In this paper it will be presented polemics about kalam cosmological argument developed in medieval islamic theology and philosophy. Main moments of that polemics was presented for a centuries earlier in Philoponus criticism of Aristotle?s thesis that the world is eternal, and of impossibilty of actual infinity. Philoponus accepts the thesis that actual infinity is impossible, but he thinks that, exactly because of that, world cannot be eternal. Namely, according to Philoponus, something can?not come into being if its existence requires the preexistence of an infinite number of other things, one arising out of the other. Philoponus and his fellowers in medieval islamic theology (Al-Kindi and Al-Ghazali), called kalam theologians, have offered arguments against the conception of a temporally infinite universe, under?stood as a succesive causal chain. On other side, medieval islamic thinkers, called falasifah /philosophers/ or aristotelians (Al-Farabi, Avicenna, and Averro?s), have offered arguments in favor of Aristotele?s conception of the eternity of the universe. Decisive problem in disccusion between kalam i falsafa medieval muslim thinkers was the problem of infinity. They have offered very interesting arguments and counterarguments about concept of infinity. In this paper it will be presented some of the crucial moments of that arguments.