The traversal of the infinite: considering a beginning for an infinite past

Abstract This paper offers a critical assessment of the Successive Addition Argument (SAA) in support of past finitism, i.e., the thesis that the past of the universe is finite in duration. This old philosophical argument, re-popularized by William Lane Craig in modern times, contends that the universe’s past cannot be infinite because an infinite series cannot be formed by successive addition. I first address a recently popular objection to the argument, namely the Zeno Objection, showing that it can be easily dismissed once each addition is taken to have the same duration. Nevertheless, I contend that the onus of the proof lies on those who propose the SAA, and that their main argumentative strategies fail. Indeed, many of their arguments are based on the supposedly uncontroversial claim that one cannot traverse the infinite by starting somewhere. I argue that a complete traversal of the infinite, with a beginning infinitely far from its end, is logically and metaphysically possible. Other popular arguments against traversed infinities are based on thought experiments such as the backward counter or the Tristram Shandy thought experiments. I argue that, once infinitely far beginnings are granted, none of the arguments based on such thought experiments prove effective, so that the SAA must be rejected.