On 28 Sep 2011, at 15:53, Pierz wrote:

## Advertising

At what point does mathematical truth stop? It seems to be theexistence ofsome would imply the existence of all.Like I said, I need to let this marinate in my consciousness a while. I agree that all mathematical constructs must have the same kind of existence, the same ontological status. But I see a distinction between the type of existence pi has, and the type of existence that time, space and matter have. Well, obviously. The question is, are they prior to such instantiated entities, or emergent from them? Similar to the question, are physical laws objectively extant, or mere descriptions of 'habits'?Do you agree that at least something has to be primitively real?Well I can't really escape that, can I? :) I favour consciousness as a prior reality, a spiritual position I suppose, though I also believe these categories may well just be prejudices in our mental make-up. For physicists, it's the quantum field, for mathematicians it's number, for saints it is love. All perhaps faces of an unnameable prior something. I've read Bruno arguing for number's capacity to explain qualia, and I find it unconvincing.

Do you mean by this that you think that we are not machine? Are you rejecting Theaetetus theory of knowledge (true opinion)? What is not convincing?

Mathematics is pure structure and qualia are non structural, non quantifiable, not that they are 'uncomputable', but just don't fall into the computable/ uncomputable opposition at all.

`Modal logic is both mathematics, and it handle the non-computable, and`

`the qualitative.`

`In particular some of the variant of self-reference modal logic handle`

`explicitly and in a formal way the knowledge that the machine itself`

`is unable to formalise. It is (meta) formal logic of the non`

`formalisable.`

If a person had no right brain at all, he might argue the way Bruno does on this point. (I'm worried about insulting him again now. I don't mean it's half brained. I mean it is blind to all but the quantifiable, and therefore will never satisfy an artist, for instance).

`Those who have the less problem with mechanism and its consequences`

`are the artists and the engineers.`

So qualia make me prefer to seek my ontological roots in the notion of consciousness rather than number.

`This is frequent with mystically inclined people, but I think it is`

`just due to a reductionist conception of numbers and machines, which`

`is provably untenable since GĂ¶del's discovery of incompleteness. You`

`are the one dismissing qulaia for a vast type of entity, in case you`

`use this to refute mechanism.`

We also are aware of every possible goodness or blessing. At aminimum,this realization should compel us to treat each other better. Inthe end,the conclusion is little different from the golden rule or theconcept ofkarma. All the good things we do are experienced by others(ourselves),same with all the bad things.Yes, yes and double yes. I made the exact same point in that blog post I mentioned on the subject. If we knew this, truly believed in this unity of the observer, we would move quick smart to a society optimized for the benefit of all. We can never gain at another's expense. Not "There but for the grace of God go I" but simply "There go I."

`OK. But this is non communicable by (sound) machines. In fact in the`

`ethics of the ideally correct machine, asserting moral principle is`

`immoral. We can only encourage people to understand or discover this`

`by themselves.`

Bruno

On Sep 28, 3:09 pm, Jason Resch <jasonre...@gmail.com> wrote:On Tue, Sep 27, 2011 at 10:44 PM, Pierz <pier...@gmail.com> wrote:OK, well I think this and the other responses (notably Jason's) have brought me a lot closer to grasping the essence of this argument. I can see that the set of integers is also the set of all possibleinformation states, and that the difference between that and theUD isthe element of sequential computation. I can also see that my objection to infinite computational resources and state memory comes from the 1-p perspective. For me, in the "physical" universe, any computation is restricted by the laws of matter and must be embedded in that matter. Now one of the fascinating revelations of thecomputational approach to physics is the fact that a quantity suchasposition can only be defined to a certain level of precision by the universe itself because the universe has finite informationalresources at its disposal. This was my objection to the UD. But Icansee that this restriction need not necessarily apply at the'higher' 3-p level of the UD's computations. What interests me is the question: does UDA predict that the 1-p observer will see a universe with suchrestrictions? If it explains why the 1-p observer seems to existin aworld where there is only a finite number of bits available, despite existing in a machine with an infinite level of bit resolution, thenthat would be a most interesting result. Otherwise, it seems to metoremain a problem for the theory, or at least a question in need ofananswer, like dark matter in cosmology.I am going to have to meditate further on arithmetical realism.Nice.I don't believe in objective matter either (it seems refuted by Bell's Theorem anyway),Do you agree that at least something has to be primitively real?but a chasm seems to lie between the statement "17 is prime" and "the UDA (Robinson arithmetic) executes all possible programs". The problem is one of instantiation. I can conceive of a universe - a singularity perhaps, with only one bit of information -in which the statement "17 is prime" can never be made. Toformulate,ie instantiate, 17, requires a certain amount of information.True, a certain amount of information is required to realize orrepresentcertain mathematical truths. Our universe may be large, but therearenumbers so big we cannot represent them either. My opinion is thatthispractical restriction placed on us does not mean such mathematicaltruth isnon-existent, only inaccessible. In the same sense that beforethere werehigh-powered computers, finding large Mersenne primes was beyond ourcapacity, but that did not mean they were not already there waitingto befound.To saythat a program executes, as opposed to saying it merely is impliedbya set of theoretical axioms, requires the instantiation of that algorithm. I suppose this is a restatement of the problem above. Arithemetical realism then would be the postulate that everything implied in arithmetic is actually instantiated. It seems to me I cangrant 17 is prime, without granting this instantiation ofeverything.At what point does mathematical truth stop? It seems to be theexistence ofsome would imply the existence of all. If you think Pi has anobjectivevalue, then you should also accept that Chaitin's constant (http://mathworld.wolfram.com/ChaitinsConstant.html) has a certain value.If it does, it requires the platonic execution of all programs.Sadly when you start to talk about the difficulty of proving thatourhistories in the UD are more random than the actual histories weobserve, I can't follow you any more - too much theory I'munfamiliarwith. I can see however that many (nearly all) of the infinite computations passing through our aware states will destroy us, as it were, so we can never exist in those computations (sort of anthropicprinciple). This also suggests a kind of immortality, the samekind asI propose in a blog post I wrote called the 'cryogenic paradox' inwhich I argue that there can only be a single observer, a singlelocusof consciousness underlying all apparently separate consciousnesses, which would really be just different perspectives of this one observer. It seems irresistible as a conclusion (from philosophicalarguments quite different to the UDA), and yet also kind ofhorrific.Only a sort of state-bound recall barrier prevents us from beingawarethat we suffer every fate possible.We also are aware of every possible goodness or blessing. At aminimum,this realization should compel us to treat each other better. Inthe end,the conclusion is little different from the golden rule or theconcept ofkarma. All the good things we do are experienced by others(ourselves),same with all the bad things. In a sense this thought is scary,but it isalso can be unifying and fill us with awe at the infinitepossibility andexperience that awaits us. Jason--You received this message because you are subscribed to the GoogleGroups "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.

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.