Le 19-juil.-06, à 18:01, John M a écrit :

Bruno,

George wrote an admirably wise note and you picked positively on the roadmap with the fruitful mind of a logician.

It looks like you both start out from "not agreeing because of non-understanding math sufficiently" - which may be true, but not necessarily the "real" root.

I think many of us have the wrong information about 'math' in question. You called "numbers" the series of '1,2,3...many' and "we" think 'math' is a manipulation of such, even if many substitute and functional symbols are used.

All right.

My question (and I asked it several times here and on diverse other lists and got no satisfactory answer) - still prevails:

What are (in the new meaning) NUMBERS - how can we handle the non-number concepts by numbers - (whatever they are)? Rephrased: What is the 'new' meaning of "math" and how can non-math concepts be handled by math?

OK, OK, but this is a difficult question, John. Let me give you a standard answer, which should be simple, and then add a comp nuance, which is probably a little bit more subtle.

First I don't think there is new meaning of math. Just new branch of math like mathematical logics, philosophical logics, metamathematics, computer science, etc.

Since Euler I think mathematician are more and more aware that the numbers are mysterious, and since Godel we have results which somehow explain why numbers are necessarily mysterious. Such limitation results are made *general* (machine or formalism independent) with Church thesis. And then with comp above, those results will bear on the limitation of *humans*: in that sense we can say that we begin to understand why the numbers are mysterious, why we cannot find unifying theory for the numbers, etc.

Now for the question "How can non-math concept be handled by math?"

The standard answer goes trough the label "applied mathematics". You just need to make a correspondence between some term of the theory and some element of the "reality" you want to modelize with the math theory. This is what physicists do all the time, and this what theologians have done during one millenia (before "religion" has been used as a political power (say)(*))

It just applied mathematics.

Unfortunately with comp there is a big nuance here.

Indeed, when you are using some theory (model in the physicist sense) to predict the whether (say), it is clear that the "model" is a thorough simplification of "reality". In the case of whether prediction, we have no "exact equations", and worst, the few equation we have are not analytically soluble, so that a computer simulation is in need. Similarly you can *apply* math to simulate neural networks and (perhaps) learn something about the brain.

OK, but now, when you are willing to say "yes" to a doctor when he proposes to you an artificial digital brain body things are fundamentally different. The artificial brain is no more supposed to *modelize* you brain, like in the whether case, but to save your "soul". In this case the "model" is supposed to be the reality. That is obviously quite a jump, but it is made reasonable through the computer scientist distinction between "emulation" and "simulation". It is known that universal machine can not only simulate many things, but can also emulate exactly all digital processes (thanks to Church thesis). Eventually this can be explained through diagonalization and "semantical fixed points", but I don't want to be technical here. So with comp (= mainly "yes doctor") you apply math to a part of pure math, like in metamathematics or theoretical computer science, which, through comp, describe the living realm we are inhabiting.

(*) See perhaps the following PDF on "Mathematics and Theology" Note that I disagree with the main conclusion.

http://www2.hmc.edu/www_common/hmnj/davis2brieflook1and2.pdf

Norman touched it, 1Z goes around it, David Bohm even went that far as to state: numbers (and so math) are human inventions, probably based on Plato, who made the biggest (philosophical) argument - as the product of HIS mind.

Bohm is even more coherent with respect to the comp consequence than Chalmers in the sense that he explictly postulate non-comp (in its "intricate order" book).

Words are loaded with different meanings and people tend to use their favorite - mostly from the mother tongue. I admire George's open mind accepting the diverse positions and I am also no missionary who wants to convert people, but even if I think differently, I like to follow the mental ways of others. It may add usefully to my own thinking.

Note, and this is a key point, I am not defending any position at all. I try not to insist too much because it could look pretentious, but I do think even just the UDA (including the Movie-Graph) does not leave any choice in the matter. In a nutshell I believe the UDA shows that IF comp is taken sufficiently seriously (as to say purposefully yes to a doctor for example) then Plato's conception of reality is correct and Aristotle's one is incorrect.

