The major modern proponent of the 'kalam cosmological argument', William Lane Craig, sets out the argument as follows:
             1. Whatever began to exist has a cause of its existence.
             3. Therefore, the universe has a cause of its existence.
             The second premise is in turn defended by two deductive arguments. Each argument reasons that it is impossible for the past to be infinite, because:
             i. infinity cannot exist in reality. When one considers the idea of either infinite space or infinite time, it is argued that one is inevitably confronted with contradictions and absurdities that demonstrate 'actual infinity' to be impossible.
             ii. even if infinity were possible, time could never in fact become infinite. Because time is formed by the successive addition of events, no matter how many events one adds together, one can never actually reach infinity.
             The second premise is also defended by two inductive arguments. As these two arguments rest primarily on scientific rather than philosophical reasoning, it is sufficient to observe that scientific hypotheses concerning the origins of the universe are highly controversial, the theories remain incomplete, and there are competitors to the Big Bang theory which do not involve the universe ever having a beginning. So the question of whether the universe is finite or infinite is still open for useful philosophical contribution.
             This essay demonstrates that Craig's two deductive objections to infinite time are incorrect, and therefore his second premise is unproved. We also identify a number of problems with the first premise. Then the argument as a whole is shown to be invalid. Finally, the identification of the First Cause with God is shown to remain unsatisfied.
             Premise 2: a) Is actual infinity impossible?
             Craig's deductive argument for the impossibility of infinity presents a number of situations that appear at first to be quite counter-intui...