One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must have (...) a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

In a recent paper, I claimed that if a familiar line of argument against the possibility of a beginningless series of events worked as advertised, it would work just as well against the possibility of an endless series of pre-determined events. The present paper is my response to objections by William Lane Craig. It argues that neither Craig’s claim that an endless series of events is a merely potential infinite nor his claim that future events don’t exist is successful in (...) blocking my original conclusion. (shrink)

Wes Morriston contends that William Lane Craig's argument for the impossibility of a beginningless past results in an equally good argument for the impossibility of an endless future. Craig disagrees. I show that Craig's reply reveals a commitment to an unmotivated position concerning the relationship between actuality and the actual infinite. I then assess alternative routes to the impossibility of a beginningless past that have been offered in the literature, and show that, contrary to initial appearances, these routes similarly seem (...) to support the impossibility of an endless future. (shrink)

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must have (...) a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.

Wes Morriston argues that even if we take an endless series of events to be merely potentially, rather than actually, infinite, still no distinction between a beginningless and an endless series of events has been established which is relevant to arguments against the metaphysical possibility of an actually infinite number of things: if a beginningless series is impossible, so is an endless series. The success of Morriston’s argument, however, comes to depend on rejecting the characterization of an endless series of (...) events as a potential infinite. It turns out that according to his own analysis it is vitally relevant whether the series of events is potentially, as opposed to actually, infinite. If it is reasonable to maintain that an endless series of events is potentially infinite while a beginningless series is actually infinite, then a relevant distinction has been established for any person who thinks that an actual infinite cannot exist. (shrink)

The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality as usually (...) conceived. (shrink)

Approximately 1500 years ago John Philoponus proposed a simple and compelling argument for the existence of God: (1) Whatever comes to be has a cause of its coming to be; (2) The universe came to be; (3) Therefore, the universe has a cause of its coming to be. Due to the influence of William Lane Craig — analytic philosopher, Christian apologist, champion of Philoponus’s position, and author of The Kalam Cosmological Argument — this argument and the family of subarguments that (...) support it have come to be known as the Kalam Cosmological Argument (KCA). The term kalam comes from Medieval Arabic philosophy and broadly means "natural theology" or "philosophical theism." Despite being one of the most widely discussed and hotly debated arguments in philosophy today, it has been more than twenty-five years since any systematic presentation of the argument as a whole has been attempted. The present book helps remedy that situation, laying bare the logical structure of the KCA as it has emerged from continuous philosophical refinement. A handy taxonomy of major objections and replies to the KCA has been included as an aid to understanding the argument and its background literature. This book breaks new ground by arguing that future progress on the KCA requires that the argument be situated within a substance-based metaphysics. In addition to providing an analytic account of substances, this book describes a modal theory sensitive to the possibilities and necessities that obtain for substances. With these conceptual tools, the characteristic thought-experiments supporting the KCA can be properly assessed. (shrink)