Spacetime singularities and a novel formulation of indeterminism
  Spacetime singularities in general relativity are commonly thought to be
problematic, in that they signal a breakdown in the theory. We address the
question of how to interpret this breakdown, restricting our attention to
classical considerations (though our work has ramifications for more general
classical metric theories of gravity, as well). In particular, we argue for a
new claim: spacetime singularities in general relativity signal indeterminism.
  The usual manner in which indeterminism is formulated for physical theories
can be traced back to Laplace. This formulation is based on the non-uniqueness
of future (or past) states of a physical system -- as understood in the context
of a physical theory -- as a result of the specification of an antecedent state
(or, respectively, of a subsequent state). We contend that for physical
theories generally, this formulation does not comprehensively capture the
relevant sense of a lack of determination. And, in particular, it does not
comprehensively capture the sense(s) in which a lack of determination (and so,
indeterminism) arises due to spacetime singularities in general relativity.
  We thus present a novel, broader formulation, in which indeterminism in the
context of some physical theory arises whenever one of the three following
conditions holds: future (and/or past) states are (i) not unique -- as for
Laplacian notions of indeterminism; (ii) not specified; or (iii) `incoherent'
-- that is, they fail to satisfy certain desiderata that are internal to the
theory and/or imposed from outside the theory. We apply this formulation to
salient features of singularities in general relativity and show that this
broader sense of indeterminism can comprehensively account for (our
interpretation of) the breakdown signaled by their occurrence.
