On two mathematical definitions of observational equivalence: Manifest isomorphism and ε-congruence reconsidered

摘要

In this paper I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss's ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence are unpromising. Despite this critique, I suggest that Werndl's proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence.