The Successive Addition Argument (SAA) is one of the arguments proposed by the defenders of the Kalām Cosmological Argument to support the claim that the universe has a beginning. The main premise of SAA states that a collection formed by successive addition cannot be an actual infinite. This premise is challenged by an argument originally proposed by Fred Dretske. According to Dretske’s Argument (DA), the scenario of a counter who starts counting numbers and never stops can provide a counterexample to (...) the main premise of SAA. I argue that neither DA nor its past-oriented counterpart—which discusses the scenario of a counter who has always been counting negative integers from the infinite past—can play a decisive role in our evaluation of the strength of the arguments that are intended to establish the finitude of the past based on the impossibility of an actually infinite number of successive additions. (shrink)

ABSTRACT According to an influential line of argument, the past must be finite because no infinite series can be formed by successive addition. The present paper pinpoints the non sequitur at the heart of this argument, disentangles the ambiguities that disguise it, and dismantles the misleading picture of ‘traversing the infinite’ that gives the argument so much of its allure. Finally, the paper critically explores the related argument that a beginningless series of past events is impossible because there could be (...) no explanation of its having been ‘completed’ at one time rather than another. (shrink)

The second premise of the Kalām cosmological argument, as defended by William Lane Craig, has two supporting arguments; the Hilbert’s Hotel argument and the suc.

In this article, I take on a classic objection to Kant’s arguments in the Antinomy of Pure Reason: that the arguments are question-begging, as they draw illicit inferences from claims about representation to claims about reality. While extant attempts to vindicate Kant try to show that he does not make such inferences, I attempt to vindicate Kant’s arguments in a different way: I show that, given Kant’s philosophical backdrop, the inferences in question are not illicit. This is because the transcendental (...) realists that Kant was arguing against have certain philosophical commitments about the nature of ground which, if true, warrant the inferences that Kant draws. This historical corrective not only allows us to better understand Kant’s own thinking in the Antinomies but it also has important upshots for our understanding of Kant’s transcendental idealism. (shrink)

Craig's second philosophical argument for a beginning of the universe presupposes a dynamic theory of time, a limitation which makes the argument unacceptable for those who do not hold this theory. I argue that the argument can be modified thus: If time is beginning -less, then it would be the case that a person existing and counting as long as time exists would count an actual infinite by counting one element after another successively, but the consequent is metaphysically impossible, hence (...) the antecedent is metaphysically impossible. I defend the premises and show that this argument does not presuppose the dynamic theory. (shrink)