Paradoxes that can supposedly occur if causality is violated are discu
ssed. It is shown that the existence of ''trajectories of multiplicity
zero'' (i.e., trajectories that describe, say, a ball hitting its you
nger self so that the latter cannot fall into the time machine) is not
paradoxical by itself. This apparent paradox can be resolved (at leas
t sometimes) without any harm to local physics or to the time machine.
Also a simple model is adduced for which the absence of true paradoxe
s caused by self-interaction in an acausal world is proved. The conclu
sion 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 ti
me machine guarantee that a system remains isolated after it intersect
s the Cauchy horizon.