Infinity is paradoxical in many ways. Some paradoxes involve deterministic supertasks, such as Thomson's Lamp, where a switch is toggled an infinite number of times over a finite period of time, or the Grim Reaper, where it seems that infinitely many reapers can produce a result without doing anything. Others involve infinite lotteries. If you get two tickets from an infinite fair lottery where tickets are numbered from 1, no matter what number you saw on the first ticket, it is almost certain that the other ticket has a bigger number on it. And others center on paradoxical results in decision theory, such as the surprising observation that if you perform a sequence of fair coin flips that goes infinitely far back into the past but only finitely into the future, you can leverage information about past coin flips to predict future ones with only finitely many mistakes. Alexander R. Pruss examines this seemingly large family of paradoxes in Infinity, Causation and Paradox. He establishes that these paradoxes and numerous others all have a common structure: their most natural embodiment involves an infinite number of items causally impinging on a single output. These paradoxes, he argues, can all be resolved by embracing 'causal finitism', the view that it is impossible for a single output to have an infinite causal history. Throughout the book, Pruss exposits such paradoxes, defends causal finitism at length, and considers connections with the philosophy of physics (where causal finitism favors but does not require discretist theories of space and time) and the philosophy of religion (with a cosmological argument for a first cause).

Infinity is paradoxical in many ways. Some paradoxes involve deterministic supertasks, such as Thomson's Lamp, where a switch is toggled an infinite number of times over a finite period of time, or the Grim Reaper, where it seems that infinitely many reapers can produce a result without doing anything. Others involve infinite lotteries. If you get two tickets from an infinite fair lottery where tickets are numbered from 1, no matter what number you saw on the first ticket, it is almost certain that the other ticket has a bigger number on it. And others center on paradoxical results in decision theory, such as the surprising observation that if you perform a sequence of fair coin flips that goes infinitely far back into the past but only finitely into the future, you can leverage information about past coin flips to predict future ones with only finitely many mistakes. Alexander R. Pruss examines this seemingly large family of paradoxes. He establishes that these paradoxes and numerous others all have a common structure: their most natural embodiment involves an infinite number of items causally impinging on a single output. These paradoxes, he argues, can all be resolved by embracing 'causal finitism', the view that it is impossible for a single output to have an infinite causal history. Throughout the book, Pruss exposits such paradoxes, defends causal finitism at length, and considers connections with the philosophy of physics (where causal finitism favors but does not require discretist theories of space and time) and the philosophy of religion (with a cosmological argument for a first cause).

Actuality, Possibility and Worlds is an exploration of the Aristotelian account that sees possibilities as grounded in causal powers. On his way to that account, Pruss surveys a number of historical approaches and argues that logicist approaches to possibility are implausible. The notion of possible worlds appears to be useful for many purposes, such as the analysis of counterfactuals or elucidating the nature of propositions and properties. This usefulness of possible worlds makes for a second general question: Are there any possible worlds and, if so, what are they? Are they concrete universes as David Lewis thinks, Platonic abstracta as per Robert M. Adams and Alvin Plantinga, or maybe linguistic or mathematical constructs such as Heller thinks? Or is perhaps Leibniz right in thinking that possibilia are not on par with actualities and that abstracta can only exist in a mind, so that possible worlds are ideas in the mind of God?

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason.

Necessary Existence breaks ground on one of the deepest questions anyone ever asks: why is there anything? The classic answer is in terms of a necessary foundation. Yet, why think that is the correct answer? Pruss and Rasmussen present an original defense of the hypothesis that there is a concrete necessary being capable of providing a foundation for the existence of things. They offer six main arguments, divided into six chapters. The first argument is an up-to-date presentation and assessment of a traditional causal-based argument from contingency. The next five arguments are new "possibility-based" arguments that make use of twentieth-century advances in modal logic. The arguments present possible pathways to an intriguing and far-reaching conclusion. The final chapter answers the most challenging objections to the existence of necessary things.

This updated edition by one of the world's leading apologists presents a systematic, positive case for Christianity that reflects the latest work in the contemporary hard sciences and humanities. Brilliant and accessible.

An expansive, yet succinct, analysis of the Philosophy of Religion – from metaphysics through theology. Organized into two sections, the text first examines truths concerning what is possible and what is necessary. These chapters lay the foundation for the book’s second part – the search for a metaphysical framework that permits the possibility of an ultimate explanation that is correct and complete. A cutting-edge scholarly work which engages with the traditional metaphysician’s quest for a true ultimate explanation of the most general features of the world we inhabit Develops an original view concerning the epistemology and metaphysics of modality, or truths concerning what is possible or necessary Applies this framework to a re-examination of the cosmological argument for theism Defends a novel version of the Leibnizian cosmological argument