Empirical set theory

Hirokazu Nishimura

Hirokazu Nishimura

Paul A. Benioff

In this work, a definition of agreement between a physical theory and experiment, proposed in earlier work, is extended to be relative to τ where τ is Zermelo-Fraenkel set theory. The main aim of this work is to show that this definition, unlike that of earlier work, is sufficiently powerful to include relations between limit properties of empirical outcome sequences and expectation values obtained from the physical theory. We also extend, to the more powerful τ, some earlier results on randomness and the empirical determinability of the probability measure which a physical theory assigns to the outcome set of an infinite sequence of experiments.

Satoko Titani, Haruhiko Kozawa

Laura Ruetsche

Abstract This chapter attempts to bring the foregoing foundational discussion of QM∞ to bear on issues in the philosophy of science more generally construed. Taking one lesson of the foregoing foundational discussions to be that no single interpretation of QM∞ is adequate to the myriad explanatory and developmental demands faced by theories of QM∞, the chapter draws morals for scientific realism and related issues. One moral is that there might be no single structure or interpretation belief in which is warranted by the many successes of a physical theory. Another is that a physical theory might be best understood, not in terms of a unique set of physically possible worlds specified antecedently to the messy business of applying that theory, but in terms of many different such sets, indexed to contexts of application. A third moral is that semantic indecision of the sort just described could be an empirical virtue, insofar as semantically indecisive theories are more flexibly responsive to diverse sets of empirical demands.

Chrysovalantis Stergiou