On 18 Feb 2011, at 17:13, benjayk wrote:

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Bruno Marchal wrote:Hi, What do you mean by Platonia? The kind of Platonia in Tegmark or in Peter's (1Z) post does not make sense for mathematicians. Even if you are using a theory like Quine's NF, which allows mathematical universes, you still have no mathematical description of the whole mathematical reality.Do you have to have a description of the whole mathematical reality to assert it exists?

`You need it to make sense of it. Mathematical attempts lead to either`

`inconsistent theories, or to a definition of a putative mathematician`

`(like with the theory of topos), which is very interesting but not`

`quite "platonic".`

`As a figure of speech Platonia can make sense, but it is doubtful in a`

`theoretical context, like when we search for a TOE.`

Isn't it enough to say everything that we *could* describe in mathematics exists "in platonia"?

`The problem is that we can describe much more things than the one we`

`are able to show consistent, so if you allow what we could describe`

`you take too much. If you define Platonia by all consistent things,`

`you get something inconsistent due to paradox similar to Russell`

`paradox or St-Thomas paradox with omniscience and omnipotence.`

`And then when you try to convey something which is counter-intuitive`

`and against the current main paradigm, like your poor servitor, you`

`have to base things on what the most agree (but this is not an`

`argument, just a methodological remark).`

Bruno Marchal wrote:Like in Plotinus, the ultimate being (arithmetical platonia) isnot abeing itself (nor is matter!).Could you explain what you mean with that?

