This “fun, brain-twisting book... will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden) Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create (...) the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more. (shrink)

This Introduction has three sections, on "logical fatalism," "theological fatalism," and the problem of future contingents, respectively. In the first two sections, we focus on the crucial idea of "dependence" and the role it plays it fatalistic arguments. Arguably, the primary response to the problems of logical and theological fatalism invokes the claim that the relevant past truths or divine beliefs depend on what we do, and therefore needn't be held fixed when evaluating what we can do. We call the (...) sort of dependence needed for this response to be successful "dependence with a capital 'd'": Dependence. We consider different accounts of Dependence, especially the account implicit in the so-called "Ockhamist" response to the fatalistic arguments. Finally, we present the problem of future contingents: what could "ground" truths about the undetermined future? On the other hand, how could all such propositions fail to be true? (shrink)

Does traditional Christianity involve paradoxical doctrines, that is, doctrines that present the appearance (at least) of logical inconsistency? If so, what is the nature of these paradoxes and why do they arise? What is the relationship between "paradox" and "mystery" in theological theorizing? And what are the implications for the rationality, or otherwise, of orthodox Christian beliefs? In Paradox in Christian Theology, James Anderson argues that the doctrines of the Trinity and the incarnation, as derived from Scripture and formulated in (...) the ecumenical creeds, are indeed paradoxical. But this conclusion, he contends, need not imply that Christians who believe these doctrines are irrational in doing so. In support of this claim, Anderson develops and defends a model of understanding paradoxical Christian doctrines according to which the presence of such doctrines is unsurprising and adherence to paradoxical doctrines cannot be considered as a serious intellectual obstacle to belief in Christianity. The case presented in this book has significant implications for the practice of systematic theology, biblical exegesis, and Christian apologetics. (shrink)

This book deals with an old conundrum: if God knows what we will choose tomorrow, how can we be free to choose otherwise? If all our choices are already written, is our freedom simply an illusion? This book provides a precise analysis of this dilemma using the tools of modern ontology and the logic of time. With a focus on three intertwined concepts - God's nature, the formal structure of time, and the metaphysics of time, including the relationship between temporal (...) entities and a timeless God - the chapters analyse various solutions to the problem of foreknowledge and freedom, revealing the advantages and drawbacks of each. Building on this analysis, the authors advance constructive solutions, showing under what conditions an entity can be omniscient in the presence of free agents, and whether an eternal entity can know the tensed futures of the world. The metaphysics of time, its topology and the semantics of future tensed sentences are shown to be invaluable topics in dealing with this issue. Combining investigations into the metaphysics of time with the discipline of temporal Logic this monograph brings about important advancements in the philosophical understanding of an ancient and fascinating problem. The answer, if any, is hidden in the folds of time, in the elusive nature of this feature of reality and in the infinite branching of our lives. (shrink)

Philosophers have argued about the nature and the very existence of free will for centuries. Today, many scientists and scientifically minded commentators are skeptical that it exists, especially when it is understood to require the ability to choose between alternative possibilities. If the laws of physics govern everything that happens, they argue, then how can our choices be free? Believers in free will must be misled by habit, sentiment, or religious doctrine. Why Free Will Is Real defies scientific orthodoxy and (...) presents a bold new defense of free will in the same naturalistic terms that are usually deployed against it. -/- Unlike those who defend free will by giving up the idea that it requires alternative possibilities to choose from, Christian List retains this idea as central, resisting the tendency to defend free will by watering it down. He concedes that free will and its prerequisites—intentional agency, alternative possibilities, and causal control over our actions—cannot be found among the fundamental physical features of the natural world. But, he argues, that’s not where we should be looking. Free will is a “higher-level” phenomenon found at the level of psychology. It is like other phenomena that emerge from physical processes but are autonomous from them and not best understood in fundamental physical terms—like an ecosystem or the economy. When we discover it in its proper context, acknowledging that free will is real is not just scientifically respectable; it is indispensable for explaining our world. (shrink)

This Element considers the relationship between the traditional view of God as all-powerful, all-knowing and wholly good on the one hand, and the idea of human free will on the other. It focuses on the potential threats to human free will arising from two divine attributes: God's exhaustive foreknowledge and God's providential control of creation.

Can belief in God be rationally justified? Reviewing in detail traditional and modern arguments for and against the existence of God, Professor Plantinga concludes that they must all be judged unsuccessful. He then turns to the related philosophical problem of the existence of other minds, and defends the so-called analogical argument against current criticisms. He goes on to show, however, that although this argument affords us the best reasons we have for belief in other minds, it finally succumbs to the (...) same malady that afflicts the teleological argument of God. (shrink)

A compelling contribution to the field, The Dilemma of Freedom and Foreknowledge will appeal to students and scholars of theistic philosophy and the philosophy ...

Omniscience is the divine attribute of possessing complete or unlimited knowledge. This article examines motivations for taking such a property to be a divine attribute, attempts to define or analyse omniscience, possible limitations on the extent of divine knowledge, and, finally, objections either to the coherence of the concept or to its compatibility with other divine attributes or with widely accepted claims.

Religious believers react in one of four ways to apparent contradictions among their beliefs: Redirection, Resistance, Restraint, or Resolution. This paper evaluates positive mysterian Resistance, the view that believers may rationally believe and know apparently contradictory religious doctrines. After locating this theory by comparing and contrasting it with others, I explore the best developed version of it, that of James Anderson’s Paradox in Christian Theology. I argue that it faces steep epistemic problems, and is at best a temporarily reasonable but (...) ultimately unsustainable stance. (shrink)

This book investigates what it means, and whether it is coherent, to say that there is a God.

