Probability in the Philosophy of Religion

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)

History as a subject area is facing increasing demands from the society to be more profitable and, sometimes, more conformist. The Tuning methodology, developed in cooperation with a large number of Universities worldwide, could offer a viable and sustainable way to take societal needs into account without compromising academic soundness.

Pascal, with his famous wager, argued in favour of religious practice and faith by appeal to expected payoffs. Here I discuss an asymmetry in similar pragmatic arguments for decisions about God. I begin with the observation that apostates pay costs not shared by those who never adopt a religion in the first place. Noticing this asymmetry shows these arguments from a new perspective and may also contribute to an explanation of the endurance of religion.

We are probably alone in the universe—a conclusion based on observations of over 4,000 exoplanets and fundamental physical constraints. This article updates earlier arguments with the latest astrophysical results. Since the discovery of exoplanets, theologians have asked with renewed urgency what the presence of extraterrestrial intelligence says about salvation and human purpose, but this is the wrong question. The more urgent question is what their absence says. The “Misanthropic Principle” is the observation that, in a universe fine-tuned for life, the (...) circumstances necessary for intelligence are rare. Rabbis for 2,000 years discussed the existence of ETI using scriptural passages. We examine the traditional Jewish approaches to ETI, including insights on how ETI affects our perception of God, self, free-will, and responsibility. We explore the implications of our probable solitude, and offer a Jewish response to the ethical lessons to be drawn from the absence of ETI. (shrink)

Evolution is a time process. It proceeds in steps of definite length. The probability of each step is relatively high, so self organization of complex systems will be possible in finite time. Prerequisite for such a process is a selection rule, which certainly exists in evolution. Therefore, it would be wrong to calculate the probability of the formation of a complex system solely on the basis of the number of its components and as a momentary event.

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)

William James presents Pascal's wager in this manner: if you believe in God and God exists, then your gain is infinite; if you believe in God and God doesn't exist, then your loss is finite. Therefore, since a finite loss is reasonable where there is the possibility of infinite gain, you ought to believe in God. ‘What have you to lose?’ James asks . 1.

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)

Our laws of nature and our cosmos appear to be delicately fine-tuned for life to emerge. First, if the initial conditions prevailing immediately after the Big Bang had been ever so slightly different, then the universe would either have recollapsed immediately, or would have expanded far too quickly into a chilling, eternal void. Second, if any one of the fundamental forces of nature had been a tiny bit different in strength, or if the masses of some elementary particles had been (...) a little unlike they are, there would have been no stars and no recognizable chemistry, and hence no Sun, no Earth, no carbon, et cetera. These highly special conditions and numbers suggest some sort of a conspiracy of literally cosmic proportions, which seems rather hard to attribute to chance. Some theologians and religiously oriented scientists and philosophers have taken advantage of this apparent fine-tuning of the clockwork of the universe to revive the scholastic Argument from Design, but also secular thinkers have felt the need to explain fine-tuning, typically by proposing the existence of a `Multiverse', i.e., a vast family of universes existing in parallel, of which ours is merely one, singled out by the `Anthropic Principle' to the effect that it is the only one that can possibly contain observers and hence can be observed. We analyze this issue from a sober perspective. Having reviewed the literature and having added several observations of our own, we conclude that cosmic fine-tuning turns out to support neither Design nor a Multiverse, both of which fail to explain fine-tuning or even to increase its likelihood. In fact, fine-tuning and Design rather seem to be at odds with each other, except when one makes an additional assumption that is practically indistinguishable from Design and hence renders the whole argument circular. Likewise, the inference from fine-tuning to a Multiverse only works if the latter is underwritten by a startling metaphysical hypothesis we consider unwarranted. Instead, we conclude that fine-tuning requires no special explanation at all, since it is not the Universe that is fine-tuned for life, but life that has been fine-tuned to the Universe. (shrink)