So I propose a 'starting' point to the 'roadmap':

How may one consider the new version(s) of number and math instead of the arithmetic-based and binary computer founded conventional ignorance? (It is not a 101 course what this list should be above, it may draw in 'more-sided' opinions into the discussion - which is now pretty much on the math - physics base only. Extending to other planes of 'everything'.)

Then we may proceed in understanding the 'stuffy' matter (as e.g.. a photon - ha ha) and the physicists' concepts mostly based on some mathematical application, including the most esoteric 'everything' topics.

After all that I may try to speak about my ways how I am not in controversy with all that - only regarding it as a partial view of the totality (which is hard to talk about). Not for converting you or others, just for proving to myself some (Levy-type) sanity.

So how should I include the validity of a legal opinion into the numbers?

Here I am not sure I follow you. When I talk about (natural) numbers I am really talking about those (non definable) entities that every schoolchild learn about through table of addition, multiplication, etc. They are the same as Euclid's one in the sense that all what Euclid proved about them is still valid today.

How should I 'comp'(?) the feeling of love?

In principle there will no be problem for that, although I still cannot explain this without explaining more about the G-G* gap. Later perhaps. Note that such a question is more difficult for a physicalist who believes only in atoms or strings (or quantum gravity loops ...) because they don't have (yet) the equivalent of the G-G* gap (akin to the explanation gap of the philosopher of mind). Try to explain why you like potatoes using only terms from string theory, for example.

But comp provides an explanation why anything describable in a seemingly third person way, will automatically be extended into a math structure divided in two parts: a 3-communicable part (deriving from G), and a non-3-communicable part (deriving from the corona G* minus G).

I recall that G is a mathematical theory describing completely the (skeleton) of what a correct machine can prove about itself, and G* describes the (skeleton) of all the truth---including the non provable one---concerning what a machine can (and cannot) prove about itself.

For those who have read a bit on the difference between programmable function Fi and the total computable function fi could perhaps already smell the mathematical justification of that "explanatory" gap.

How should I 'materialize' (physically?) the beauty of a sunset?

(all without flattening those qualia into a quantitative plane)?

It is exactly here that it is hard for me non going technical because I find it is worth. Indeed it can be proved that when a universal machine M1 introspects herself, she will discover both sharable (provable) quantitative truth and non sharable qualitative (non quantitative, nor even 3-describable) truth. Actually any much stronger (in term of its set of beliefs) universal machine, M2 say, will be able to show that those non quantitative truth are really disguised form of quantitative truth, but M2 can understand why, from the many points of view of M1 itself (including both the 1 and 3 povs), although quantitative, those truth cannot *appear* to be quantitative. M1 can grasp those personal truth only in a qualitative way. This will explain qualia, but also why in some sense a universal machine cannot know she is a machine, nor even any 3-entity.

Later I will come back on the "arithmetical notion of persons" we encounter through the self-reference theories (G and G*) in computer science. I call them "hypostases" so that people who read Plotinus can see how close we are, with comp, to Plato, and even to Plotinus' critics of Aristotle "misunderstanding" of Plato.

But that is probably on the last point of the roadmap, so I stop, momentarily here. If I have already been too technical just tell me or ask questions. Hope this helps a bit,

Bruno

Eager to learn

John Mikes

<x-tad-bigger>----- Original Message -----</x-tad-bigger>

<x-tad-bigger>From:</x-tad-bigger><x-tad-bigger> </x-tad-bigger><x-tad-bigger>Bruno Marchal</x-tad-bigger><x-tad-bigger> </x-tad-bigger>

<x-tad-bigger>To:</x-tad-bigger><x-tad-bigger> </x-tad-bigger><x-tad-bigger>everything-list@googlegroups.com</x-tad-bigger><x-tad-bigger> </x-tad-bigger>

<x-tad-bigger>Sent:</x-tad-bigger><x-tad-bigger> Wednesday, July 19, 2006 10:39 AM</x-tad-bigger>

<x-tad-bigger>Subject:</x-tad-bigger><x-tad-bigger> Re: K the Master Set (+ partial answer to Tom's Diagonalization)</x-tad-bigger>

Hi George,

A roadmap could be a very good idea. I will think about it. <snip>

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

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