This comprehensive reference provides an exhaustive guide to current scholarship on the perennial problem of Free Will--perhaps the most hotly and voluminously debated of all philosophical problems. While reference is made throughout to the contributions of major thinkers of the past, the emphasis is on recent research. The essays, most of which are previously unpublished, combine the work of established scholars with younger thinkers who are beginning to make significant contributions. Taken as a whole, the Handbook provides an engaging and (...) accessible roadmap to the state of the art thinking on this enduring topic. (shrink)

This original analysis examines the three leading traditional solutions to the dilemma of divine foreknowledge and human free will--those arising from Boethius, from Ockham, and from Molina. Though all three solutions are rejected in their best-known forms, three new solutions are proposed, and Zagzebski concludes that divine foreknowledge is compatible with human freedom. The discussion includes the relation between the foreknowledge dilemma and problems about the nature of time and the causal relation; the logic of counterfactual conditionals; and the differences (...) between divine and human knowing states. An appendix introduces a new foreknowledge dilemma that purports to show that omniscient foreknowledge conflicts with deep intuitions about temporal asymmetry, quite apart from considerations of free will. Zagzebski shows that only a narrow range of solutions can handle this new dilemma. A compelling contribution to the field, The Dilemma of Freedom and Foreknowledge will appeal to students and scholars of theistic philosophy and the philosophy of religion. (shrink)

Foreknowledge arguments attempt to show that infallible and exhaustive foreknowledge is incompatible with creaturely freedom. One particularly powerful foreknowledge argument employs the concept of accidental necessity. But an opponent of this argument might challenge it precisely because it employs the concept of accidental necessity. Indeed, Merricks (Philos Rev 118:29–57, 2009, Philos Rev 120:567–586, 2011a) and Zagzebski (Faith Philos 19(4):503–519, 2002, Stanford Encyclopedia of Philosophy, 2011) have each written favorably of such a response. In this paper, I aim to show that (...) responding to the accidental necessity version of the foreknowledge argument by disputing the concept of accidental necessity, including doing so in the ways these authors do, does not constitute a successful response to the foreknowledge argument. This is because there is an only slightly modified but still well-motivated version of the foreknowledge argument which employs the notion of uncausability rather than accidental necessity; and this argument is not threatened by objections to the concept of accidental necessity, including those objections offered by Zagzebski and Merricks. As recent literature on the foreknowledge argument has emphasized, when a response to a foreknowledge argument fails to threaten an only slightly modified but still well-motivated version of that argument, the response in question is not successful. So the responses to the accidental necessity version of the foreknowledge argument I have mentioned are not successful. Moreover, those working on foreknowledge arguments more generally should take seriously the uncausability version of the foreknowledge argument articulated here, as it may well be that still more responses to the foreknowledge argument will not threaten it, either. (shrink)

What are the philosophical views of contemporary professional philosophers? We surveyed many professional philosophers in order to help determine their views on 30 central philosophical issues. This article documents the results. It also reveals correlations among philosophical views and between these views and factors such as age, gender, and nationality. A factor analysis suggests that an individual's views on these issues factor into a few underlying components that predict much of the variation in those views. The results of a metasurvey (...) also suggest that many of the results of the survey are surprising: philosophers as a whole have quite inaccurate beliefs about the distribution of philosophical views in the profession. (shrink)

This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is (...) false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed. (shrink)

This paper argues that at least one of the following propositions is true: the human species is very likely to go extinct before reaching a "posthuman" stage; any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history ; we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently (...) living in a simulation. A number of other consequences of this result are also discussed. (shrink)

I argue that at least one of the following propositions is true: the human species is very likely to become extinct before reaching a ’posthuman’ stage; any posthuman civilization is extremely unlikely to run a significant number of simulations of its evolutionary history ; we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we shall one day become posthumans who run ancestor-simulations is false, unless we are currently living (...) in a simulation. I discuss some consequences of this result. (shrink)

In Paradox in Christian Theology I argued that the Christian doctrines of the Trinity and the Incarnation are paradoxical—that is, they appear to involve implicit contradictions—yet Christians can still be rational in affirming and believing those doctrines. Dale Tuggy has characterized my theory of theological paradox as a form of “positive mysterianism” and argues that the theory “faces steep epistemic problems, and is at best a temporarily reasonable but ultimately unsustainable stance.” After summarizing my proposed model for the rational affirmation (...) of theological paradox and considering whether my proposal is indeed a form of “positive mysterianism” as Tuggy defines the term, I address the two main criticisms raised in Tuggy’s paper: first, that the doctrine of divine incomprehensibility cannot bear the weight required by my defense of paradox; and second, that my proposed model is afflicted with epistemic instability. I conclude that Tuggy has failed to show that a mysterian stance with respect to paradoxical Christian doctrines is in principle unreasonable, unnatural, or unsustainable. (shrink)

Proposes and defends a novel account of the mechanics of divine foreknowledge and providence, arguing that this account is consistent with libertarian freedom.

In this companion volume to Warrant: The Current Debate, Plantinga develops an original approach to the question of epistemic warrant; that is what turns true belief into knowledge. He argues that what is crucial to warrant is the proper functioning of one's cognitive faculties in the right kind of cognitive environment.

This book discusses and exemplifies the philosophy of religion, or philosophical reflection on central themes of religion.