On 11 Sep 2010, at 00:42, Stephen P. King wrote:

## Advertising

Hi Bruno, -----Original Message----- From: everything-list@googlegroups.com [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal Sent: Friday, September 10, 2010 11:16 AM To: everything-list@googlegroups.com Subject: Re: What's wrong with this? On 09 Sep 2010, at 14:37, Stephen P. King wrote:Hi Bruno, My thought is to look at the transformation group around which some property is invariant to act as a generator of the properties of the, say, quark.[BM] Good idea. That is related with the importance of group theory and (soon) category theory in physics.For simple numbers this would be a permutation over fields, one field per number,[BM] Why? We may have use combinators instead of numbers. Their role areintensional, and representational. Their intrinsic mathematicalstructurecertainly plays some role, but I don't see why to use them directly tomirror physics. Even if that works (by chance) it would hidden themind-bodyproblem. Of course it might be very interesting, and the relationbetweenphysics and number theory suggest that such approach have theirmerits.[SPK] YES!!! You nailed it! Let me paste a little note here that I just wrote up. I apologize in advance for the crudeness of this. *** Integers as Arithmetic Equivalence Classes and implications by S. P. King 9/10/2010 Zero-ness _______ 0 + 0 = 0 0 - 0 = 0 0^1 - 0^1 = 0 1 - 1 = 0 2 - 2 = 0 3 - 3 = 0 ... 0 x 0 = 0 _______ One-ness _______ 0 + 1 = 1 1^1 + 0 = 1 1 - 0 = 1 1^1 - 0 = 1 2 - 1 = 1 3 - 2 = 1 4 - 3 = 1 . 1 x 1 = 1 2 / 2 = 1 3 / 3 = 1 4 / 4 = 1 . _____ Two-ness ________ 1 + 1 = 2 1^1 + 1^1 = 2 0 + 2 = 2 3 - 1 = 2 4 - 2 = 2 5 - 3 = 2 . 4 / 2 = 2 6 / 3 = 2 8 / 4 = 2 .. _______ Etc. External symmetry = 3rd person aspect. Each Class has aleph_null tuples and thus has the same cardinality.We could use the permutation symmetry over the cardinality toidentify anexternal or 3rd person notion of Integer. This would generate anotion ofthat is an Integer that is invariant to a change from one of the Nclassesto another. What would be the internal symmetry? Internal Symmetries = 1st person aspect. Note that we can substitute equivalent elements of the tuples witheach other by the use of bracketing or some other push/pop method.Thiswould ultimately show that the tuples are combinations of "images"of eachother's elements so that there is 1) no primitive atom and 2) that thepattern of similarities and differences over this tapestry ofcombinatoricswould encode the operations of Arithmetic. Property 1 is the reasonI usenon-well founded set theory, by the way... *************

`It is difficult for me to follow. In ZF there is no atom, yet it is`

`well-founded. Non well-foundedness is motivate by introducing set`

`having themselves as elements, or having elements having elements ...`

`having elements having the starting set as an element.`

It is my suspicion that the mind-body problem is caused by a lack ofunderstanding of what is involved. It is far too easy to throw upone'shands and settle for some silly eliminatism; Ignorance is Bliss.Notice thatboth the internal and external symmetry notions here yield a kind ofindefiniteness that Plotinus would point to, as per yourdiscussions, todefine Matter.

`You should elaborate, but you should make clear the relation between`

`math and philosophy/theology.`

But what about the information content itself of the relations themselves? Is Information identical to Indeterminateness?

`Information is a tricky word having different meaning in different`

`theories. It can be a measure of surprise, like in the old Shannon`

`theory, or something related to meaning, like in logics and in the`

`press. We can relate all that, but then we have to be almost formal`

`for not falling in the traps of non genuine analogies.`

Itseems to me that the answer is a resounding NO! I claim that it isits Dual.Thus I advocate a form of mind-matter dualism in terms of anInformation-Matter dualism following the lines of the Pontryagin andStonedualities. http://en.academic.ru/dic.nsf/enwiki/327868