"Multiverse" cosmologies imagine our universe as just one of a vast number of others. While this idea has captivated philosophy, religion, and literature for millennia, it is now being considered as a scientific hypothesis--with different models emerging from cosmology, quantum mechanics, and string theory. Beginning with ancient Atomist and Stoic philosophies, Mary-Jane Rubenstein links contemporary models of the multiverse to their forerunners and explores the reasons for their recent appearance. One concerns the so-called fine-tuning of the universe: nature's constants are (...) so delicately calibrated that it seems they have been set just right to allow life to emerge. For some thinkers, these "fine-tunings" are evidence of the existence of God; for others, however, and for most physicists, "God" is an insufficient scientific explanation. Hence the allure of the multiverse: if all possible worlds exist somewhere, then like monkeys hammering out Shakespeare, one universe is bound to be suitable for life. Of course, this hypothesis replaces God with an equally baffling article of faith: the existence of universes beyond, before, or after our own, eternally generated yet forever inaccessible to observation or experiment. In their very efforts to sidestep metaphysics, theoretical physicists propose multiverse scenarios that collide with it and even produce counter-theological narratives. Far from invalidating multiverse hypotheses, Rubenstein argues, this interdisciplinary collision actually secures their scientific viability. We may therefore be witnessing a radical reconfiguration of physics, philosophy, and religion in the modern turn to the multiverse. (shrink)

The purpose of this thesis is to gain an accurate appreciation of the force of David Hume's arguments against reasonable belief in the truth of miracle reports. To avoid the possibility of misrepresenting Hume's arguments, which are found in his essay "Of Miracles," I expend considerable effort in attempting to interpret them fairly and charitably. Because an important claim in Part One of his two-part essay is understood by Hume in private correspondence to mean something significantly different from its obvious (...) meaning; because Hume does not bother to change the claim in any of the multiple editions of the essay; and because each of the meanings allows the argument of Part One to be interpreted differently yet coherently with respect to the arguments of Part Two and with respect to broader contextual considerations: I set out two micro-interpretations of the argument of Part One and two macro-interpretations of the arguments in "Of Miracles" as a whole. Also, by close attention to the text of Hume's arguments as well as to his understanding of the concepts of proof and probability vis-a-vis the evidence for and against miracle, I show that Hume's argument of Part One centres on the fact that our experience of a miracle is infrequent relative to our experience of the natural law the miracle purports to violate, and I show that Hume takes our experience of the allegedly-violated natural law as bearing completely, directly, and destructively on the credibility of miracle testimony. I show too that along with his arguments of Part Two, Hume takes the destructive experiential effect of the relative infrequency of a miracle to be a practically insurmountable barrier to the credibility of miracle reports. Source: Masterss International, Volume: 33-04, page: 1099. Supervisor: John P. Wright. Thesis --University of Windsor, 1994. (shrink)

Kit Fine has replied to my criticism of a technical objection he had given to the version of Millianism that I advocate. Fine evidently objects to my use of classical existential instantiation in an object-theoretic rendering of his meta-proof. Fine’s reply appears to involve both an egregious misreading of my criticism and a significant logical error. I argue that my rendering is unimpeachable, that the issue over my use of classical EI is a red herring, and that Fine’s original argument (...) commits the straw-man fallacy. I argue further that contrary to Fine’s gratuitous attribution, what Kripke’s Pierre lacks and a typical bilingual has is not knowledge of a “manifest-making” premise, but the capacity to recognize London when it is differently designated. Fine’s argument refutes a preposterous theory no one advocates while leaving standard Millianism unscathed. The failure of his argument threatens to render Fine’s central notion of “coordination” redundant or empty. (shrink)

Recent discussions about the anthropic principle and the argument from design can perhaps be summarized as follows : The world is very unusual, so it must have been made by an intelligent creator. The world is very unusual, but unusual things do occur by chance. Both and , in their ordinary interpretations, have been labelled probabilistic fallacies. In my paper I will discuss in particular the following two aspects: The contemporary relevance of Cicero's discussions on chance. The fact that any (...) talk of chance events is only possible subject to the more encompassing idea of "limited belief in chance". (shrink)

From cosmology to the fact that the existence of God and nature, to address these issues, the development of two kinds of controversial contemporary line of argument, I compared and assessed in this paper: the physical cosmology as a starting argument and the natural design as a starting point of the argument. I made ​​some preliminary assessment of the court. The results showed that the Big Bang argument are quite reasonable, however, found the natural design of the demonstration clearly insufficient. (...) I compare and evaluate two contemporary and controversial lines of argument from cosmological facts to the existence and nature of God: the argument from physical cosmology and the argument from design in nature. As a preliminary step, some criteria for such an evaluation are proposed. It turns out that the Big Bang argument keeps considerable plausibility , whereas the Design argument can be shown to be deficient. (shrink)

