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Such failures of determinism can arise in other field theories.
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This question arises acutely in gauge theories because of the apparent failure of determinism.
A failure of CM to dictate a well-defined result can then be seen as a failure of determinism.
It is important to see that the unhappy consequence does not consist merely of a failure of determinism.
Nonetheless most philosophers of physics seem to have concluded that if spacetime points do have primitive identity then the substantivalist who is committed to them must regard the failure of haecceitistic determinism as a genuine failure of determinism.
The problem with the failure of determinism in the hole argument is not the fact of failure but the way that it fails.
Thus, hole freeness precludes an important mode of failure of determinism which we wish to exclude in our discussion of time machines.
Giving a critical realist reading of epistemology and ontology, Polkinghorne seeks to link the epistemological barrier with an ontological failure of determinism because of ontological openness to influences not fully accounted for in our physics descriptions.
This follows recent philosophical practice of sharply distinguishing views and theories of what causation is from any conclusions about the success or failure of determinism (cf. Earman, 1986; an exception is Mellor 1994).
The other canonical example is the Aharanov-Bohm effect, and we can use this to illustrate the interpretational problem associated with gauge theories, sometimes characterized as a dilemma: failure of determinism or action-at-a-distance (see Healey, 2001).
(For an entry into philosophical problems associated with gauge transformations, see the entry on symmetry and symmetry breaking, especially Section 2.5; and Brading and Castellani (2003).) A hole argument type failure of determinism can often be achieved in field theories, depending, of course, on the specific properties of the field theory.
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