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

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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References found in this work

What Are the New Implications of Chaos for Unpredictability?Charlotte Werndl - 2009 - British Journal for the Philosophy of Science 60 (1):195-220.
Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?Charlotte Werndl - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):232-242.
The Ergodic Hierarchy, Randomness and Hamiltonian Chaos.Joseph Berkovitz, Roman Frigg & Fred Kronz - 2006 - Studies in History and Philosophy of Modern Physics 37 (4):661-691.
The Transcendental Character of Determinism.Patrick Suppes - 1993 - Midwest Studies in Philosophy 18 (1):242-257.

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Citations of this work

Determinism.Charlotte Werndl - 2016 - In Meghan Griffith, Kevin Timpe & Neil Levy (eds.), Routledge Companion to Free Will. Routledge.

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