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)

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. (shrink)

Might we be parts of a divine mind? Could anything like an afterlife make sense? Starting with a Platonic answer to why the world exists, _Immortality Defended_ suggests we could well be immortal in all of three separate ways. Tackles the fundamental questions posed by our very existence, among them, "why does the cosmos exist?", "is there a divine mind or God?", and "in what sense might we have afterlives?" Defends a belief in immortality, without the need for a religious (...) affiliation or rejection of modern science Explores the ideas of "Einsteinian immortality", the divine afterlife, and the theory of an infinite and divine mind Draws from the work of a wide-range of philosophers, from ancient Greece to the present day, and incorporates up-to-date scientific findings Written in a thought-provoking and engaging manner, accessible to anyone intrigued by the wonder of our being. (shrink)

Principles of Philosophy was written in Latin by Rene Descartes. Published in 1644, it was intended to replace Aristotle's philosophy and traditional Scholastic Philosophy. This volume contains a letter of the author to the French translator of the Principles of Philosophy serving for a Preface and a letter to the most serene princess, Elizabeth, eldest daughter of Frederick, King of Bohemia, Count Palatine, and Elector of the Sacred Roman Empire. Principes de philosophie, by Claude Picot, under the supervision of Descartes, (...) appeared in 1647 with a letter-preface to Queen Christina of Sweden. (shrink)

A. Either God can create a stone which He cannot lift, or He cannot create a stone which He cannot lift. If God can create a stone which He cannot lift, then He is not omnipotent. If God cannot create a stone which He cannot lift, then He is not omnipotent. Therefore, God is not omnipotent.In a paper published in Analysis I tried to show that any attempt to find something wrong with all arguments of the general form of A (...) above, any attempt to resolve the “paradox,” must fail, that the reason these attempts must fail is that at least some arguments of this form are essentially sound, and that the only thing which makes these arguments seem paradoxical, their conclusion to the effect that God is not omnipotent, is, like at least some versions of the arguments to this conclusion, quite correct. (shrink)

How do we know that God exists? One of Britain's greatest 18th-century philosophers addresses the age-old question in this timeless dialogue. Equally captivating as a philosophical argument and as a work of literature, this classic is particularly relevant in terms of its criticism of the reasoning behind Intelligent Design.

This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...) decision. Throughout, Lewis analyzes global features of the world in such a way as to show that they might turn out to supervene on the spatiotemporal arrangement of local qualities. (shrink)

God is traditionally taken to be a perfect being, and the creator and sustainer of all that is. So, if theism is true, what sort of world should we expect? To answer this question, we need an account of the array of possible worlds from which God is said to choose. It seems that either there is (a) exactly one best possible world; or (b) more than one unsurpassable world; or (c) an infinite hierarchy of increasingly better worlds. Influential arguments (...) for atheism have been advanced on each hierarchy, and these jointly comprise a daunting trilemma for theism. In this paper, I argue that if theism is true, we should expect the actual world to be a multiverse comprised of all and only those universes which are worthy of creation and sustenance. I further argue that this multiverse is the unique best of all possible worlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)

I show that if the ontological argument is sound, it proves that a number of maximally great beings must exist. I show that maximal greatness does not imply uniqueness, that such beings can be omnipotent and yet not restrict each other's power, and that each must have its own separate stream of consciousness. I also show that attempts to unify the beings by unifying the streams of consciousness leads to a form of pantheism.

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)

The structure of the second, Or so-Called modal version of anselm's ontological argument is discussed in relation to various systems of alethic modal logic. It is argued that there are three current problems standing in the way of acceptance of the argument, Each related to its modal structure, And each an analogue of a traditional objection to anselm's original argument. Two of these problems can probably be solved, But the third remains recalcitrant.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly.

On the basis of Chapter 15 of Anselm's Proslogion, I develop an argument that confronts theology with a trilemma: atheism, utter mysticism, or radical anti‐Anselmianism. The argument establishes a disjunction of claims that Anselmians in particular, but not only they, will find disturbing: (a) God does not exist, (b) no human being can have even the slightest conception of God, or (c) the Anselmian requirement of maximal greatness in God is wrong. My own view, for which I argue briefly, is (...) that (b) is false on any correct reading of what conceiving of requires and that (c) is false on any correct reading of the concept of God. Thus, my own view is that the argument establishes atheism. In any case, one consequence of the argument is that Anselmian theology is possible for human beings only if it lacks a genuine object of study. (shrink)