This paper concerns two objections to Pascal's wager. The first claims that Pascal's recommendation to habituate oneself to believe in God is tantamount to religious brainwashing. I argue that this construal misses important aspects of what Pascal had in mind, which may render the habituation process a legitimate means to acquire new understanding. The second objection is based on the idea that a key assumption of the wager – that theistic belief is required for eternal felicity – is morally absurd. (...) I argue that theistic belief, as Pascal understands it, is a necessary aspect for spiritual restoration, not merely an isolated belief in an imperious deity. (shrink)

Pascal's wager has fascinated philosophers far in excess of its reputation as effective apologetics. Very few of the wager's defenders, in fact, have retained more than an academic interest in its power to persuade. Partly this is a matter of good manners. Pascal is supposed to have pitched his wager at folks who understand only self-interested motivations, and today it is no longer fashionable for defenders of theism to disparage the character of their opponents. But partly the low-key concern with (...) apologetics expresses a philosophical judgement. Pascal's defenders have found the question of the wager's audience to be less philosophically engaging than the logic of its argument. I believe that this assessment is mistaken. The most puzzling feature of Pascal's wager is its invocation of infinite utility. What are finite human beings, theists or otherwise, supposed to make of the idea of an infinitely desirable happiness? There are, I will argue, two sorts of response to this question, and depending on which sort Pascal had in mind, the logic of his wager comes out very differently. (shrink)

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)

Is the no-minimum claim true? I have argued that it is not. Andrew Cullison contends that my argument fails, since human sentience is variable; while Michael Schrynemakers has contended that the failure is my neglect of vagueness. Both, I argue, are wrong.

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)

Pascal's Wager is analyzed and critiqued in Part I. The main objections to Pascal's argument are raised and various attempts to salvage the argument are discussed. These problems include the dubious assumption that one is forced to believe either that God exists or that God does not exist, and the questionable assumption that one will gain infinite happiness if and only if God exists and one believes in God's existence. Also problematic is the use of an infinite value in an (...) expected-value calculation. Part II argues for a pragmatic justification of religious faith that is inspired by but significantly different from Pascal's Wager. To construct this argument it is necessary to refine some traditional theological notions. God is conceived as "transcendent" in that he is qualitatively superior to any other possible being, yet "immanent" in that it is possible for him to have personal relationships with human beings. A "devout religious person" has an overriding goal to attain a good personal relationship with God; a person is "religious" to the extent that he pursues this goal. Certain kinds of personal relationships, such as love, constitute an extraordinarily valuable kind of human good, and such a relationship with God would constitute a kind of human good that is absolutely qualitatively superior, that is, qualitatively superior to any other possible kind of human good. The Principle of Expected Value is tailored for decision problems where goods of varying quality are deemed to be at stake, and the application of this principle yields that it is pragmatically rational to have an overriding goal to attain a good which is absolutely qualitatively superior. Thus it is pragmatically rational to be a devout religious person. This in turn yields that it is pragmatically rational to have "religious faith", which is viewed as a pragmatic commitment or assumption for practical purpose that God exists, and is to be distinguished sharply from other propositional attitudes such as the "belief" or "hope" that God exists. (shrink)

Three topics are discussed concerning the application probability and explanation to the confirmation of theories. The first concerns the debate over prediction versus accommodation. I argue that we typically have reason to be more confident of a theory given that it was constructed independently of the knowledge of certain data than if it was designed to accommodate those data. The second concerns the puzzle of the apparent 'fine-tuning' of the universe for life. I argue that the fact that our universe (...) meets the extremely improbable yet necessary conditions for life provides no evidence for the thesis that there are, or have been, very many universes. The third chapter concerns the need to explain the existence of life. I argue that if life's existence needs an explanation at all, the place to look is in a teleological explanation. If this option is rejected, we should be content to see the origin of life as an extremely improbable fluke. (shrink)