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 the contingent to be necessary? As far as I have found, it cannot show necessity of the contingent. In the rush to define the perfect, all means to show the necessity of contingency was thrown out. This is why I propose that we define existence as necessary possibility; we have contingency built into our ontology in that definition. ;-)

In which modal logic?

Hi Bruno,

Why is there a formal modal logic implied in my remarks? I do not think in a formal math form. I think visually and proprioceptively. Ideas have 'texture' for me. ;-) Good theories have a different 'feel' than wrong theories for me. Maybe this is just 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 use that for public communication.

Dear Bruno,

Please never forget that I am a philosopher, a 'lover of knowledge'. I have seen a weakness in the tacit ontological assumptions of many philosopher, mathematicians and scientists for a long time as I have done my studies. They consistently neglect the effect of mutual agreement between many entities. I thought that I was just wrong in this presumption until I studied semiotic theory and the work of Peirce. After reading the writings of David Bohm and other scientific contrarians I am convinced that I am correct.

Necessity and possibility have been controversial notion from Aristotle to Feys and Kripke (say). After Kripke, we can give a mathematical meaning, and btw, the first remarkable fact is that those modal notion have transfinities of mathematical meaning, but then 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 in elementeray logic, by very complex controversial notion. So I can't understand them.

I am trying to construct a notion of existence that is not contingent on anything, not a theory, not a physical implementation, not on the possibility of measurement or observation. Many philosophers, including that knavish Kant and Schopenhauer and even Satre, have pointed out that the existence of an entity cannot be contingent on anything. Some, like Ayn Rand, tell us that we can only claim that existence exists, but this reduced the concept to a empty tautology. My proposal is that we can think of existence as necessary 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 - in that 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 no properties or particularities or distinctions or any other feature that 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 without properties. This just makes no sense for me.

This is what my definition of existence requires. To define object in my system you must simultaneously define the means that the properties can be distinguished from all possible properties for that class of objects. In this way we might get closer to an ontology 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 are told that physical laws and effects much be formulated in a way that does 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 is theory 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 deeply problematic 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, at many different levels the necessity of the possible.

OK, I'll bite your metaphorical bait. What does Gödel's theorem tell us about the necessity of the possible at most ontologically fundamental level?

We even get that for all (true) sigma_1 sentences (the "atomic events in the UD execution) p -> []<>p,

Can you see that this is just a statement in a particular language?

In arithmetic. All the modalities like [] and <> are entirely defined, either directly by an expression in arithmetic, or by appeal to well defined infinities of arithmetical expressions.

Yes, all of which is dependent on a particular set of formal theoretical 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 different languages!

Perhaps, but then you must give the dictionary.

I have been trying to do exactly that. Have you seen the definitions that I have already written? For example, I define a "reality" as that which 3 or more observers (that can communicate with 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 you understand that I am not assuming that observers are human or similarly sapient? I am defining an observer as a sheaf of an infinite number of computations (all of which generate bisimilar content of first person experience) that can be located by some other observers as existing persistently in some space (where a space 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 necessary possible 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* or X1* logic, and playing the role of observable with "probability 1".

I miss-wrote my reading above. It would read: "the necessary possibility 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 how Pratt considers a logical algebra to be atomic, in that it cannot be reduced to a structure with fewer components and cannot have components added to it without altering its Satisfiability, but I do not know what 'atomicity' means to you.

The usual one in logic. Atomic formula are the formula from which we build the non atomic. In propositional calculus the atomic formula 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 formalism that 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 possibility of p,

I do not see that at all! The truth of p is in its referent, it is what p tells us that is True (or false) and I read the implication arrow in the opposite direction as you.

I thought it was typo, above. The you read "->" in the opposite sense of all the logicians. If you dare doing things like that, it will not help you to be understood. It is better to use the accepted conventions, or at least, if you change one, to make that clear and explicit before all things.

I fixed my typo. The arrow "->" is reverse for logical implication, 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 must be true as well.


The logical necessitation of existence flows backwards by the truth of the precedent. If you read Pratt's papers you might have seen a discussion 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 the antecedents and implicated precedents in its derivation. Logic does not and must not be considered to "anticipate" a truth. Truth is the end result of the process of logic, not its beginning.

This sentence has no meaning. When doing logic, we abstract from truth. We let truth come back in the model theory, but then it is defined 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 can have knowledge without any cause wonder why I am asking you to justify 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 the box of the intelligible or sensible matter (Z1* and X1*). The modal logics becomes well defined, and allows, in Platonia, all the imperfections that you can dream of (which of course is not necessarily a good news).

All of these claims are coherent only after we assume that we exist and can formulate theories.

This is does not make sense. Logicians put all their assumption the table, and our existence does not figure in them.

So the existence of "us" that are evaluating the assumptions is never 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 there where no way to write them on a chalkboard or any other physical medium, so too are the content of any assumptions vacuous without the 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 worlds exist independent of observers? But how could this be given that I am demanding that reality, here of a physical world, is observer dependent - not dependent on any one, but dependent on the totality of 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 can get away with the naive idea that "the moon exists independent of me" only because we naively imagine ourselves to be vastly more powerful that any one else that might be concurrently observing the moon.

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 of the minds that believe in it.


This is how I can believe in comp. I see comp as an existentially 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 to understand it) can agree that the result follows automatically from its 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 keep showing that you don't even want to learn logic. It is a technical subject.

Excuse me, is it necessary to know how to write a language in order 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.PDF for detailed analysis. My disability is known as "Dyscalculia" "a specific learning disability involving innate difficulty in learning or comprehending arithmetic. It is akin to dyslexia and includes difficulty in understanding numbers, learning how to manipulate numbers, learning maths facts, and a number of other related symptoms (although there is no exact form of the disability)." You might as well ask Stephen Hawking to dance a pantomine version of his ideas to "prove" that he understand it. I have overcome this disability but learnign to think in a different way, but my disability 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 a philosophical argument. same for logic, especially when applied 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 that you 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 the problem 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 how to define arithmetic bodies by using the Stone duality, which is a well understood mathematical concept, and some extensions of the concept of universal computers.

Go for it.

Philosophically, my proposed solution is to pull back from the full throated endorsement of immaterialism and think about the ways that 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 properties that are persistent for some finite transformations. They could all have identical minds and imagine themselves to be different from each other because the minds "locate" themselves differently with respect to each other. The key idea is that it is a physical world, ontologically primitive or purely an agreement of some collection of 1p, that allows minds to interact with each other and validate their beliefs.

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 the Doctor 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.




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