Applications of Probability

This manuscript is about how to start from relying on science to be more certain about Christianity. This is because science is so pervasive in our everyday life that we expect that it works almost every time. However, when it comes to Christianity, we need to have faith because most of the time God does not appear to respond to us. Therefore, we feel uncertain about beliefs in Christianity. Instead of being uncertain, this manuscript tries to find a way so (...) that we are more certain about our beliefs in Christianity. We borrow our method to be certain from science. Science faces a similar situation as in believing in Christianity because its knowledge is fallible. Scientists themselves cannot be certain that the scientific knowledge is true all the time. So, they rely on a method called hypothesis testing to make their decisions to believe or not in scientific knowledge. We borrow this method to believe in Christianity. Therefore, we need evidence to make our decision of belief. We mention some evidence from past miracles to help us to make decisions. These include Eucharistic miracles, Marian apparitions, incorruptible corpses, etc. After we decide to believe in Christianity, we work out a theory of Christianity based on the salvation plan of God. We try to substantiate the principles in the theory by referencing testimonies from the Bible and from evidence of miracles that happened. We show that these principles are related to models and experiments that we formulate based on our beliefs in Christianity. Having obtained an understanding of Christianity like a (historical) science, we formulate our practice as a Christian. (shrink)

Humean arguments from evil are some of the most powerful arguments against Theism. They take as their data what we know about good and evil. And they argue that some rival to Theism better explains, or otherwise predicts, that data than Theism. However, this paper argues that there are many problems with various methods for defending Humean arguments. I consider Philo’s original strategy; modern strategies in terms of epistemic probability; phenomenological strategies; and strategies that appeal to scientific and metaphysical explanations. (...) None of these methods have been sufficiently developed to provide a clear and distinctive defense of Humean arguments. Defenders of Humean arguments need to spend more time on the underlying methodology of their arguments. (shrink)

Pascal’s Wager involves expected utilities. In this chapter, we examine the Wager in light of two main features of expected utility theory: utilities and probabilities. We discuss infinite and finite utilities, and zero, infinitesimal, extremely low, imprecise, and undefined probabilities. These have all come up in recent literature regarding Pascal’s Wager. We consider the problems each creates and suggest prospects for the Wager in light of these problems.

This paper regiments and responds to an objection to skeptical theism. The conclusion of the objection is that it is not reasonable for skeptical theists to prevent evil, even when it would be easy for them to do so. I call this objection a “Dominance-Reasoning Objection” because it can be regimented utilizing dominance reasoning familiar from decision theory. Nonetheless, I argue, the objection ultimately fails because it neglects a distinction between justifying goods that are necessary for the existence of a (...) good and those that are necessary for God’s permission of the good. (shrink)

In his article, ‘What's Wrong with Tooley's Argument from Evil?’, Calum Miller's goal was to show that the evidential argument from evil that I have advanced is unsound, and in support of that claim, Miller set out three main objections. First, he argued that I had failed to recognize that the actual occurrence of an event can by itself, at least in principle, constitute good evidence that it was not morally wrong for God to allow events of the kind in (...) question. Miller's second objection was then that, in attempting to show that it is unlikely that God exists, I had failed to consider either positive arguments in support of the existence of God or possible theodicies, and thus that I was unjustified in drawing any conclusions concerning the probability that theism is true in the light of the total evidence available. Miller's third and final objection was that one of the approaches to logical probability that I employed – namely, that based upon a structure-description equiprobability principle, rather than a state-description equiprobability principle – was unsound since it has clearly unacceptable implications. In response, I argue that all three of Miller's objections are unsound. The third objection, however, is nevertheless important since it shows that my type of argument from evil cannot be based merely on the evils found in the world. One must also consider good states of affairs, and their relations to bad ones. I show, however, that that deficiency can be addressed in a completely satisfactory manner. (shrink)

