It seems that we need to discuss more basic ideas as it seems that my attempted explanations are not bisimulating with your thoughts. From: firstname.lastname@example.org [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal Sent: Tuesday, September 14, 2010 9:40 AM To: email@example.com Subject: Re: What's wrong with this? On 12 Sep 2010, at 21:43, Stephen P. King wrote: Hi Bruno, -----Original Message----- From: firstname.lastname@example.org [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal Sent: Saturday, September 11, 2010 11:36 AM To: email@example.com Subject: Re: What's wrong with this? On 11 Sep 2010, at 00:42, Stephen P. King wrote: Hi Bruno, -----Original Message----- From: firstname.lastname@example.org [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal Sent: Friday, September 10, 2010 11:16 AM To: email@example.com Subject: Re: What's wrong with this? snip *** 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 to identify an external or 3rd person notion of Integer. This would generate a notion of that is an Integer that is invariant to a change from one of the N classes to another. What would be the internal symmetry? Internal Symmetries = 1st person aspect. Note that we can substitute equivalent elements of the tuples with each other by the use of bracketing or some other push/pop method. This would ultimately show that the tuples are combinations of "images" of each other's elements so that there is 1) no primitive atom and 2) that the pattern of similarities and differences over this tapestry of combinatorics would encode the operations of Arithmetic. Property 1 is the reason I use non-well founded set theory, by the way... ************* [BM] 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. [SPK] Yes, in my example above it seems to be the case that the N-ness classes can have themselves as elements and so forth. For example, in the Zero-ness class, there is a couple of 0s that are equaling 0 when added, subtracted or multiplied. Is this not an example of an element having itself as an element? My wording might be incorrect according to the usual definition of class, etc. but I hope that my meanings are communicated. [BM] Honesty I am a bit lost. [SPKnew] OK, did you make sense of the idea of representing Integer with a sort of equivalence class that have members that are the arithmetic generators or creators or acts that equal examples of the number? We can think of 1 in the Platonic sense as the class of all arithmetic operations that are equal to 1, 2 as the class of all arithmetic operations that equal 2, etc. OK, given that then it seems to follow that, say a 2 in the operation that equals some other number is in a sense a mapping of the entire class of 2 into that other class. Does this make sense so far? snip [SPK] Let me quote something from Carlo Rovelli that I found in "Quo Vadis Quantum Mechanics?" referring to C. E. Shannon's 1949 book: "...the definition of Shannon, not the popular one, but the one in his book, where you have two systems with many states, and there is a possible state of the couple but there is only a restricted subset of all joint states. Information is simply the way of counting the allowed joint possible states. The fact that there is a common allowed state tells you that if you know something about one system you also know something about the other one. This is exactly what you need in communication theory when you have a channel, a receiver and a transmitter. So I have two systems. If there is a quantum correlation of the two, I can say that, if this system is UP, the other is DOWN, and vice versa. This is what I mean by information, period." I am attempting to be faithful to this definition. Interestingly, it seems that since the equivalence classes that I pointed out above are countably infinite then the property that any proper subset of infinity is isomorphic to the infinity would apply and this would make the notion of information for such classes to vanish, no? It would be a zero-information system of sorts! [BM] ? [SPK] How do we consider the information content of infinite sets? Given that and the way that we see mapping from classes into classes as pointed out about, does this not give us a notion of "the way of counting the allowed joint possible" elements? It seems to me that the answer is a resounding NO! I claim that it is its Dual. Thus I advocate a form of mind-matter dualism in terms of an Information-Matter dualism following the lines of the Pontryagin and Stone dualities. http://en.academic.ru/dic.nsf/enwiki/327868 [BM] You may elaborate, but Stone dualities are very technical hard matter. I guess you are alluding to Vaughan Pratt's work on Chu Spaces. [SPK] Yes, it is Pratt's idea that inspires this thinking. What he has found is that is possible to solve the problem of Cartesian Dualism, but in solving the problem we chance the notion of "substance" into one that is emergent from underlying Process and not taken to be a primitive. [BM] ? (like with the UD argument?). [SPK] I don't understand how your UDA does this. I need to study it further. I need to understand how you obtain the notion of concurrency in your model, for it is not sufficient to encode transitivity for a single system, we need to show how a vast number of systems synchronize and correlate their states with each other, otherwise our model is solipsistic; incapable of modelizing beyond itself. [SPK] What convinced me of the validity of his idea is that it offers a very neat and novel solution to the measurement problem of QM. [BM] Different from Everett's solution? (Which appears to extend the mind-body problem with digital mechanism). Is Pratt a many-worlder? [SPK] No, Pratt's ideas follow the interaction interpretation of John Cramer. Resent work by Aharonov, Elitzur and other is looking in this direction. See for example: http://a-c-elitzur.co.il/site/siteArticle.asp?ar=71 snip [BM] You lost me. You know how I work. I start from an assumption about some link between consciousness and Turing 'machine', and from this I derived step by step