inducesdegeneracy.

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When one defines a number in terms of other numbers, it makes theidentity - the uniqueness - of particular numbers degenerate. 2+2=4is no longer just a single transcendental fact when we include Godelnumberings in our model as we are literally requiring that numbers(and their combinations) to have multiple meanings.

`? I can be OK, and the "meaning" variates with respect of the`

`universal numbers. But from the 1pov, this just make the measure`

`problem more difficult.`

This effectively destroys 3p meaningfulness, as it will take aninfinite tower of levels and indexing to sort which numbers havewhich meanings and even in this case we have to allow for non-well-founded cases (such as a number that names itself).

`Indeed. But that is what I defend since the beginning. No need to`

`postulate non-well-foundedness because we have it for free from`

`computer science.`

Again, even if true, it cannot be relevant, given that I explainwhy and how physics (both the sharable part (quanta) and the nonsharable part (qualia) are entirely reduced to number's theology,and this in a way which refutes once and for all any reductionistconception of the soul/person.On the theology part of your result we agree 100%. Reductionismfails utterly. What you are not understanding is that the actionsthat you are assuming occur at the arithmetic level

`OK in a large sense of "action", but the physical actions does not`

`occur at the arithmetical level, but at the level of the material`

`hypostases (povs).`

in fact cannot occur in the absence of interactions between"persons" however those might be defined.

`Yes, that is the point. You need persons and souls to get physics.`

`That is the result. But you don't and can't use matter and person to`

`get them. You can use only the numbers and their laws (or equivalent).`

The problem is that you have "thrown the baby out with thebathwater" by the claim in step 8.

`But it is a logical, semi-axiomatic deduction, so you have to find the`

`flaw.`

You seem to always start from the conclusion, and criticize it forphilosophical reason. You should proceed in the other way round:start from the assumption (comp) and use your philosophical idea tofind a flaw in the reasoning.If and when an argument yields an absurd conclusion, one canonly start at the end and work backwards to see where and when theabsurdity vanishes (if at all). Sometimes the absurdity is is astep near the end, sometimes it could be at the beginning. Componly is absurd, IMHO, at step 8. By denying the necessity of anyphysical world you are effectively removing the means by which theelementary arithmetical constructs can both have unique identitiesand interact with each other.

`You get it wrong. UDA shows the necessity of the physical worlds. It`

`just shows also the necessity of not making it primitive, but a number`

`(psycho)-logical consequence in the comp theory.`

You do not seem to understand that concepts that you are using suchas "interviewing the Modest Machine" become the meaninglessstatements by a single solipsistic entity when you make claims suchas this:"Instead of linking [the pain I feel] at space-time (x,t) to [amachine state] at space-time (x,t), we are obliged to associate [thepain I feel at space-time (x,t)] to a type or a sheaf ofcomputations (existing forever in the arithmetical Platoniawhich is accepted as existing independently of our selveswith arithmetical realism)."

`This is just the first person indeterminacy on the whole UD*, or on`

`arithmetic.`

Meaningfulness is a public fact. It is not a private truth.Consider what would happen in your narrative of the UDA if one wherenot permitted to keep a diary of the experiences of theteleportations.

`But this does not occur. In UD* observers can take note of result in`

`diaries. They are just not primitively real.`

It is the "diary" that acts as a publicly accessible source thatallows meaningfulness to emerge for the statements like "I am inWashington". The diary is a proxy for a physical world, just as theyes Doctor is a proxy for the physical world. Please understand thatI am claiming that the physical world cannot be "ontologicallyprimitive" in agreement with you, but I am also claiming thatneither can elementary arithmetics be ontologically primitive.

`This means you have not studied logic and arithmetic. Arithmetic has`

`to be primitive in any theory (except physicalist ultrafinitism, which`

`is incomptaible with comp).`

It is the "existing forever in the arithmetical Platonia" ideathat is the poison that is causing the absurdity in your result. AsI have been trying to explain, "existing" is not a state of "beingdefinite of property"; it is merely "necessarily possible".

