Causality violation and paradoxes

Paradoxes that can supposedly occur if causality is violated are discussed. It is shown that the existence of ``trajectories of multiplicity zero'' (i.e., trajectories that describe, say, a ball hitting its younger self so that the latter cannot fall into the time machine) is not paradoxical by itself. This apparent paradox can be resolved (at least sometimes) without any harm to local physics or to the time machine. Also a simple model is adduced for which the absence of true paradoxes caused by self-interaction in an acausal world is proved. The conclusion is made that the paradoxes appear if and (within this model) only if the fact is neglected that no conditions fixed to the past of a time machine guarantee that a system remains isolated after it intersects the Cauchy horizon.