In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such as mathematical truths. We argue, however, that the (...) infinite God objection is based on two questionable assumptions, namely, that it is possible for an omniscient being to know an actually infinite number of things and that there exist an actually infinite number of abstract objects for God to know. (shrink)

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally classified (...) as a dichotomy. I show how the form is exploited to generate paradox. Introduction The form of the Benardete dichotomy 2.1 The unsatisfiable pair diagnosis Applying the unsatisfiable pair diagnosis 3.1 Perez Laraudogoitia 3.2 Hawthorne 3.3 Angel 3.4 Yablo and Sorensen Exploiting the form. (shrink)

Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.

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)

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)

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.

We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

In this note, I consider an argument advanced by William Lane Craig and James D. Sinclair against the possibility of actual infinite collections based onHilbert’s Hotel and alleged problems with inverse operations in transfinite arithmetic. I aim to show that this argument is misguided, since it is based on a mistaken view that the impossibility of defining ℵ0 - ℵ0 entails the impossibility of removing an infinite subcollection from an infinite collection.