Probability in the Philosophy of Religion

Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections (...) and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

This report documents the program and the outcomes of Dagstuhl Seminar 13401 "Automatic Application Tuning for HPC Architectures". This workshop featured a series of talks and four breakout sessions on hot topics in the are of autotuning. The field of autotuning for HPC applications is of growing interest and many research groups around the world are currently involved. However, the field is still rapidly evolving with many different approaching being taken to autotuning. This workshop provided an opportunity to discuss these (...) many approaches, and help to unify the terminology used by different groups. (shrink)

. The present study applies results and methods of psychobiology to intellectual history. Pascal's syndrome is a depressive neurosis associated with morbid effects of scientific certainty. The syndrome is characterized by self‐mortification and conversion experience that represses distressing certainties. The dynamics of the syndrome are assessed from Blake Pascal's psychosis. The ideation of the syndrome is evaluated by reference to the neurology of altered states of consciousness and the biogenic amine hypothesis of depression and mania. The evaluation yields a description (...) of the relation between psychogenic and biogenic factors in the syndrome's etiology. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

Why would God institute the practice of efficacious petitionary prayer? Why would God not simply give us what we need before we ask? I examine recently proposed solutions to this puzzle and argue that they are inadequate to explain why an omniscient and perfectly good God would act differently in response to prayer. I propose that God has reasons to not always maximize a creature’s good, even in a sinless world, and that petitionary prayer functions as a means to reward (...) those who trust God, to enable us to actively love those we cannot otherwise help, and to give the petitioner personal evidence of God’s existence and care for her, creating a virtuous cycle of increasing faith. I refine this proposal by responding to several objections involving human responsibility and the epistemology of divine action. Along the way, I offer several ways petitioners can recognize God’s having answered a prayer and how God might help us with some common obstacles to prayer. (shrink)

My previous Alternate View column (ANALOG 9/84) described the widely accepted "inflationary scenario" of modern cosmology in which our Universe is just one among very many "bubble universes", all popping out of the general medium of the Big Bang like bubbles forming in a glass of beer. Somewhere perhaps there are many universes more or less like ours, some very similar to and others radically different from the universe we call "home".

I argue that, while Hume’s approach to Newton is sometimes critical and sometimes not, Hume’s position with regard to newtonian method is coherent overall. Rather than speaking of two Humes , from an humean perspective we should rather speak of two Newtons: the positivist and the theologian.

: This essay argues that Pascal's work both questions the accuracy of perspective in an infinite universe, and describes a model for moral truth that escapes the limitations of perspective. This model, rooted in Christianity, requires a total reorientation of approach towards moral truth. By asserting the limits of rational method, making use of recent scientific developments, and constructing a new model for moral truth, Pascal's work sought to update the role of Christianity to be not only consonant with the (...) secular thinking of his day but also as the only solution to the implications of that thinking. (shrink)

Could God have created a better universe? Well, the fundamental scientific laws and parameters of the universe have to be within a certain miniscule range, for a life-sustaining universe to develop: the universe must be ‘Fine Tuned’. Therefore the ‘embryonic universe’ that came into existence with the ‘big bang’ had to be either exactly as it was or within a certain tiny range, for there to develop a life-sustaining universe. If it is better that there exist a life-sustaining universe than (...) not, then it was better that the embryonic universe was one of this small set of very similar embryonic universes than that it was not. Furthermore, there are no firm grounds for claiming that of this small set of very similar embryonic universes, there is one which would have developed into a universe better than ours. Therefore there are no firm grounds for claiming that God could have created a better universe than ours. (shrink)

In the first section of this paper, I discuss a quantum mechanical account, which is endorsed by the MIT physicist, Alan Guth, of the origin of what Guth believes to have been an absolutely first universe. I argue that, though his explanation is unsound, there is no reason to think that it needs to be replaced by a supernaturalist one. In the second section, I argue that though Professor Steven Weinberg's tentative explanation of the apparent fine-tuning of the cosmological constant (...) is unacceptable, we need not accept a supernaturalist account of the coming about of intelligent life. (shrink)

A fine book, but who’s it for? Content Type Journal Article Pages 1-3 DOI 10.1007/s11016-011-9582-9 Authors John Dupré, ESRC Centre for Genomics in Society (Egenis), University of Exeter, Byrne House, St. German’s Road, Exeter, EX4 4PJ UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

In The Enquiry Concerning Human Understanding Hume argues that there can in principle be no good reason for believing a miracle has occurred. Recently, Richard Swinburne has disagreed, arguing that there could be good reason to believe a miracle has occurred. I will argue that both Hume and Swinburne are correct. So long as we accept Hume's notion of a miracle, his argument against the rationality of belief in such events stands firm. In this respect, Swinburne's attempted refutation fails. In (...) a deeper sense, however, Swinburne's project succeeds. Hume's critique of miracles turns on a truncated understanding of the supernatural. Making use of suggestions drawn from Swinburne's unsuccessful argument, the concept of miracle can be reformulated so as to allow for the possibility of rational belief. (shrink)

Infinite Minds is the fourth book of John Leslie, which follows Value and Existence (1979), Universes (1989) and The End of the World (1996). Infinite Minds presents a very rich content, and covers a number of particularly varied subjects . Among these latter, one can notably mention: omniscience, the problem of Evil, the fine-tuning argument, observational selection effects, the identity of indiscernables, time, infiniteness, the nature of consciousness.

I describe in this paper the basic elements of the n-universes, a methodological tool originally introduced in Franceschi (2001) in the context of the study of Goodman's paradox. As the n-universes can be used in wide-ranging applications, such as thought experiments, I describe them from an essentially pragmatic standpoint, i.e. by describing accurately the step-by-step process which leads to a given modelisation.

The Dark Ages The Gregorian Revolution The Glossators Invent "Half-Proof" Presumptions in Canon Law Innocent III Grades of Evidence, and Torture The Post-Glossators Bartolus and Baldus: The Completed Theory The Inquisition Maimonides on Testimony Law in the East Ch. 3 Renaissance Law..

Naturalism has been characterized both as a claim about what exists and as a commitment to a certain methodology . The fine-tuning argument for God's existence presents a significant challenge to each way of characterizing naturalism. The claim naturalist faces the fact that the best response to the fine-tuning argument requires the existence of many universes that are not clearly naturalistic themselves. Method naturalism faces the challenge that it does not have the resources to ground the preference of the many-world (...) hypothesis to the designer hypothesis. (shrink)