On 10 Nov 2012, at 00:04, Stephen P. King wrote:

On 11/9/2012 12:25 PM, Bruno Marchal wrote:On 09 Nov 2012, at 00:01, Stephen P. King wrote:On 11/8/2012 10:22 AM, Bruno Marchal wrote:On 08 Nov 2012, at 14:45, Stephen P. King wrote:On 11/8/2012 6:43 AM, Roger Clough wrote:Hi meekerdb So how does Platonia's perfect necessary classes restrain or contain this world of contingency ? Or does it ?Hi Roger,That is exactly my question! How does Platonism show thecontingent to be necessary? As far as I have found, it cannotshow necessity of the contingent. In the rush to define theperfect, all means to show the necessity of contingency wasthrown out. This is why I propose that we define existence asnecessary possibility; we have contingency built into ourontology in that definition. ;-)In which modal logic?Hi Bruno,Why is there a formal modal logic implied in my remarks? I donot think in a formal math form. I think visually andproprioceptively. Ideas have 'texture' for me. ;-) Good theorieshave a different 'feel' than wrong theories for me. Maybe this isjust an intuitive form of thinking but it has served me well so far.It might suit well your 1p-intuition. Good for you. But you can usethat for public communication.Dear Bruno,Please never forget that I am a philosopher, a 'lover ofknowledge'. I have seen a weakness in the tacit ontologicalassumptions of many philosopher, mathematicians and scientists for along time as I have done my studies. They consistently neglect theeffect of mutual agreement between many entities. I thought that Iwas just wrong in this presumption until I studied semiotic theoryand the work of Peirce. After reading the writings of David Bohm andother scientific contrarians I am convinced that I am correct.Necessity and possibility have been controversial notion fromAristotle to Feys and Kripke (say). After Kripke, we can give amathematical meaning, and btw, the first remarkable fact is thatthose modal notion have transfinities of mathematical meaning, butthen we can be more precise.Yes. I am studying Kripke, Hinttikka and others on this.You define existence, which is simlple and rather well handled inelementeray logic, by very complex controversial notion. So I can'tunderstand them.I am trying to construct a notion of existence that is notcontingent on anything, not a theory, not a physical implementation,not on the possibility of measurement or observation. Manyphilosophers, including that knavish Kant and Schopenhauer and evenSatre, have pointed out that the existence of an entity cannot becontingent on anything. Some, like Ayn Rand, tell us that we canonly claim that existence exists, but this reduced the concept to aempty tautology. My proposal is that we can think of existence asnecessary possibility

`With S5? I mean "necessary possibility" is too much vague. It looks`

`like the arithmetical quantization, []<>p, which define a notion of`

`physical existence, but this is in the context of translating UDA in`

`arithmetic. I can not see if they are related. There the box and`

`diamond can be defined in arithmetic (meaning with s, 0, + and *, and`

`the logical usual symbols.`

and thus have a concept that can be ontologically primitive - inthat it is not contingent.

`Sorry but 2+2=4 is not contingent, so I don't see why you are using`

`something which up to now is only fuzzy talk.`

This allows it to be ontologically neutral in that it has noproperties or particularities or distinctions or any other featurethat would make it subservient on some special condition.

But how can you explain anything from something like that?

Like for "primitive", that you want having objects withoutproperties. This just makes no sense for me.This is what my definition of existence requires. To defineobject in my system you must simultaneously define the means thatthe properties can be distinguished from all possible properties forthat class of objects. In this way we might get closer to anontology that is not language dependent.

`But comp (by UDA), and a bit of computer science makes physics`

`independent of the phi_i system used. That is already a big invariant,`

`which use comp to make it precise in computer science terms.`

I am just taking a page from the Book of Modern Physics where we aretold that physical laws and effects much be formulated in a way thatdoes not depend on some special coordinate system or observable basis.

Comp generalizes this a lot. No need of physics, here too.

