The Untraversable Past: Why, According to A-Theory, the Beginning of the Universe Is a Truth of Logic, Not of Physics

Contemporary defenses of a beginning of the universe typically lean on empirical cosmology — the Big Bang model, the Borde–Guth–Vilenkin theorem, entropy considerations. This paper argues that such defenses, while useful, are strategically unnecessary and dialectically weaker than they need to be. A purely a priori argument is available, and it is defended here explicitly conditionally: on the assumption that the A theory of time is correct — that moments genuinely come to be present and then genuinely elapse, rather than merely standing in a static ordering relation within an unchanging four dimensional manifold — it follows that if the past is infinite, an actually infinite sequence of moments must already have elapsed in order for the present moment to have arrived; but an actual infinite cannot be elapsed, or "traversed," by successive addition. Therefore, given the A-theory, the past is finite, i.e., time — and with it, the universe — began to exist. The paper's central contribution is to isolate, with maximal precision, the single premise on which the whole conditional argument turns: the fact that an infinite series has no first member is irrelevant to whether the whole of it has passed. This paper calls the conflation of these two questions the Enumeration/Elapsing Fallacy, and argues that once it is exposed, the standard "no-starting-point" objection to the argument collapses. Mathematical actual infinities (e.g., the negative integers) are shown to be disanalogous to a beginningless temporal series, because mathematical sets do not stand in relations of successive generation, whereas moments of time do, on the A-theory. Restricting the argument's scope explicitly to the A-theory is not a concession but a clarification of exactly what work the argument is designed to do: it is a conditional proof, valid regardless of whether its antecedent is ultimately accepted, and it situates the argument within the existing literature on the kalam cosmological argument.