Most people, believers and nonbelievers alike, are unfamiliar with the variety and force of arguments for the impossibility of God. Yet over recent years a growing number of scholars have been formulating and developing a series of increasingly powerful arguments that the concept of God, as variously understood by the world's major religions and leading theologians, is contradictory in many ways, and therefore God does not and cannot exist. This unique anthology brings together for the first time most of the (...) important arguments for the impossibility of God that have been published. The collection includes papers and book selections by J. L. Mackie, Quentin Smith, Theodore Drange, Michael Martin, and many other distinguished scholars. The editors provide a general introduction and brief summaries of the arguments to help the reader grasp the crucial issues involved. Both students and teachers of philosophy and the philosophy of religion will find this anthology to be an indispensable resource. (shrink)

The cosmos exists just because of the ethical need for it We, and all the intricate structures of our universe, exist as thoughts in a divine mind that knows everything worth knowing. There could also be infinitely many other universes in this mind....It may be hard to believe that the universe is as Leslie says it is--but it is also hard to resist his compelling ideas and arguments.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

‘Rival creator’ arguments suggest that God must have created the best of all possible worlds. These arguments are analyzed and evaluated, and Leibniz’s position defended.

This chapter contains section titled: The Good of Plato as a Creative Principle God as a Creative Principle; God as a Creating Person; or God as the Entire Cosmos Initial Objections to the Platonic Theory If the Platonic Approach is Correct, Why Struggle to Produce Good Things? How Creative Power might be Real Necessarily Creative Value Would Not Be Something Complex.

"Translated with an uncanny sense for the overall point of Augustine's doctrine. In short, a very good translation. The Introduction is admirably clear." --Paul Vincent Spade, Indiana University.

On the basis of Chapter 15 of Anselm's Proslogion, I develop an argument that confronts theology with a trilemma: atheism, utter mysticism, or radical anti-Anselmianism. The argument establishes a disjunction of claims that Anselmians in particular, but not only they, will find disturbing: (a) God does not exist, (b) no human being can have even the slightest conception of God, or (c) the Anselmian requirement of maximal greatness in God is wrong. My own view, for which I argue briefly, is (...) that (b) is false on any correct reading of what conceiving of requires and that (c) is false on any correct reading of the concept of God. Thus, my own view is that the argument establishes atheism. In any case, one consequence of the argument is that Anselmian theology is possible for human beings only if it lacks a genuine object of study. (shrink)

One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.

The tape is divided into squares, each square bearing a single symbol—'0' or '1', for example. This tape is the machine's general-purpose storage medium: the machine is set in motion with its input inscribed on the tape, output is written onto the tape by the head, and the tape serves as a short-term working memory for the results of intermediate steps of the computation. The program governing the particular computation that the machine is to perform is also stored on the (...) tape. A small, fixed program that is 'hard-wired' into the head enables the head to read and execute the instructions of whatever program is on the tape. The machine's atomic operations are very simple—for example, 'move left one square', 'move right one square', 'identify the symbol currently beneath the head', 'write 1 on the square that is beneath the head', and 'write 0 on the square that is beneath the head'. Complexity of operation is achieved by the chaining together of large numbers of these simple atoms. Any universal Turing machine can be programmed to carry out any calculation that can be performed by a human mathematician working with paper and pencil in accordance with some algorithmic method. This is what is meant by calling these machines 'universal'. (shrink)

Long before the current dispute in the USA about the teaching of evolution, Hume's dialogues presented and critically analyzed the idea of intelligent design. What should we teach our children about the creation of the world? What should we teach them about religion? The characters Demea, Cleanthes, and Philo passionately present and defend different answers to that question. Demea opens the dialogue with a position derived from René Descartes and Father Malebranche — God's nature is a mystery, but God's existence (...) can be proved logically. Cleanthes attacks that view, both because it leads to mysticsm and because it attempts the impossible task of trying to establish existence on the basis of pure reason, without appeal to sense experience. As an alternative, he offers a proof of both God's existence and God's nature based on the same kind of scientific reasoning established by Copernicus, Galileo, and Newton. Taking a skeptical approach, Philo presents a series of arguments that question any attempt to use reason as a basis for religious faith. He suggests that human beings might be better off without religion. The dialolgue ends without genuine agreement among the characters, justifying Hume's choice of dialogue as the form of presentation. (shrink)

"Lectures on Philosophical Theology is an indispensable addition to Kant's works in English.