On Wed, Jun 18, 2014 at 8:52 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> > On 17 Jun 2014, at 19:51, Platonist Guitar Cowboy wrote: > > > > > On Tue, Jun 17, 2014 at 7:17 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: > >> Thanks. It looks interesting. K is amazing by itself. It is "löbian" in >> the sense that the theorems of K are closed for the Löb rule: if K proves >> []A -> A, for some modal formula A, then K proves A. []([]A->A)->[]A is >> true about K. >> >> I will take a look when I have the times, and I hope it is not "trivial", >> as K is indeed very weak and very general, and I could argue that there is >> some substance (pun) in Birkhoff and von Neumann. >> > > I felt a bit uneasy about this going through the paper with "refutation" > ringing in my head, so any observations are most welcome :-) PGC > > > > Quantum logic usually designates the logical structure associated to the > lattice of the subspaces of an (infinite dimensional) Hilbert space, where > lives the atomic physical states (the rays, or unit vectors, the so called > pure states). A base of pure states define an observable, and the linear > structure of the Hilbert spaces determine the yes-no logic obeyed by the > observable. Typical axioms of classical logic are violated, like the > distributivity (a & (b V c) is no more equivalent with (a & b) V (a & c). > The logic is rich, but miss the tensor products to get close to the quantum > formalism per se. Also, von Neumann algebras and non commutative geometry > formalism can be related, although nothing is very easy there. QL can also > be related to quantum computation, but here too, the relation are not > trivial at all. > > When I say that comp + classical theory of knowledge is refutable, > I'm not sure we're on the right level here, as I wasn't precise enough. Apologies. I meant the paper's claim that Van Neumann thesis is refuted, that logic of QM is non-classical. I think I can see the outlines of the point, but my answer would still be "yes and no!' at this point. PGC > I mean that you can compare the QL infered by empiric studies, and the QL > given by Z1*, X1*, S4Grz1. > van Fraassen wrote a paper entitled "the labyrinth of quantum logics", but > comp provides only three one, and it should be compared to the more > reasonable (empirically) quantum logic. the comparison must be done in term > of the "measure one" logic, not necessarily in term of this or that > formalism, which can ofetn be related by representation theorems. > > UDA should explain why we have to proceed in this way, and the advantage > is that we get the nuances, on the physical reality, between the core > physics, the geography, the communicable, the sharable, etc. > > The translation in arithmetic is made necessary by the self-reference > incompleteness (Gödel, Löb) and the nuances on provability brought by that > incompleteness. > > May be I am quick explaining the importance of the logic of > self-reference, but UDA is based only on self-referential question (like > probability of surviving here or there). > > Feel free to ask for any precision. (Just expect some answer delays due to > June business). > > Bruno > > > > > >> He might also be fuzzy on observer. The comp hypothesis automatically >> enrich the normal and non normal modalities. >> >> Bruno >> >> >> On 16 Jun 2014, at 08:16, meekerdb wrote: >> >> This may be of interest. >> >> Brent >> >> >> Quantum Logic as Classical Logic >> Simon Kramer >> (Submitted on 13 Jun 2014) >> >> We propose a semantic representation of the standard quantum logic QL >> within the classical, normal modal logic K via a lattice-embedding of >> orthomodular lattices into Boolean algebras with one K-modal operator. Thus >> the classical logic K is a completion of the quantum logic QL. In other >> words, we refute Birkhoff and von Neumann's classic thesis that the logic >> (the formal character) of Quantum Mechanics would be non-classical as well >> as Putnam's thesis that quantum logic (of his kind) would be the correct >> logic for propositional inference in general. The propositional logic of >> Quantum Mechanics is modal but classical, and the correct logic for >> propositional inference need not have an extroverted quantum character. The >> normal necessity K-modality (the weakest of all normal necessity >> modalities!) suffices to capture the subjectivity of observation in quantum >> experiments, and this thanks to its failure to distribute over classical >> disjunction. (A fortiori, all normal necessity modalities that do not >> distribute over classical disjunction suffice.) The key to our result is >> the translation of quantum negation as classical negation of observability. >> >> Subjects: Quantum Physics (quant-ph); Logic in Computer Science >> (cs.LO); Mathematical Physics (math-ph); Logic (math.LO); Quantum Algebra >> (math.QA) >> Cite as: arXiv:1406.3526 [quant-ph] >> (or arXiv:1406.3526v1 [quant-ph] for this version) >> >> -- >> 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 everything-list+unsubscr...@googlegroups.com. >> To post to this group, send email to everything-list@googlegroups.com. >> 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 everything-list+unsubscr...@googlegroups.com. >> To post to this group, send email to everything-list@googlegroups.com. >> 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. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > 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 everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > 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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