`No, that will be "physically existing", which is defined in the higher`

`level hypostases. For the ontology, existence is defined by the rules`

`obeyed by the existencial quantifier. ExP(x) is true if it exists a`

`number n such that it is the case that P(n).`

It is not even a state of being as it cannot be contingent ofanything or supervene on anything. The truthfulness of a arithmeticstatement is contingent on the ability of entities to bothsubjectively ascertain the validity of a claim and the public( which is emergent from the intercommunication between manyentities) availability to prove the claim (as in demonstrativeprofs). It is not an a priori definite property as there cannot beany such thing.

`That is arithmetical idealism, and if that is true, comp does not make`

`sense at all.`

The degeneracy can be see in your illustrations in SANE04, inthe figures 7 and 8. You are identifying the DU operations with the1 of sigma_1 sentences of arithmetic. Here are your exact statementsin SANE04."Suppose now, for the sake of the argument, that our concrete and‘‘physical’’ universe is a sufficiently robust expandinguniverse so that a ‘‘concrete’’ UD can run forever, asillustrated in figure 7."and then later you write:"Figure 8 illustrates our main conclusion, where the number 1 isput for the so called Sigma1 sentences of arithmetic."This makes the infinite set of distinct identities of all of thequantities and qualia that are supervening on the DU collapse intothe singleton of a sigma_1 sentence (not a plurality of sigma_1sentences!).

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How so you ask? Because the diagonalization of Godel numberingsstrips away the unique identity of numbers or combinators or anyother entity that is isomorphic to the N of {+,*, N}.

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You even allude to this yourself in SANE04: "If comp is correct,the appearance of physics must be recovered from some point ofviews emerging from those propositions. Indeed, taking intoaccount the seven steps once more, we arrive at the conclusionthat the physical atomic (in the Boolean logician sense)invariant proposition must be given by a probability measureon those propositions. A physical certainty must be true inall maximal extensions, true in at least one maximal extension(we will see later why the second condition does not followfrom the first) and accessible by the UD, that isarithmetically verifiable. "An atom in the Boolean logic sense is defined as: "... thoseelements x such that x∧y has only two possible values, x or 0." Butguess what, there does not exist a atom for a Boolean algebra whathas an infinite number of propositions *prior* to the solution of anNp-complete problem, as Boolean Satisfiability is an NP-completeproblem.

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Let me be more explicit here on this claim. We cannot make anyclaims of the definiteness of a truth value when such is notavailable for inspection.

`*that* is solipsism/idealism. Even Gödel's incompleteness would not`

`have sense if that was the case.`

You are effectively asking for the read to believe that an actionthat requires an infinity of steps occur prior to (so as to beavailable for) the truthfulness of the Sigma_1 sentence.

`This comes from the first person indeterminacy on the whole UD*. It`

`makes sense because we have that p -> Bp for the sigma_1 sentences,`

`and thus p -> [] <> p, in Z1*, and X1* (and S4Grz1), and this provides`

`the arithmetical quantization defining already the "measure one" and`

`its (quantum-like) logic.`

We cannot assume that that which requires an actual eternity toobtain is available any time prior to the end of that eternity. Thisstatement is absurd itself!

`No problem, because that infinity is a machine pov. We don't need an`

`actual infinity in the ontology. But we cannot avoid it in the`

`epistemology, and thus in physics.`

It just occurs to me that this is a possible problem for yourBp&p theory of knowledge; the "accidentalist" theory. Anaccidentalist theory of knowledge requires an infinitely extendiblestring of uncorrelated "lucky accidents" to justify arbitrary claimsof a priori truth. The probability measure of such is already known.It is measure zero. It never happens! Therefore the Bp&p conceptmust be augmented with some postulates that force the accidents tohappen "regularly", but this removes the "accidental" nature oftheory!

`A good thing, done by the presence of "Bp". Bp & p is not accidental`

`at all. Indeed, before Gödel, everyone thought that Bp -> p would be a`

`theorem. Since Gödel we know that this is false with p = f, and since`

`Löb we know that Bp -> p implies p. So the "accidental" feature is in`

`Bp and is a consequence of incompleteness. We have to live with that`

`if we assume comp and our local correctness. But this accidental`

`feature is exactly the one needed to relate the "dream argument" to`

`comp in the formal setting, so Gödel's incompleteness makes a bridge`

`between classical metaphysics and computer science.`

Let me ask you a seemingly unrelated question. Are you familiarwith the concept of "synthetic a priori"?

`You keep escaping forward. Just use any notion you want to find a`

`flaw, or assess the result, please.`

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.