We discuss some of the choices that arise when one tries to make the
idea of physical determinism more precise. Broadly speaking,
`ontological' notions of determinism are parameterized by one's choice
of mathematical ideology,
whilst `epistemological' notions of determinism are parameterized by the
choice of an appropriate notion of computability.
We present some simple examples to show that these choices can indeed make
a difference to whether a given physical theory is `deterministic' or not.