On Monday, September 21, 2020 at 12:49:22 PM UTC-5 Brent wrote:
> > > On 9/21/2020 4:44 AM, Philip Thrift wrote: > > > *Some Remarks on the Logic of Quantum Gravity* > Andreas Doering > > > https://www.academia.edu/5456772/Some_Remarks_on_the_Logic_of_Quantum_Gravity > > We discuss some conceptual issues that any approach to quantum gravity has > to confront. In particular, it is argued that one has to find a theory that > can be interpreted in a realist manner, because theories with an > instrumentalist interpretation are problematic for several well-known > reasons. Since the Hilbert space formalism almost inevitably forces an > instrumentalist interpretation on us, we suggest that a theory of quantum > gravity should not be based on the Hilbert space formalism. We briefly > sketch the topos approach, which makes use of the internal logic of a topos > associated with a quantum system and comes with a natural (neo-)realist > interpretation. Finally, we make some remarks on the relation between > system logic and metalogic. > > ... > > Finally, when we commit ourselves to describing the whole universe using > structures in a topos, and if we use the internal logic of the topos to > assign truth values to propositions etc., we do not have to do all our > proofs and mathematical arguments internally in the topos, i.e., > constructively. Doing physics necessarily means to separate oneself from > the system to be described, even if this system is the whole universe. > > > Where does that "necessarily" come from? Is it a theorem?...from what > axioms? > > Since we have to ‘step out’ of the system, we have to argue using the > (typically Boolean) metalogic in which we define the mathematical > structures, e.g. topoi and state objects, that we use in the mathematical > description of the system at hand. It is this Boolean metalogic in which we > do physics. > > > Smells like Platonism. > > Brent > > > Topos (Category) language is *an alternative language* for physics. There is no God that handed down the language physics must adopt. But it is a language closer to programming: https://github.com/AlgebraicJulia/Catlab.jl *Review of the Topos Approach to Quantum Theory* https://www.researchgate.net/publication/51913885_Review_of_the_Topos_Approach_to_Quantum_Theory Topos theory has been suggested as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of physics is and what its conceptual framework looks like. The motivation of using topos theory to express quantum theory lies in the desire to overcome certain interpretational problems inherent in the standard formulation of the theory. In particular, the topos reformulation of quantum theory overcomes the instrumentalist/Copenhagen interpretation thereby rendering the theory more realist. In the process one ends up with a multivalued/intuitionistic logic rather than a Boolean logic. In this article we shall review some of these developments. @philipthift -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/7e589031-e8ed-4062-b080-cc6830a06d0bn%40googlegroups.com.
