On Wed, Sep 04, 2002 at 10:48:38AM -0700, Tim May wrote: > And, putting in a plug for modal/topos logic, the essence of nearly > every interpretation, whether MWI or Copenhagen or even Newtonian, is > that observers at time t are faced with unknowable and branching > futures.
How useful is modal logic in dealing with these unknowable and branching futures? Modal logic is the logic of possibility and necessity, but to make decisions you need to reason about probabilities rather than modalities. How does modal logic "fit in" with or relate to probability theory? As far as I know, the logic used in probability theory is classical logic. For example, P(not not A) = P(A) is assumed, and there are no axioms in probability theory that deal with modal qualifiers. Are there versions of probability theory based on modal logic or other logics? Also, can you clarify something else for me. The elements in the poset that is used to interprete modal logic are the possible worlds, whereas the elements of the poset in your "causal time" post are space-time events. If we re-interpret modal logic using the poset of events instead of the poset of possible worlds, <>A would mean A is true sometime somewhere in the future lightcone of here-now, and []A would mean A is true all-the-time everywhere in the future lightcone of here-now. Are you advocating such usage of modal logic? I had argued earlier that in the case of possible worlds, we might as well just use classical logic and talk about possible worlds and the accessibility relationship directly. That seems to apply even more to the poset of space-time events. I really fail to see what benefits modal logic brings in this case.