`Platonia, the platonia of Plato, is the Noûs, also called the`

`Intelligible Realm, or the World of Ideas, with the idea that Ideas`

`are more true/real than any of their terrestrial approximation/`

`incarnation. For example the perfect circle is in Platonia, together`

`with PI, but any natural circle is a gross and "less real" imitation`

`of the "eternal ideas". What we see is conceived as being only the`

`shadow of that "intelligible reality".`

`But in the Parmenides, Plato understood that the Intelligible Realm`

`has to come from something completely unified, and Plotinus attributes`

`his notion of ONE to the Parmenides of Plato. In neoplatonism the ONE,`

`which is really without name, nor description of any kind, truly`

`ineffable, is the principle from which both the Intelligible Realm`

`will "emanate" 'followed' by the "Universal Soul". The Universal Soul`

`is a sort of product of both the ONE (the soul keeps its umbilical`

`cord uncut with "GOD" (the ONE), and the Intelligible Realm, also`

`called the Divine Intellect. That are the three primary hypostases of`

`Plotinus: the One, the Divine Intellect, and the Universal Soul. They`

`correspond more or less to the origin, the reason, and the experience,`

`but are presented as three Gods, in the usual greek manner. The One`

`has many things in common with the "God" of the monotheist religion,`

`and the Universal Soul has many things in common with the Inner God of`

`the mystic and many schools of Eastern religions.`

`There is a inevitable tension between the Divine Intellect and the`

`Soul, and eventually the Soul will fall, and that is how Matter, a`

`quasi synonymous of Evil, rises. The notion of existence or being is`

`defined by the Divine Intellect. What exist is what the Divine`

`Intellect can talk about, and it cannot talk about the One, because of`

`its absolute ineffability and inaccessibility, and it cannot talk`

`about Matter, which cannot belong to the Intelligible Realm, because`

`it is so much unintelligible that even God (the one) has no control on`

`it. This makes the One, and Matter outside 'existence' or being. They`

`are the antipode of the intelligible existing things. Intelligible`

`by ... the divine intellect, note, which has to be distinguished from`

`"Man", i.e. the terrestrial intellect, or discursive reasoner, which`

`is the one who dies and pays taxes, and try to understand.`

`Now, it has been shown that if you give to a universal machine some`

`provability and inductive inference abilities (easy to do), and ask`

`such a machine to introspect itself, the machine is able to`

`distinguish truth, belief (proof) and knowledge (proof of truth). She`

`can know that a truth encompassing herself is not nameable or`

`describable. She can distinguish the terrestrial believer from the`

`divine believer, and even guess a part of the "divine discourse", with`

`"divine" meaning "true" on that level where truth is not definable.`

`She can understand and feel (accepting some definition already in`

`Plato and Plotinus) the inevitable tension between the "Divine`

`Intellect" and the "Universal Soul", she can understand (believe,`

`proof) that the Universal Soul (which actually is also unnameable) has`

`already "a foot in matter', and that the Soul will fall (by connecting`

`inappropriately the terrestrial intellect with the divine intellect),`

`and the soul glues itself in that part of the internal border of`

`reality where God loose control. That generates a logic which should`

`correspond to the logic of the observable.`

`Technically, albeit roughly, with p arithmetical proposition, you have`

`the following arithmetical interpretation of Plotinus' three primary`

`hypostases, which I put in a lozenge:`

`The`

`ONE = arithmetical truth (p)`

`The terrestrial believer = Gödel's provability (Bp, logic G) ----------`

`the divine Intellect (the truth on the Gödel's provability) (Bp, but a`

`different logic (G*)`

`The`

`Universal Soul (Bp & p); logic = S4Grz`

`That represent the happy harmonic state "before the fall". The fall`

`comes from the fact that although G* proves that Bp is equivalent with`

`Bp & ~B~p, G cannot prove that, but the one who want to bet on a`

`reality has to follow the Bp & Dp logic (D = ~B~) and this gives the`

`two Matter of Plotinus, which both inherit from the G/G* splitting`

`(due to the disticntion between proof and truth, that is due to`

`incompleteness).`

`the terrestrial intelligible matter (Bp & Dp, controlled by G)`

`-----------the divine intelligible matter (Bp & Dp,controlled by G*)`

`the terrestrial sensible matter (Bp & Dp & p, controlled by`

`G)----------the divine intelligible matter (Bp & Dp & p, controlled by`

`G*)`

`You can see a lozenge above a square. It is good memo for the 8`

`variants of provability (arithmetical hypostases). Again:`

p Bp------- Bp Bp & p Bp & Dp----------- Bp & Dp Bp & Dp & p------Bp & Dp & p

`At the left you have the terrestrial (effective) realm. At the right`

`you have the divine (true) realm. The lozenge gives the three primary`

`hypostases on the right. And the poor terrestrial man on the left.`

`Magically, the Universal Soul belongs to both the terrestrial and`

`divine realm, but splits in two (terrestrial/divine) in the fall. This`

`is not easy to prove. The first person pov (the "soul") confuses`

`naturally provability/knowability and truth, like an intuitionist (and`

`this can be made very precise). The lozenge is the harmonic state of`

`the universal machine, and the square will glue the machine in the`

`realm of the consistent (Dp) extensions (histories). Note that 5`

`variants of provability lead to 8 "hypostases" dues to the G/G*`

`splitting of three of them.`

`Then, you can model computationalism, or interview the machine on`

`comp, by restricting the arithmetical interpretation of p to the`

`Sigma_1 sentences, which are the arithmetical equivalent of the`

`"border of the universal dovetailer", and this gives you 8 more`

`refined logics. By the UDA argument, The universal Soul, the divine`

`intelligible matter, and the the divine intelligible matter (with`

`some other variants of them) can provide the logic given by the`

`measure one for the observation and sensation. There, we get the truth`

`of DDf (the possibility of the possibility of the false), which is`

`similar to the early Lewis modal logics. The white rabbits seems to`

`disappear but remain very close, perhaps.`

`Gödel's theorem, which originates that "Bp" logic (G), is often used`

`as an argument that we are not machine (Lucas, Penrose), but what`

`people rarely take into account is that machines can prove their own`

`incompleteness, making the left part of the diagram provable by the`

`machine, and the right part inductively inferable, 'bettable',`

`'hopable', 'fearable', etc. (doesn't look like english, but you see`

`the point).`

`This gives a TOE, (necessitated by Comp + the classical theory of`

`knowledge), which is ontologically just (sigma_1) arithmetical truth`

`(which is really weaker than most formalism), and which admits as`

`internal epistemology provability and its variants. Each variants is a`

`different view of the same unique tiny arithmetical reality. But those`

`views from inside imposes rich topologies and measures, but also`

`complex mathematical problems.`

`Basically, for the ontology, you need only classical logic + the`

`axioms of addition and multiplication`

x+0 = x x+s(y) = s(x+y) x*0 = 0 x*s(y) = (x*y) + x

`In that system you can define the Löbian Bp and variants (a very long`

`and tedious fact shown by Gödel & Co), which "believe" in more things`

`already (the axioms of addition and multiplication + the axioms of`

`induction, which makes them Löbian and obeying, like all their sound`

`extensions to the 8 hypostases).`

`There is a subtle tour de force here, if you indulge me to say, which`

`consists to use Tarski notion of truth (p) in the place of the`

`impossible (by a theorem of Tarski) task to define truth in the`

`language of the machine, by some predicate V('p'). The same for`

`knowledge and sensibility. Quanta and qualia should appear (and does`

`appear a little bit already) at the extreme bottom right of the`

`diagram. All this is a sum up of "AUDA" the arithmetical UDA. It is`

`not needed for understanding UDA (physics is arithmetic seen from`

`inside). But UDA is useful to motivate AUDA and to relate it to the`

`mind-body problem.`

`Any universal programming system can be used instead of numbers. With`

`the combinators, the ontology is given by an even shorter theory: the`

`laws of elimination and duplication:`

Kxy = x Sxyz = xz(yz)

`I mean, the choice of the initial universal system is free. You can`

`take a quantum computer, but this is cheating with the goal of solving`

`the mind body problem, which by UDA needs a derivation of the local`

`universal observable structure. This one has to be justified properly`

`to get both the quanta and the qualia, avoiding the elimination of the`

`person and consciousness.`

`The god of Plotinus is not omniscient, nor omnipotent. "He" is`

`overwhelmed by its first emanation, the Divine Intellect, and then`

`both the ONE and the Divine Intellect are overwhelmed by the Universal`

`Soul, which truly put the mess (matter, notably) in the (arithmetical)`

`Platonia.`

`Like in Pratt's Chu transform (cf Stephen), or like in Galois`

`connections, Plotinus dynamics go in two opposite directions:`

`emanation and conversion.`

`- God (the One) by a sort of excess of generosity let the Divine`

`Intellect emanates from him, and then let the Universal Soul emanate,`

`which eventually generates nature up to matter (where God lose control`

`and man needs a "bastard calculus" on the non determination)). That's`

`the emanation part, from the One to the soul and matter.`

`- The terrestrial soul then tries hard to leave matter, and eventually`

`succeeds in reaching the Divine Intellect (by math, music, astronomy,`

`notably), and eventually recovers The inner God and the ONE phase.`

`That's the conversion path, from Matter and Soul to the One.`

`The two processes correspond to the same truth, again seen from`

`different views (the One and the Soul)`

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-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.