Hi Stephen,

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OK, did you make sense of the idea of representingInteger with a sort of equivalence class that have members that arethe arithmetic generators or creators or acts that equal examples ofthe number? We can think of 1 in the Platonic sense as the class ofall arithmetic operations that are equal to 1, 2 as the class of allarithmetic operations that equal 2, etc. OK, given that then itseems to follow that, say a 2 in the operation that equals someother number is in a sense a mapping of the entire class of 2 intothat other class. Does this make sense so far?

With a lot of effort!

`Why introduce impredicativity for the numbers? It does not make a lot`

`of sense: it introduces complexity. It seems to me like doing alpinism`

`with a microscope. It is akin to the 1004 fallacy.`

[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 Turingmachine"! I ampointing at the content, using Descartes' brain in a vat and relatedgedankenexperiments to show how there is an equivalence relationbetween thecontent of experience (minus "agency" notions, self-awareness,etc.) andthe content of what can be generated by universal Virtual realitymachines,as explained by D. Deutsch in Fabric of Reality, that can be used. Thenotion of a physical resource is allowed because I am assuming thatbothmind (crudely an information structure, like a Boolean algebra) andmatter(crudely as a Cantor dust or completely disconnected Hausdorffspace) areboth equally existent and "real". The idea in Pratt's work is thatLogic andTime (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 ofExistence, there is no measure or differentiation, thus no matter ortime in that fundamental sense. Thatâ€™s why the dualism that I amadvocating is one that degenerates to a neutral monism in thatlimit. But the Totality includes the finite and in that finite casewe 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 meansexplicit. The factthat we can map Bp & p, etc. to some abstract structure and use theorderings of those relations to act as a quotienting does nothing toobtainthe 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. Themain problem, I suspect, obtains from the enumerability of thecontent of experiential logic as I see in your Model.

It is enumerable, but not recursively enumerable.

This makes a computation of logical sentence something that hasproperties in-it-self independent of any notion of interaction;

Well, yes. At least in the third person global view.

therefore it is, in a deep sense, solipsistic.

It is platonistic. Why solispsist. You lost me again I' afraid.

To boil this down, we need to start with the existence of aplurality of minds, explaining why it is necessary that there ismore than just the One. You move toward this in SIENA.pdf but notsufficiently to nail down the reasoning.

What is missing?

[BM]Nobody said that. I said only that the natural numbers does providea kind of computational time, but the subjective time (and spacetime) comes from the first person logic S4Grz (and S4Grz1), in theideal case under scrutiny.[SPK]A Liebnitzian "order of succession" aspect of time, certainly obtainin what you point out here, but that is cheap, for there are no apriori alternatives in the notion of the number that is subsequentto n, for example n +1 or n+2 have only a single and uniqueproperty. We do not see this kind of singular one- to one and ontolike map of determination in our notions of free-will andresponsibility. We see a selection process from a menu ofalternatives, alternatives that are all given concurrently. This isa very different notion than what we see in natural numbers.

`That would be the case if all the hypostases (modal points of view, Bp`

`& p, Bp & Dp, etc.) were obeying classical logic, but S4Grz gives an`

`intuitionist logic, Z1 and X1 give quantum logics, etc. What you say`

`don't follow.`

SnipLet us deal with the rest of my critique of Plotinus'smodel some other time. It is of great interest to me as it helps meunderstand details that are absent in Leibnitz' Monadology and needto be considered, but I need to focus on developing a mutualunderstanding of the ideas here so far.

`All what I say is that we cannot have both mechanism and materialism,`

`and that mechanism explain the perception of physical laws, were`

`materialism has to postulate those laws, and use an identity thesis`

`not capable of being sustained by digital machine. So materialist have`

`to be non mechanist dualist, or have to eliminate the first person out`

`of the picture.`

Bruno Marchal 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.