On 30 Sep 2011, at 13:44, Stephen P. King wrote:

On 9/30/2011 5:45 AM, Bruno Marchal wrote:

If comp +Theaetus is correct, you have to distinguish physical existence, which is of the type []<>#, and existence, which is of the type "Ex ... x...". I will use the modal box [] and diamond <> fro the intelligible hypostases ([]X = BX & DX).

[SPK]

It seems that we have very different ideas of the meaning of the word Existence. "Ex ... x..." seems to be a denotative definition and thus is not neutral with respect to properties. I may not comprehend you thoughts on this.

It seems that you introduce meta-difficulties to elude simple question.



Do you have a concept for "the totality of all that exists"?

A priori and personally: no.

Assuming comp: yes. N is the totality of what exists, but, assuming comp, I have to add this is a G* minus G proposition. It is not really communicable/provable. You have to grasp it by your own understanding (of UDA, for example).



Would such be unnamable for you? It is for me.

Yes. Arithmetical truth, which relies on the ontic N whole, is unnamable for me, that is why I can only refer to it indirectly, by making the comp assumption explicit.


As I see it, existence itself is the neutral primitive ground of all things, abstract and concrete. Perhaps my philosophy is more like dual-aspect monism than neutral monism.

Can you elaborate shortly on the difference between dual-aspect and neutral monism? Comp is octal-aspect monism, when Theaetetus enters into play.




[SPK]
Once I have constructed a mental representation of the subject of a reasoning or concept I can use the symbolic representations in a denotative capacity. This is how we dyslexics overcome our disability. :-)

Why don't you do that for "Ex ... x ...."? in the numbers domain?







My result is: mechanism entails immateralism (matter can exist but as no more any relation with consciousness, and so is eliminated with the usual weak occam principle). This should be a problem for you if you want to keep both mechanism and weak materialism, but why do you want to do that. On the contrary, mechanism makes the laws of physics much more solid and stable, by providing an explanation relying only on diophantine addition and multiplication.

[SPK]
I reject all form of monism except neutral monism. Existence itself is the only primitive.

In what sense would mechanism, after UDA, not be a neutral monism.
When you use the word "existence" without saying what you assume to exist, it look like the joke "what is the difference between a raven?".

[SPK]
    The totality of all that exists, it merely exists.

In non founded set theories, perhaps. But this is assuming far too much, again in the comp frame. The totality of all that exists does not make much sense to me. I can imagine model of Quine New Foundation playing that role, but that is too much literal, and seems to me contradictory, or quasi-contradictory. But with comp this would be a reification of the epistemological. We just cannot do that.



Prior to the specification of properties, even distinctions themselves, there is only existence. Existence is not a property such as Red, two or heavy. It has no extension or form in itself but is the possibility to be and have all properties.


This seems to me quite speculative, and useless in the comp theory. If you were betting that comp is false, I could understand the motivation for such postulation, but are you really betting that comp is false?




[SPK]
Numbers and arithmetic presuppose a specific meaning, valuation and relation.

This is fuzzy. In the TOE allowed by comp, we can presuppose only 0, s, *, and + and the usual first order axioms.



This implies, in my reasoning, that they are not primitive.

They are ontologically primitive, in the sense that ontologically they are the only things which exist. even computations don't exist in that primitive sense. Computations already exists only relationally. I will keep saying that computations exists, for pedagogical reasons. For professional logicians, I make a nuance, which would look like total jargon in this list.




You seem to assume that they are objects in the mind of God, making God = Existence. I disagree with this thinking.

But with comp, God = arithmetical truth, although we have to be careful, because no machines, including perhaps me, can really assert that. It is a just non rationally communicable, but "betable", once we bet on comp.




Could you define to me what you mean by topological dual of a number, or a program?


[SPK]
I do not recognize the idea that a number or a program has a meaning isolate from all else. I do not understand your theory of meaningfulness. How does meaningfulness arise in your thinking? I use a non-well founded set type Dictionary model and have discussed it before.

Meaning arise in the mind of number, and the mind of numbers arise by the computational relations they have with other numbers, probably so in the comp theory.


I have never stop to give references on this, beyond my own work. See the name Boolos, Smorynski, Smullyan in my papers and books, or in my URL. What is it that you don't understand in the second part of the sane paper.

[SPK]
I do not understand how you ignore the fact that one must have a means to implement a set of distinguishable symbols, configuration of chalk mark on slate, etc. to denote and connote an abstraction. It is as if you presuppose physicality without giving it credit for what it does. I do not know what else to say now to make this idea more clear.

You keep confusing the number 17, with physical representation of it.
I do have symbols, but why should they be physical. I use the mark "0", but I can use anything else, physical or not. Arithmetic does not presuppose physicalness? Book on numbers say nothing about any possible relations with physics.





Physicist seems not to have the notion of models, and use that term where logician use the term "theory". Roughly speaking, for a logician "model" is for "a reality". I remind you also that Deutch advocates physicalism, and so, if you get the UDA as you said, you know that Deustch physicalism is incoherent with digital mechanism (which he advocates in FOR).


[SPK]
I wish that you would write more addressing this critique of Deutsch's argument.

Recently on the FOR list Deustch admitted not having a reply to my objection. I think he wants still searching one.




Arithmetical truth is the territory. Machines and numbers are what build maps of the territory. When you say "yes" to a doctor, you are just changing a map for another. Nowhere is a confusion between map and territory, except for the fixed points, like the here and now indexical consciousness. But we can be thankful that this is possible (in computer science) because it makes the map/brain useful when relating with a probable part of the territory.


[SPK]
But are when maps and territories are made of the "same stuff" we have problems.

Not necessarily. Or you take the word stuff too literally perhaps.


[SPK]
I used the word 'stuff" in quotes so that it would not be taken as literal.

OK, but then there is no problem with maps and territories having the same "stuff". You can use Kleene second recursion theorem, of your unfounded set theories to provide sense to such fixed points.




You can use Scott topology to modelize computations. Stopping programs will correspond to fixed point transformations. But my question was more easy, and can be recasted in physical terms: does a machine stop or not stop (accepting a robust physical universe, and no accidental asteroid destructing the machine)?


[SPK]
OK, I still do not comprehend how you can say this and still be a ideal monist. I am tired.

Take a nap, and then you might answer the simple question: accept you the truth that [phi_i(j) converge V phi_i(j) does not converge].

I remind you also that you can classify me as an ideal monist only if you accept that numbers are ideas (in God's mind, perhaps), but I prefer to classify the comp's consequence as being neutral monism, or octal-monism. But this might only be a vocabulary problem.

I am not arguing for or against any philosophical truth. My point is technical. It is that IF we can survive with a material digital body/ brain, THEN the physical laws emerge, in a precise way, from already only addition and multiplication of (non negative) integers. Another way to put it: IF we can survive in a digital "matrix", then we are already in a digital matrix.

I am not pretending that the proof is without flaw, but up to now, I can find flaws in the way people describe flaws in the reasoning: they almost introduce systematically a supplementary philosophical hypothesis implicitly somewhere. No philosophical hypothesis can refute a deductive argument per se (it might certainly help to find a flaw, but then they have to find it).

Bruno

http://iridia.ulb.ac.be/~marchal/



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