a frame which is closer to Plato and Plotinus than to Aristotle, at least on the "Matter" notion. [SPK] Yes and I use the assumption that any 1st person "content" of consciousness can be show to be equivalent to the content of some virtual reality generated by a Turing Machine (given with sufficient physical resources) [BM] 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. [SPK] No no no! I am not "capturing consciousness by Turing machine"! I am pointing at the content, using Descartes' brain in a vat and related gedankenexperiments to show how there is an equivalence relation between the content of experience (minus "agency" notions, self-awareness, etc.) and the content of what can be generated by universal Virtual reality machines, as explained by D. Deutsch in Fabric of Reality, that can be used. The notion of a physical resource is allowed because I am assuming that both mind (crudely an information structure, like a Boolean algebra) and matter (crudely as a Cantor dust or completely disconnected Hausdorff space) are both equally existent and "real". The idea in Pratt's work is that Logic and Time (the evolution of physical systems) form a duality see: http://boole.stanford.edu/pub/dti.pdf [BM] This pleads for no fundamental matter, nor time. [SPK] Yes, but bOnly in the limit of the totality of Existence, there is no measure or differentiation, thus no matter or time in that fundamental sense. That’s why the dualism that I am advocating is one that degenerates to a neutral monism in that limit. But the Totality includes the finite and in that finite case we have matter and time. snip [SPK] Your modelization so far seems to only consider a "frozen" perspective and there is scant mention of how the model is extended to cover a plurality of entities, except for the diamond^alpha aspect mentioned below. As far as I can tell, your Model offers a logical structure to a new version of the individual Leibnizian Monad ( http://www.iep.utm.edu/leib-met/#H8 ) that I am trying to develop, but only in the static sense. There is no dynamic in it. [BM] 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 knowledge, or time. It is due to the "& p". It makes the first person intuitionist, the builder of its mental reality. [SPK] It may exist there Bruno, but it is by no means explicit. The fact that we can map Bp & p, etc. to some abstract structure and use the orderings of those relations to act as a quotienting does nothing to obtain the experiential transitivity that is explicit in the 1st person. [BM] Why? The experiential logic is typically transitive, and anti-symmetrical. [SPK] Yes, that is true but in a static Platonic Idea sense. The main problem, I suspect, obtains from the enumerability of the content of experiential logic as I see in your Model. This makes a computation of logical sentence something that has properties in-it-self independent of any notion of interaction; therefore it is, in a deep sense, solipsistic. To boil this down, we need to start with the existence of a plurality of minds, explaining why it is necessary that there is more than just the One. You move toward this in SIENA.pdf but not sufficiently to nail down the reasoning. snip [BM] 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. [SPK] So does this allow us to not consider the alternative? This is so frustrating, we have a beautiful way of deriving the appearance of changelessness from fundamental change, by using the notion of automorphisms within a wider context of morphism, and this is rejected out of hand? That is about the most irrational thinking that I can witness! The only explanation that I can think of for this is that the hope of an impersonal determinism that obtains from the block-static reality doctrine allows it adherents to avoid all notions of personal responsibility for their behaviors. [BM] On the contrary, it is explained that free-will and responsibility is unavoidable from inside. To use the determinacy of the big whole would be like to give a name to God, and that is explicitly making any Löbian machine inconsistent, and worth: incorrect. We are typically partially responsible for our normal futures. [SPK] This subtle proof has still eluded me. I want to be sure that no one is projecting anthropomorphic notions into the model without sufficient reasons that these obtain. [SPK] As to the non-trivial ordering of numbers, it should be obvious that there does not exist a unique ordering over the class of possible 1st person experiences, or computational strings; the class is not equivalent to a simply connected space which is, essentially, what is required for a unique ordering to be possible. We see this in physics in the Foliation Problem of General Relativity and in differential topology. See: www.cmp.caltech.edu/~dannyc/papers/fpams.pdf.gz we are fooling ourselves if we think that time is just the ordering of natural numbers. [BM] Nobody said that. I said only that the natural numbers does provide a kind of computational time, but the subjective time (and space time) comes from the first person logic S4Grz (and S4Grz1), in the ideal case under scrutiny. [SPK] A Liebnitzian "order of succession" aspect of time, certainly obtain in what you point out here, but that is cheap, for there are no a priori alternatives in the notion of the number that is subsequent to n, for example n +1 or n+2 have only a single and unique property. We do not see this kind of singular one- to one and onto like map of determination in our notions of free-will and responsibility. We see a selection process from a menu of alternatives, alternatives that are all given concurrently. This is a very different notion than what we see in natural numbers. Snip Let us deal with the rest of my critique of Plotinus's model some other time. It is of great interest to me as it helps me understand details that are absent in Leibnitz' Monadology and need to be considered, but I need to focus on developing a mutual understanding of the ideas here so far. Onward! Stephen P. King -- 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.