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

Is Time Travel Too Strange to Be Possible? Determinism and Indeterminism on Closed Timelike Curves