That you seem to repeatedly advocate is an ontology that istheory dependent.

`No it is not. That why the laws of addition and multiplication are`

`enough, but that if you don't like nulber, you can take the laws of`

`the cominators: Kxy = x, and Sxyz = xz(yz). That's enough too. With`

`comp physics is theory independent in a mathematically precise sense,`

`which has been exploited, notably by the self-reference logic, which`

`are also theory independent, after a precise complexity treshold`

`(universality, Löbianity).`

Just as your notion of truth is theory dependent,

`In a superficial sense only, for the ontology. But not for`

`consciousness and matter.`

so too are the results or implications of comp. This is deeplyproblematic for me.

`Again your critics don't work, as comp leads to a theory of the`

`coupling consciousness/realities which is independent of the starting`

`theory.`

What you say directly contradict Gödel's theorem, which shows, atmany different levels the necessity of the possible.OK, I'll bite your metaphorical bait. What does Gödel's theoremtell us about the necessity of the possible at most ontologicallyfundamental level?We even get that for all (true) sigma_1 sentences (the "atomicevents in the UD execution) p -> []<>p,Can you see that this is just a statement in a particularlanguage?In arithmetic. All the modalities like [] and <> are entirelydefined, either directly by an expression in arithmetic, or byappeal to well defined infinities of arithmetical expressions.Yes, all of which is dependent on a particular set of formaltheoretical definitions.

`Not at all. It depends only on the assumption that you survive with a`

`digital brain (to be short), then it follows from computer science`

`which has already developed the notion of theory independent truth and`

`proof. I just show that this extend to the physical laws and theology,`

`once we assume comp.`

We should be able to refer to the very same ideas using differentlanguages!Perhaps, but then you must give the dictionary.I have been trying to do exactly that. Have you seen thedefinitions that I have already written? For example, I define a"reality" as that which 3 or more observers (that can communicatewith each other about) agree to be empty of contradictions.

`If 3 appears in your axioms, your critics of arithmetical realism is`

`contradicted. In the fundamental nothing must be taken for granted.`

`Neither the basic level, nor the metalevels.`

Do you have any idea why I require at least 3 observers? Do youunderstand that I am not assuming that observers are human orsimilarly sapient? I am defining an observer as a sheaf of aninfinite number of computations (all of which generate bisimilarcontent of first person experience) that can be located by someother observers as existing persistently in some space (where aspace is a set with some additional relational structure).

That looks like the comp physics.

Truth is, after all, independent of any particular representation!One thing: that "p -> []<>p" reads to me as "the necessarypossible existence of p implies the existence of p".?"p -> []<>p" is for, p being any sigma_1 arithmetical proposition:p implies box diamond p", with the box being defined in the Z1* orX1* logic, and playing the role of observable with "probability 1".I miss-wrote my reading above. It would read: "the necessarypossibility of p implies the existence of p"

?

. I don't see the need to refer to a particular formal model of math.

`No need indeed. especially to show a flaw in the informal UDA, which`

`still needs an understanding of the UD, and thus some intuition of`

`what a digital machine, or program is, and how universal numbers can`

`interpret them in arithmetic (or anything you want, as long as it is`

`Turing complete).`

As to the idea of atomicity in the UD. I understand a bit howPratt considers a logical algebra to be atomic, in that it cannotbe reduced to a structure with fewer components and cannot havecomponents added to it without altering its Satisfiability, but Ido not know what 'atomicity' means to you.The usual one in logic. Atomic formula are the formula from whichwe build the non atomic. In propositional calculus the atomicformula are p, q, r, ... In arithmetic, the atomic formula are (t =s) with t and s beings terms; etc.Atomic formulas are formulas withing a theoretical formalismthat are irreducible to formulas with fewer propositions, no?

