Constraints on data in worlds with closed timelike curves

It is claimed that unacceptable constraints on initial data are imposed by certain responses to paradoxes that threaten time travel, closed timelike curves (CTCs) and other backwards causation hypotheses. In this paper I argue against the following claims: to say "contradictions are impossible so something must prevent the paradox" commits in general to constraints on initial data, that for fixed point dynamics socalled grey state solutions explain why contradictions do not arise, and the latter have been proved to avoid constraints on initial data.