On 01 Feb 2012, at 21:48, Stephen P. King wrote:

On 2/1/2012 3:06 PM, Bruno Marchal wrote:



I don't get it.

Many people have discussed this idea that Existence, in-itself, is primitive and neutral (has no properties or divisions). It is not original with me. For example, Bertrand Russell's discussion of neutral monism and Russell Standish's ToN explain it well.

There might exist phenomenological hermeneutic of the monist kind, but this, once we chose to do science, is a private affair, which can inspire but cannot be communicated. So by a neutral monist theory, its is meant a theory which does not assume mind, nor matter, and explain them from something else. That something else needs to be able to be described in first order logic, at least. It should have terms for the existing objects, and axioms for the laws to which those objects obey. Without those two components, we can do nothing.









What I ask is a scientific theory, by which I mean a first order logical theory about what you assume to exist, and then theorems justifying the other form that "existence" can take.

All that does not contradict itself and is thus necessarily possible exists, thus I claim that existence is necessary possibility.

That's an old idea in philosophy. It is the indexical idea that existence is consistence seen from inside. In first order logic it makes a lot of sense, given that consistence is equivalent with the existence of a model. And in AUDA, the necessity of the possibility of p, BDp, is the consequence of sigma_1 truth, and its leads to an arithmetical quantization. Here Bp is for (Bew(p) & Diamond("1=1")), and Dp is (Diamond(p) v Bew(f) 'relative consistency)). p is sigma_1.

Once you are using notion of necessity or possibility, being precise forces you to suggest in which modal logic you are working, and how you justify it. There are infinities of modal logics. UDA justifies the use of the self-reference modal logic, and their variants. Gödel's results (and Löb's one, and Solovay) don't let many possible choice for the ideally correct machines. The variant described above are the one needed to find the correct physic (correct with respect to comp, if you get UDA).

I don't know if comp is true or not, but comp makes theoretical computer science a lantern to find the key. It allows a mathematical formulation of many subproblems of the (comp) mind body problem.


Bruno

http://iridia.ulb.ac.be/~marchal/
Hi Bruno,

On these particulars we can agree. Our only disagreement is that you seem to consider that Arithmetic is at the same level as bare Existence and I see bare existence as neutral and that both logics (including arithmetic) and physicality are non-primitive.

Then tell me what you mean by "Existence", and show me how you derive logics, arithmetic and physicality from that. Unfortunately, people mature enough in logic know that you can't do that. No formal arithmetic can be deduced from anything less than itself. Our beliefs in the natural numbers is authentically mysterious. But with comp we can, and we must, explain everything from them. And it works, because arithmetic emulate the ... self-referential resonance of numbers, which appears to be very rich and full of surprise.





Have you noticed that I claim that the duality that I am considering vanishes at the level of Existence itself?

I have still not the slightest clue of what you mean by "Existence".





This is because we cannot consider Existence to be partitioned without specifying a basis for the partition, in other words our ontological models have to start at our level of substitution and cannot remain coherent if we subtract out our existence as entities that can distinguish, for example, 0 from 1.

This does not follow logically. We, the distinguishers of 0 and 1, certainly exist at some level, from some point of view. But that existence might be derivable (and is derivable) in arithmetic, once we assume comp. Some aspect of it are not derivable, and yet are still true and existing, and can be meta-justified for simpler machines than us, so that we can grasp them indirectly, including our incompleteness with respect to those truth, and which comes from our local relative finiteness.

If not, like Craig, perhaps like Rex Allen and Benjayk, you are postulating that comp is false. If that is the case, I encourage you to make that precise, and to study comp and computer science to even just define "non-comp". That will not be easy. AUDA works, for example, for many transfinite sequences of weakening of comp.

Bruno


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



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