On Mon, Jun 15, 2015 at 3:23 PM, Bruno Marchal <[email protected]> wrote:
> > On 15 Jun 2015, at 15:32, Terren Suydam wrote: > > > On Sun, Jun 14, 2015 at 10:27 AM, Bruno Marchal <[email protected]> wrote: > >> >> We can, as nobody could pretend to have the right intepretation of >> Plotinus. In fact that very question has been addressed to Plotinus's >> interpretation of Plato. >> >> Now, it would be necessary to quote large passage of Plotinus to explain >> why indeed, even without comp, the "two matters" (the intelligible et the >> sensible one) are arguably sort of hypostases, even in the mind of >> Plotionus, but as a platonist, he is forced to consider them degenerate and >> belonging to the realm where God loses control, making matter a quasi >> synonym of evil (!). >> >> The primary hypostase are the three one on the top right of this diagram >> (T, for truth, G* and S4Grz) >> >> T >> >> G G* >> >> S4Grz >> >> >> Z Z* >> >> X X* >> >> >> Making Z, Z*, X, X* into hypostases homogenizes nicely Plotinus >> presentation, and put a lot of pieces of the platonist puzzle into place. >> It makes other passage of Plotinus completely natural. >> >> Note that for getting the material aspect of the (degenerate, secondary) >> hypostases, we still need to make comp explicit, by restricting the >> arithmetical intepretation of the modal logics on the sigma-& >> (UD-accessible) propositions (leading to the logic (below G1 and G1*) >> S4Grz1, Z1*, X1*, where the quantum quantization appears. >> >> The plain language rational is that both in Plotinus, (according to some >> passage----this is accepted by many scholars too) and in the universal >> machine mind, UDA show that psychology, theology, even biology, are >> obtained by intensional (modal) variant of the intellect and the ONE. >> >> By incompleteness, provability is of the type "belief". We lost >> "knowledge" here, we don't have []p -> p in G. >> This makes knowledge emulable, and meta-definable, in the language of the >> machine, by the Theaetetus method: [1]p = []p & p. >> >> UDA justifies for matter: []p & <>t (cf the coffee modification of the >> step 3: a physical certainty remains true in all consistent continuations >> ([]p), and such continuation exist (<>t). It is the Timaeus "bastard >> calculus", referred to by Plotinus in his two-matters chapter (ennead II-6). >> >> Sensible matter is just a reapplication of the theaetetus, on >> intelligible matter. >> >> I hope this helps, ask anything. >> >> Bruno >> >> > I'm not conversant in modal logic, so a lot of that went over my head. > > > > Maybe the problem is here. Modal logic, or even just modal notation are > supposed to make things more easy. > > For example, I am used to explain the difference between agnosticism and > beliefs, by using the modality []p, that you can in this context read as "I > believe p". If "~" represents the negation, the old definition of atheism > was []~g (the belief that God does not exist), and agnosticism is ~[]g (and > perhaps ~[]~g too). > > The language of modal logic, is the usual language of logic (p & q, p v q, > p -> q, ~p, etc.) + the symbol [], usually read as "it is necessary" (in > the alethic context), or "it is obligatory" (in the deontic context), or > "forever" (in some temporal context), or "It is known that" (in some > epistemic context), or it is asserted by a machine (in the computer science > context), etc... > > <>p abbreviates ~[] ~ (possible p = Non necessary that non p). > > All good here. > > Thus my request for "plain language" justifications. In spite of that > language barrier I'd like to understand what I can about this model because > it is the basis for your formal argument AUDA and much of what you've > created seems to depend on it. > > > In AUDA, the theory is elementary arithmetic (Robinson Arithmetic). I > define in that theory the statement PA asserts F, with F an arithmetical > formula. Then RA is used only as the universal system emulating the > conversation that I have with PA. > Everything is derived from the axioms of elementary arithmetic (but I > could have used the combinators, the game of life, etc.). So I don't create > anything. I interview a machine which proves proposition about itself, and > by construction, I limit myself to consistent, arithmetically sound (lost > of the time) machine. This determined all the hypostases. > > It is many years years of work and the hard work has been done by Gödel, > Löb, Grzegorczyck, Boolos, Goldblatt, Solovay. > > I think it's debatable that you didn't create anything. I think reasonable people could disagree on whether the 8 hypostases you've put forward as the basis for your AUDA argument are created vs discovered. I'm coming from an open-minded position here - but trying to assert that you're not creating anything strikes me as a move to grant unearned legitimacy to it. > > I still am not clear on why you invent three "new" hypostases, granting > the five from Plotinus (by creating G/G*, X/X*, and Z/Z* instead of