In response to Stephen Davis’s criticism of our previous essay, we revisit and defend our arguments that the Resurrection hypothesis is logically incompatible with the Standard Model of particle physics—and thus is maximally implausible—and that it cannot explain the sensory experiences of the Risen Jesus attributed to various witnesses in the New Testament—and thus has low explanatory power. We also review Davis’s reply, noting that he evades our arguments, misstates their conclusions, and distracts the reader with irrelevancies regarding, e.g., what (...) natural laws are, what a miracle is, and how “naturalism” and “supernaturalism” differ as worldviews. Contrary to what Davis claims (even in his abstract), we do not argue that “if the Standard Model of particle physics is true, then the resurrection of Jesus did not occur and physical things can only causally interact with other physical things.” Davis distorts our claims and criticizes straw men of his own creation. (shrink)

David Hume was clearly a critic of religion. It is still debated, however, whether or not he was an atheist who denied the existence of God. According to some interpretations he was a theist of some kind and others claim he was an agnostic who simply suspends any belief on this issue. This essay argues that Hume’s theory of belief tells against any theistic interpretation – including the weaker, “attenuated” accounts. It then turns to the case for the view that (...) Hume’s criticisms of theism were limited to the “soft” skeptical (agnostic) aim of discrediting theist arguments, and shows that he is committed to a “harder” skeptical view that denies the theist hypothesis (in all its forms). Hume’s atheistic commitments are, the paper concludes, entirely consistent with his mitigated skeptical principles. (shrink)

According to a simple Bayesian argument from evil, the evil we observe is less likely given theism than given atheism, and therefore lowers the probability of theism. I consider the most common skeptical theist response to this argument, according to which our cognitive limitations make the probability of evil given theism inscrutable. I argue that if skeptical theists are right about this, then the probability of theism given evil is itself largely inscrutable, and that if this is so, we ought (...) to be agnostic about whether God exists. (shrink)

Traditional theistic arguments conclude that God exists. Pragmatic theistic arguments, by contrast, conclude that you ought to believe in God. The two most famous pragmatic theistic arguments are put forth by Blaise Pascal (1662) and William James (1896). Pragmatic arguments for theism can be summarized as follows: believing in God has significant benefits, and these benefits aren’t available for the unbeliever. Thus, you should believe in, or ‘wager on’, God. This article distinguishes between various kinds of theistic wagers, including finite (...) vs. infinite wagers, premortem vs. postmortem wagers, and doxastic vs. acceptance wagers. Then, we’ll turn to the epistemic-pragmatic distinction, and discusses the nuances of James’ argument, and how views like epistemic permissivism and epistemic consequentialism provide unique “hybrid” wagers. Finally, we’ll cover outstanding objections and responses. (shrink)

This project retraces activations of Kierkegaard in the development of polit­ical theology. It suggests alternative modes of states of exception than those attributed to him by Schmitt, Taubes and Agamben. Several Kierkegaardian themes open themselves to 'something like pure potential' in Agamben, namely: living death, animality, criminality, auto-constitution, modification, liturgy, love and certain articulations of improbabilities. Attention is drawn to a modal ontology and auto-constitution at work in Kierkegaard's writings, as well as a complicated and indissociable operation between killing and (...) letting-live in legalist exceptionalism, comparable to similar functions found in Foucault regarding the biopowers and necropolitics of territorial and governmental apparatuses. It closes in consideration of Kierkegaard's critique of enumeration, large numbers, and statistical probability alongside contemporary tele-technoscientific social controls via the online datafication of people by surveillance or platform capitalisms. After Kierkegaard, such apparatuses are perhaps suspect as calculated to tranquilize humanity into more docile subhumans as it fools folk into becoming part of its numbers. (*Accompanying file includes only front matter, abstract, and endnotes*). (shrink)

Many people do not know or believe there is a God, and many experience a sense of divine absence. Are these (and other) “divine hiddenness” facts evidence against the existence of God? Using Bayesian tools, we investigate *evidential arguments from divine hiddenness*, and respond to two objections to such arguments. The first objection says that the problem of hiddenness is just a special case of the problem of evil, and so if one has responded to the problem of evil then (...) hiddenness has no additional bite. The second objection says that, while hiddenness may be evidence against generic theism, it is not evidence against more specific conceptions of God, and thus hiddenness poses no epistemic challenge to a theist who holds one of these more specific conceptions. Our investigation leaves open just how strong the evidence from hiddenness really is, but we aim to clear away some important reasons for thinking hiddenness is of no evidential significance at all. (shrink)

