Well , it depends . If the paradox is TRULY a contradiction , and not just something we cant understand then it ' s impossible . Example Light is a particle and a wave . This seems to be paradoxical at first but is in fact not contradictory . If it was it wouldn ' t be possible . The idea is that I can ' t threaten something , an idea , a concept , a being , with something that isn ' t possible . I would say in the situation where Can god create an X so big even he cannot lift it ? ' fits the definition of a contradictory statement . There ' s an inherent contradiction in the statement . There are much more interesting and involved arguments against the existence of God , as well as for the existence of God . I just wish people would stop throwing around the uninteresting ones that don ' t add anything to the conversation . The conversation is worth having but you have to start with defining terms , and often time omnipotence is the first truly misunderstood term .