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

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (2):69-76 (2013)
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Abstract

In this article 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.

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Christopher Belanger
University of Toronto

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