just G, > X, and Z), > > > This is not a choice. G does really split in two: the provable part by the > machine, and the true part on the machine (that the machine can prove or > not). same for Z*, and X*. > > But that is the chance, beacuse the notion of Plotinus are theological, > and side with the truth. > > In Plato the distinction between Earth and Heaven becomes a distinction > between effective/constructive and True. The Noùs is guven by G*. G is the > "man", or the discursive reasoner, that I take too as an hypostases, > although the man is a bit despise by Plotinus (which is normal when talking > about God, by the Platonists). > > > OK, I'm with you here. > except that you say "[it] homogenizes nicely Plotinus presentation, > > > > let us say that the math shows that there are 8 hypostases (roughly > speaking, as it is more like 4 + 4 * Infinity). > > Three describes well the three primary hyposates of Plotinus (divine > one!), and two describes what Plotinus called sensible matter, and > intelligible matter, and where the comp quantum logic appears, and should > apper, by the UDA. > > But they did split, which is not something we can avoid or hide. > > OK. > and put a lot of pieces of the platonist puzzle into place." Symmetry > isn't an explanation. What I'm looking for would be something along the > lines of "It makes sense to split the intellect hypostases into G & G* > because ...."), likewise for X, and for Z. > > > The splitting of G and G* comes from Gödel's theorem. It is the splitting > between what a machine can prove (notably on itself) and what is true about > the machine. > > Typical example: "I am consistent", it is the same as "I don't say the > false". For the correct machine, this belongs to G* minus G. It is true, > but the machine cannot prove it. > > So it is not "It makes sense to split the intellect hypostases into G & G* > because ....". It is: mathematician believed that a machine as a > provability predicate equivalent with a truth predicate until they discover > that provability and truth are different. Now it is a mathematical theorem > that provability obeys to the modal logic G (and indeed that G is complete > for it), and that the truth on provability obeys the modal logic G*. > > The same for the modal nuances, which existence are themselves > consequences of incompleteness. > > OK. My only confusion lies with the distinction between X and Z. And then relative to that distinction, what is the difference between X and X*. And the difference between Z and Z*. > All the math part, AUDA, is based on: > > - Church's thesis and the discovery of the universal machine > - Gödel technics of translating meta-arithmetic (with notion as > "provable") in arithmetic, > > It ought to be possible to justify the hypostases in a non-technical way. > > > Read Plotinus, or any mystic remaining rational. > > I was referring to the 8 you've identified. > > If not, then it strikes me as a weak spot of the argument, even if the > argument is technical. > > > Let me make a try. UDA is the formulation of the mind-body problem, in > "human term". > > AUDA is the translation of UDA in the language of the machine. > > Now, I ask the machine "will you believe this or that". What the box [] > represent is the thrid person self of the machine: it is the explanation of > the functioning of the machine, in the language of the machine, so that I > can ask her question about itself. This is a third person self. []p means > that the machine asserts p. To get the first person I use the Theaetetus > method, or variant, and this gives rise to the horizontal layers in the > diagram. The logics are different thanks (technically) to incompleteness. > Then three among the hypostases split in two, (x and x*) again due to > incompleteness. > > Tell me if this helps. > I was asking for a plain-language justification of the 8 hypostases, not the AUDA argument itself. I think I'm mostly there. It does make me want to get into the actual logics, but unfortunately I don't have the time to dedicate to that right now. > > In my mind, UDA *is* the layman explanation/argument of AUDA, somehow. You > might just miss a detail. []p means only the machine asserts that p. I use > the Dennett intentional stance. A machine believes p when the machine > asserts p. This is enough, as we limit ourself to ideally correct machine. > > I find it amazing that the UDA and AUDA end up leading to the same conclusions, as the arguments are so different on the surface. I understand the UDA argument but not AUDA, so my amazement there leads to skepticism, but again, my mind is open to the possibilities. > (I guess you were not on the list when I explained a bit of the modal > logic, and its relation with incompleteness). I can explain more (but not > in June as I am busy). > > I was, and wished I could have followed along in detail. Terren > Bruno > > > > > > Terren > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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