Notoriously, the Einstein equations of general relativity have solutions in
which closed timelike curves (CTCs) occur. On these curves time loops back onto
itself, which has exotic consequences. However, in order to make time travel
stories consistent constraints have to be satisfied, which prevents seemingly
ordinary and plausible processes from occurring. This, and several other
"unphysical" features, have motivated many authors to exclude solutions with
CTCs from consideration, e.g. by conjecturing a chronology protection law. In
this contribution we shall investigate the nature of one particular class of
exotic consequences of CTCs, namely those involving unexpected cases of
indeterminism or determinism. Indeterminism arises even against the backdrop of
the usual deterministic physical theories when CTCs do not cross spacelike
hypersurfaces outside of a limited CTC-region (such hypersurfaces fail to be
Cauchy surfaces). By contrast, a certain kind of determinism appears to arise
when an indeterministic theory is applied on a CTC: things cannot be different
from what they already were. We shall argue that on further consideration both
this indeterminism and determinism on CTCs turn out to possess analogues in
other, familiar areas of physics. CTC-indeterminism is close to the
epistemological indeterminism we know from statistical physics, while the
"fixedness" typical of CTC-determinism is pervasive in physics. CTC-determinism
and CTC-indeterminism therefore do not provide incontrovertible grounds for
rejecting CTCs as conceptually inadmissible
