### ELIMINATING MODALITY FROM THE DETERMINISM DEBATE? MODELS VS. EQUATIONS OF PHYSICAL THEORIES

#### Abstract

Many questions in philosophy of science are posed and discussed in terms of models. According to the semantic view of scientific theories, theories simply are classes of models, so that all questions about scientific theories – e.g., whether they are deterministic or not, or what their relation is to other theories – would have to be discussed in terms of models anyway. While the concept of a model has a variety of uses, for physical theories it is often possible to give a mathematically precise characterization of models, e.g., as classes of curves in a phase space. These curves in turn may often be determined as solutions of a theory's defining equations. Indeed it is common to answer questions about physical theories, conceived of as classes of models, by looking at the defining equations. This makes sense since these equations are often well studied by mathematical physicists, while there is little readily available information about the models. A good example of this strategy is provided by Earman's detailed investigations of the determinism or otherwise of various physical theories: the criterion for determinism of a theory is defined with respect to a class of models, but the assessment is given by studying the equations. Employing this strategy means to treat the models of a theory and the theory's defining equations as informationally equivalent. In my talk I will pose a challenge to this equivalence assumption: with respect to the definition of determinism in terms of models, I will discuss possible examples of spurious assessments of determinism and of indeterminism. I will then argue that studying the equations (which is what people do) gives the right assessment of the situation, while relying on the models (which is what the definition demands) leaves room for unwanted isomorphisms. I will conclude by drawing a parallel to the discussion of branching vs. divergence in the metaphysics of continuants.

#### Keywords

20th century philosophy; ontology; philosophy; Wittgenstein Ludwig; branching; defining determinism; descriptive metaphysics; determinism; indeterminism; isomorphism; real possibility; reduction

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