`They are formula which don't have occurences of logical symbol.`

`(0=1+s(s(0))) is atomic.`

((0=s(s(0))) -> (0=s(s(0)))) is not atomic.

that is the truth of p implies the necessity of the possibilityof p,I do not see that at all! The truth of p is in its referent, itis what p tells us that is True (or false) and I read theimplication arrow in the opposite direction as you.I thought it was typo, above. The you read "->" in the oppositesense of all the logicians. If you dare doing things like that, itwill not help you to be understood. It is better to use theaccepted conventions, or at least, if you change one, to make thatclear and explicit before all things.I fixed my typo. The arrow "->" is reverse for logicalimplication, no?

`p -> q is "if p then q", equivalent with ~(p & ~q), or with (~p v q).`

`It is the one binary connector which is false only in the case where p`

`is true and q is false, and true in the other case.`

If x then y, tells me that if Y is a fact of the world then x mustbe true as well.

No.

The logical necessitation of existence flows backwards by the truthof the precedent. If you read Pratt's papers you might have seen adiscussion of this.

`Pratt shows that there is a duality between the category of set and`

`the category of boolean algebra. you can't invoke that to change the`

`definition of "->".`

Logical necessitation (the logical form of causality) looks at theantecedents and implicated precedents in its derivation. Logicdoes not and must not be considered to "anticipate" a truth. Truthis the end result of the process of logic, not its beginning.This sentence has no meaning. When doing logic, we abstract fromtruth. We let truth come back in the model theory, but then it isdefined mathematically, and of course it is not "the truth".Why not? You assume that something exists without any cause

`That is too vague. I assume "yes doctor" and enough arithmetic to make`

`sense of Church thesis.`

and that it also has properties without any cause and that you canhave knowledge without any cause wonder why I am asking you tojustify that belief. What might cause me to not agree with you? Oh,I am just confused and misinformed (in your opinion). OK.with []p = either the box of the universal soul (S4Grz1), or thebox of the intelligible or sensible matter (Z1* and X1*). Themodal logics becomes well defined, and allows, in Platonia, allthe imperfections that you can dream of (which of course is notnecessarily a good news).All of these claims are coherent only after we assume that weexist and can formulate theories.This is does not make sense. Logicians put all their assumption thetable, and our existence does not figure in them.So the existence of "us" that are evaluating the assumptions isnever to be explained or even considered.

`On the contrary, it is what we want to explain. We cannot assume in`

`the theory what we want to explain in the possible reality.`

I reject this as inverted solipsism: instead of the belief that"only I exist", you are in effect saying that we must believe that"we do not exist". No thanks.

What you say does not follow.

Just like my claim that your equations would not knowable if therewhere no way to write them on a chalkboard or any other physicalmedium, so too are the content of any assumptions vacuous withoutthe a priori existence of evaluators of those assumptions.

`The evaluator are the universal numbers, which are thing entity, by`

`comp.`

Maybe you imagine that I am proposing that that physical worldsexist independent of observers? But how could this be given that Iam demanding that reality, here of a physical world, is observerdependent - not dependent on any one, but dependent on the totalityof the observers. Reality is "participatory" and democratic.No one vote can change the total more than by one unit of value,which for a huge number of observers is a trivial quantity. We canget away with the naive idea that "the moon exists independent ofme" only because we naively imagine ourselves to be vastly morepowerful that any one else that might be concurrently observing themoon.

`Write a paper. you have good idea, but your use of math is too much`

`"1004". Just make them clearer, and if you think you can use them to`

`find a flaw, then find the flaw. After, if the flaw is there, we might`

`ask you how you find it, and be interested in one application of your`

`theory.`

Comp floats high up in the Platonic realm on the support of all ofthe minds that believe in it.?This is how I can believe in comp. I see comp as anexistentially true result

`Comp is just a digital form of Descartes mechanism. Our bodies are`

`machine, seen at some level.`

but only because many minds (that do the due diligence to come tounderstand it) can agree that the result follows automatically fromits postulates and the defined formal theory of modal logic.

