Intervals and tenses

Concluding Remarks

Neither question (1) nor question (2) posed on page 446 have been adequately answered in this paper. Regarding (1) we have merely given functor maps onto the object languages of physical theories and regarding (2) we have merely described the algebraic structure of observables. A more satisfactory treatment will most likely involve (1) a generalization to algebraic categories, universal algebra and model theory in such a way as to capture the full inference structure of (perhaps van Fraassen's modal) quantum logic, and (2) the introduction of the category of differentiable manifolds in order to capture the full symplectic structure of (perhaps Chernoff-Marsden's) Hamiltonian dynamics. (See van Fraassen [4] and Chernoff-Marsden [5] in Other References.)

Finally, the intriguing suggestion of Finkelstein that “category theory is to metaphysics what group theory is to physics” deserves serious consideration. Indeed, although the theme has not been touched on explicitly in this paper it was central in motivating the project initially. However, it is more properly to be developed in a context external to a symposium on quantum logic.