Two New Successive Addition Arguments

Abstract

One of William Lane Craig's key arguments for the finitude of the past is the Successive Addition Argument (SAA). Malpass (2021) has recently developed a novel challenge to the SAA, utilising a thought experiment from the work of Fred Dretske, which is meant to show that it is possible to count to infinity, to argue that there is a counterexample to the SAA's second premise. In this paper, I contend that the Malpass-Dretske counterexample should not worry advocates of the SAA. First, I argue that one objection Malpass considers—the Potential Infinite Objection—reveals an interesting fact: the SAA's second premise is unnecessarily strong and can be weakened whilst still yielding the same conclusion. Second, I show how another one of the objections considered by Malpass—the Accumulation Objection—is successful, provided some clarification to the SAA's premises. The upshot of both analyses is that we generate two ‘new’ Successive Addition arguments that not only move the dialectic forward, but shed light on deeper assumptions and motivating intuitions concerning the Kalām.