Let me think aloud, Plotinus's terms:
Primary Hypostases: 1) the ONE 2) the Divine Intellect 3) the all-soul Secondary hypostases: 4) Intelligible Matter 5) Sensible Matter With the UDA, you can already try Primary Hypostases: 1) truth 2) third person communicable truth 3) first person truth Secondary hypostases: 4) probability on computationnal consistent states/histories 5) probability on computational consistent true states/histories With the lobian interview the self-referential correct intellect is given by the modal logic G, and the self-referential truth (including the non provable one) is given by G*. This gives the following interpretation of a weaker version of UDA in arithmetic (comp is not yet needed); the hypostases are with B for Godel's purely arithmetical provability predicate (Beweisbar): Primary Hypostases: 1) arithmetical truth (p) 2) provability (Bp) 3) provability-and-truth (Bp & p) Secondary hypostases: 4) provability-and-consistency (Bp & ~B~p) 5) provability-and-consistency-and-truth (Bp & ~B~p & p) But, thanks to incompleteness, and the fact that machine as rich as PA, can reflect that incompleteness, some hypostases' discourses are divided in two parts: the true, and the communicable (third person provable) one. We get 8 hypostases: Primary Hypostases: 1) arithmetical truth (p) 2) provability (G) -------- 2') the same, but described by G* 3) provability-and-truth (S4Grz, curiously enough it does not divide) Secondary hypostases: 4) provability-and-consistency (Z)-------- 4') same, but described by G* (= Z*) 5) provability-and-consistency-and-truth (X)-------- 5') same, but described by G* (X*) Until now, we have not yet introduced comp in the interview. With B = Beweisbar; comp can be translated by p -> Bp. This formula characterized the Sigma1 formula (Visser Theorem), that is the RE sets, the Wi, the accessible states by a Universal Machine (with CT). Let V = G + (p -> Bp) We get Primary Hypostases: 1) Sigma1 arithmetical truth (p) 2) provability (V) -------- 2') the same, but described by G* (V*) 3) provability-and-truth (S4Grz1, curiously enough it does not divide) Secondary hypostases: 4) provability-and-consistency (Z1)-------- 4') same, but described by G* (= Z1*) 5) provability-and-consistency-and-truth (X1)-------- 5') same, but described by G* (X1*) The logical of the physical proposition should emerge at least in Z1*. But actually the whole of S4Grz1, Z1*, and X1* define, at least formally, a notion of arithmetical quantization. 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
