An overview of the Application of Actual Infinity Concept in Kalam Cosmological Argument

One of the subjects that link mathematics and philosophy is the "infinite dimension". William Craig, an American philosopher and theologian, has attempted to prove through mathematics the non-realization of infinite events in the world and thus proves the temporality of the universe. Describing this argument as a Kalam cosmological argument, he draws on Al-Ghazali's Huduth (temporality) argument. The purpose of this article is to examine one of the philosophical reasons set forth by Craig in proving the second premise of this argument in a bid to answer this question: “Is this philosophical-mathematical reasoning capable of proving the temporality of the universe?” The present study, with a descriptive-analytical approach, elaborates on the first reason proposed for the second preamble of Craig's argument, which deals with the actual infinity debates and set theory, and then embarks on evaluating the views of Islamic thinkers. The findings of the research suggest that temporality argument, due to the impossibility of the deteriorating order of events in the world, does not meet the contiguity conditions, and therefore fails to contradict its infinity. Moreover, since a number cannot be attributed to an infinite set, it is impossible to determine the members of an infinite set. That is, the assumption of an infinite dimension, even actual infinity, does not produce contradiction. For this reason, most Islamic philosophers have been reluctant to subscribe to the universe temporality argument.