I don't see the realtion with "yes doctor" + CT.

You said that you are a beginners and want to learn, but you keepshowing that you don't even want to learn logic. It is a technicalsubject.Excuse me, is it necessary to know how to write a language inorder to understand that language? No!

`It is necessary to share minimal belief with other, and to share some`

`language with others, when you want to be understood by others.`

You ignore the consequences of my disability. see http://www.mathematicalbrain.com/pdf/LANDETAL.PDFfor detailed analysis. My disability is known as "Dyscalculia" "aspecific learning disability involving innate difficulty in learningor comprehending arithmetic. It is akin to dyslexia and includesdifficulty in understanding numbers, learning how to manipulatenumbers, learning maths facts, and a number of other relatedsymptoms (although there is no exact form of the disability)." Youmight as well ask Stephen Hawking to dance a pantomine version ofhis ideas to "prove" that he understand it. I have overcome thisdisability but learnign to think in a different way, but mydisability remains.

`But Stephen Hawking does not try to dance. if you "dyscalculkia"`

`concerns numbers, I can use combinators; or any Turing complete system`

`based on words, and not numbers. As I said the "reality" is`

`independent of the choice of the theory. You might be right as the`

`brain have special locus for the numbers, and different one for the`

`words, despite their Turing equivalence.`

Now you are the one citing math papers all the time.

Nobody will criticize a formula in differential geometry with aphilosophical argument. same for logic, especially whenapplied to philosophy.Bruno. I am not criticizing a formula in differential geometry,I am criticizing a philosophical idea that you are advocating.

`Here is your bigger misunderstanding. I don't advocate any idea. I am`

`totally agnostic on comp and its consequence. I just show that weak`

`materialism is inconsistent with digital mechanism. I don't do`

`philosophy. It is a technical point, made possible by the link between`

`comp and computer science.`

Your are advocating a form of immaterialism and I am demandign thatyou explain how you over come its "body problem".

I am showing that comp leads to immaterialism.

The fact that comp has a body problem, even if it is arithmetical,is not a surprise to me. I am more surprised that you admit theproblem exists!

`It is the modest, if not radical for the fundamentalist or dogmatic`

`aristotelians, result of the work. It might be obvious for human`

`looking inward enough, but the point here is that it is a logical`

`consequence. And it makes the physical reality belonging to the head`

`of any universal system, in some precise technical term, so that comp`

`is made testable.`

But you do not seem to want to find a solution.

`The 8 hypostases is the beginning of the solution given by the amchine`

`which looks inward, and it is already close to QM at the place it`

`should be.`

My proposed solution, within math, is that we somehow figure out howto define arithmetic bodies by using the Stone duality, which is awell understood mathematical concept, and some extensions of theconcept of universal computers.

Go for it.

Philosophically, my proposed solution is to pull back from thefull throated endorsement of immaterialism and think about the waysthat comp allows us to define physical worlds.

`UDA has done this, in the comp theory. Physics is a measure on the`

`computations, as seen from the realtive universal numbers. Most are to`

`dumb to answer most question, but the Löbian one are maximally chatty`

`about it, and then they can be given minimal inference inductive`

`capacity making them able to justify their many silence.`

Bodies are merely localizations in spaces that have some propertiesthat are persistent for some finite transformations. They could allhave identical minds and imagine themselves to be different fromeach other because the minds "locate" themselves differently withrespect to each other. The key idea is that it is a physical world,ontologically primitive or purely an agreement of some collection of1p, that allows minds to interact with each other and validate theirbeliefs.

`That can be used as a good mitivation for the first person plural, but`

`it remains to show it wins the measure on computations competition`

`among all universal numbers.`

We can bet on the Doctor only if we can know for sure that theDoctor is not a liar.

`Then we can never bet. No problem, as comp assume the doctor is not a`

`liar, and in particular the doctoir will never pretend to have found`

`the right level, as nobody can know it for sure.`

Bruno

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