`You may elaborate, but Stone dualities are very technical hard matter.`

`I guess you are alluding to Vaughan Pratt's work on Chu Spaces.`

but this seems to not really resolve the question entirely.[BM] I am not sure I have a clear idea of the question, here. [SPK] Am I making any sense so far?Itmakes me suspicious of the entire Platonic program, for what wouldactas the universal generator of "twoness" as distinguished from "threeness" be in-itself? Why not some kind of nominalism that transforms asymptotically into universalism?[BM] You lost me.You know how I work. I start from an assumption about some linkbetweenconsciousness and Turing 'machine', and from this I derived step bystep aframe which is closer to Plato and Plotinus than to Aristotle, atleast onthe "Matter" notion. [SPK] Yes and I use the assumption that any 1st person "content" ofconsciousness can be show to be equivalent to the content of somevirtualreality generated by a Turing Machine (given with sufficient physical resources)

`But this has been shown not working. You cannot both capture`

`consciousness by Turing machine states, and at the same time to invoke`

`a notion of physical resource. It is the whole point of most of my`

`posts. Physical resource including space and time have to be recovered`

`from the math of (abstract) computer science.`

and following your arguments will agree that while the contentitself is computable, *which one of the computations it is* that istheactual generator of the particular content of a particular point ofview isnot computational.

I am OK, here.

These thoughts tie back to the point about indeterminateness that Plotinus brilliantly made and you point out.

`Yes. Note that the idea of relating matter to indeterminacy is already`

`in Aristotle. Alas, Aristotle and/or its successors have reified it`

`metaphysically. That is, imo, what makes the mind-body problem`

`insolvable.`

Your modelization so far seems to only consider a "frozen"perspective and there is scant mention of how the model is extendedto covera plurality of entities, except for the diamond^alpha aspect mentionedbelow. As far as I can tell, your Model offers a logical structureto a newversion of the individual Leibnizian Monad (http://www.iep.utm.edu/leib-met/#H8 ) that I am trying to develop,but onlyin the static sense. There is no dynamic in it.

`The 'sensible' modalities, like Bp & p, and Bp & Dp & p, introduces an`

`internal dynamic. S4Grz is not just a logic of knowledge, it is a`

`logic of evolving knowledse, or time. It is due to the "& p". It makes`

`the first person intuitionist, the builder of its mental reality.`

I think that this isintentional since you are taking an explicit Platonic Idea stance intheModelization of Plotinusian Statics. I appreciate that, butunderstand thatunless we can derive change from changelessness within ourmodelizing we aredoomed to eliminatism when it comes to our 1st and 3rd notionstemporaltransitivity, duration and causality.

`That's right, but the nice thing is that the first person notion`

`automatically provides an internal dynamics.`

It is my contention that it is impossible to derive change from changelessness,

`Even physicalists can accept this though. Many physicists don't`

`believe in time. It emerges for local observers when embedded in the`

`block-static reality.`

`Of course we accept the (non trivial) ordering of the natural numbers,`

`which can be seen as the Mother of all computational times.`

but the converse is easy toshow.... Leibniz himself made this mistake so I do not fault you toomuch.;PBTW, I really enjoyed reading your SIENA paper. My only comment onitis that I wish you would elaborate more on the diamond^alpha t aspect because that is where plurality obtains.[BM]Thanks. Actually I think, but I'm still not quite sure, that the"^alpha"feature should explain the graded aspect of the quantum logics,which shouldexplains the origin of the tensor product, of the plurality ofdimension,and eventually the (quantum) structure of space-time. The manyworlds aremore due to the extreme redundancy of the computational histories in arithmetic. [SPK] In the quantum logic that I have studied so far there is the factthat there are an infinite number of instantiations (not sure ifthat is theright word) of Boolean algebraic structures within a sufficientlygeneralQuantum Logic propositional lattice. See:http://en.wikipedia.org/wiki/Quantum_logic This might be the placewhereplurality obtains. One of my interests is in looking at the extension of Qlogic thathas a Local instead of a Global change (time = measure of change)parameter.So far I think that I have an idea but it is still only embryonic. Iamlooking at whether or not it is possible to use the notion offamilies ofparameters or functors that preserve the bijective map from densityoperators to density operators which is convexity preserving betweenpairsof Quantum systems, where the QM system is taken as a Monad. Rightnow Ineed to figure out what would generate the convexity. I know that Ilackmuch of the sophisticated knowledge needed to do this quickly, so mywork isvery slow.

I wish you good luck. Bruno 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-l...@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.