This paper articulates a way to ground a relatively high prior probability for grand explanatory theories apart from an appeal to simplicity. I explore the possibility of enumerating the space of plausible grand theories of the universe by using the explanatory properties of possible views to limit the number of plausible theories. I motivate this alternative grounding by showing that Swinburne’s appeal to simplicity is problematic along several dimensions. I then argue that there are three plausible grand views—theism, atheism, and (...) axiarchism—which satisfy explanatory requirements for plausibility. Other possible views lack the explanatory virtue of these three theories. Consequently, this explanatory grounding provides a way of securing a nontrivial prior probability for theism, atheism, and axiarchism. An important upshot of my approach is that a modest amount of empirical evidence can bear significantly on the posterior probability of grand theories of the universe. (shrink)

What we've considered so far about the epistemology of human sciences comes up again as to the concept of "destiny''and human free will: who "must" tell us if we are destined or not? Either Neuroscientists or sociologists? Either Philosophers or biochemists? Has psychology anything to say? Do we need a pool to gather them all? Many other questions come up: what determines us and how much? ls there any sense in talking about destiny? We are a complex system and our (...) conscience is an epiphenomenon of a unitary hierarchical system: would this exclude any possibility of choice? And what does "free choice" mean? And what about the consequences on the ethics? Being Jung and Pauli’s thought a reference point, might we outline a comprehensive reading as regards such problems, even thinking of a sort of quantum psychoid free will? (shrink)

We respond to Stephen T. Davis’ criticism of our earlier essay, “Assessing the Resurrection Hypothesis.” We argue that the Standard Model of physics is relevant and decisive in establishing the implausibility and low explanatory power of the Resurrection hypothesis. We also argue that the laws of physics have entailments regarding God and the supernatural and, against Alvin Plantinga, that these same laws lack the proviso “no agent supernaturally interferes.” Finally, we offer Bayesian arguments for the Legend hypothesis and against the (...) Resurrection hypothesis. (shrink)

In this chapter, Logan Paul Gage examines the only real attempt to disprove God’s existence by a New Atheist: Richard Dawkins’s “Ultimate 747 Gambit.” Central to Dawkins’s argument is the claim that God is more complex than what he is invoked to explain. Gage evaluates this claim using the main extant notions of simplicity in the literature. Gage concludes that on no reading does this claim survive scrutiny. Along the way, Dawkins claims that there are no good positive arguments for (...) God’s existence. Gage attempts to show that Dawkins’s argument depends upon distinctively philosophical assumptions that do not appear to withstand scrutiny. (shrink)

There’s a growing sense among philosophers of religion that Humean arguments from evil are some of the most formidable arguments against theism, and skeptical theism fails to undermine those arguments because they fail to make the inferences skeptical theists criticize. In line with this trend, Wes Morriston has recently formulated a Humean argument from evil, and his chief defense of it is that skeptical theism is irrelevant to it. Here I argue that skeptical theism is relevant to Humean arguments. To (...) do this, I reveal the common structure of skeptical theism’s critiques. Seeing the common structure reveals why some versions of skeptical theism are irrelevant to Humean arguments from evil. It also points the way forward to formulating a relevant version. By combining skeptical theism with a plausible principle concerning reasonable belief, I formulate a version of skeptical theism that undermines Morriston’s argument that is also immune from his objections. (shrink)

The hypothesis that God supernaturally raised Jesus from the dead is argued by William Lane Craig to be the best explanation for the empty tomb and postmortem appearances of Jesus because it satisfies seven criteria of adequacy better than rival naturalistic hypotheses. We identify problems with Craig’s criteria-based approach and show, most significantly, that the Resurrection hypothesis fails to fulfill any but the first of his criteria—especially explanatory scope and plausibility.

Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us a (...) reason to pay special attention to the infinite consequences of our actions. (shrink)

It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways out of (...) the paradox, I conclude that the classical theist should accept Marilyn Adams’s view that no norms apply to gods. (shrink)

Why does God allow evil? One hypothesis is that God desires the existence and activity of free creatures but He was unable to create a world with such creatures and such activity without also allowing evil. If Molinism is true, what probability should be assigned to this hypothesis? Some philosophers claim that a low probability should be assigned because there are an infinite number of possible people and because we have no reason to suppose that such creatures will choose one (...) way rather than another. Arguments like this depend on the principle of indifference. But that principle is rejected by most philosophers of probability. Some philosophers claim that a low probability should be assigned because doing otherwise violates intuitions about freewill. But such arguments can be addressed through strategies commonly employed to defend theories with counterintuitive results across ethics and metaphysics. (shrink)

In this article, I argue that faith’s going beyond the evidence need not compromise faith’s epistemic rationality. First, I explain how some of the recent literature on belief and credence points to a distinction between what I call B-evidence and C-evidence. Then, I apply this distinction to rational faith. I argue that if faith is more sensitive to B-evidence than to C-evidence, faith can go beyond the evidence and still be epistemically rational.

In this public debate with Philippe Deterre (research director in immunology at the CNRS) – held at l'Enclos Rey in Paris' 15th district during the biennial Conference of the Réseau Blaise Pascal in March 2017 –, I defended the usefulness of natural theology. I first clarify theology's nature and understanding, then I speak about a tradition that upheld the public and exterior knowledge of God, and make an effort to show the presence of a theme reminiscent of natural theology behind (...) attempts at the good life. I then ask whether natural theology would only exist for the Christian. In the reply to my opponent's own reaction, I insist on the incongruity of separating our knowledge of God from our knowledge of science's wonderful discoveries, I ask whether nature could be said to be crafty and "ingenious," and I conclude by building a case for the return of God in public conversation, as part of an effort that our world needs in terms of finding back its compass, and restoring an ideal of living rationally. (shrink)

We use Bayesian tools to assess Law’s skeptical argument against the historicity of Jesus. We clarify and endorse his sub-argument for the conclusion that there is good reason to be skeptical about the miracle claims of the New Testament. However, we dispute Law’s contamination principle that he claims entails that we should be skeptical about the existence of Jesus. There are problems with Law’s defense of his principle, and we show, more importantly, that it is not supported by Bayesian considerations. (...) Finally, we show that Law’s principle is false in the specific case of Jesus and thereby show, contrary to the main conclusion of Law’s argument, that biblical historians are entitled to remain confident that Jesus existed. (shrink)

The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...) conception of evidence and the knowledge-first view of evidence. (shrink)

Bolzano hat seine Wahrscheinlichkeitslehre in 15 Punkten im § 14 des zweiten Teils seiner Religionswissenschaft sowie in 20 Punkten im § 161 des zweiten Bandes seiner Wissenschaftslehre niedergelegt. (Ich verweise auf die Religionswissenschaft mit 'RW II', auf die Wissenschaftslehre mit 'WL II'.) In der RW II (vgl. p. 37) ist seine Wahrscheinlichkeitslehre eingebettet in seine Ausführungen "Über die Natur der historischen Erkenntniß, besonders in Hinsicht auf Wunder", und die Lehrsätze, die er dort zusammenstellt, dienen dem ausdrücklichen Zweck, mit mathematischem Rüstzeug (...) Lehrmeinungen entgegentreten zu können, gemäß denen Wundererzählungen keine Glaubwürdigkeit zukommen könne. In der WL II (vgl. p. 171) führt Bolzano im großen und ganzen dieselben Lehrsätze an wie in der RW II, entwickelt nun aber die Wahrscheinlichkeitslehre innerhalb seiner Lehre von den Sätzen an sich. Dabei orientiert er sich zwar durchaus an den Lehrsätzen in den damaligen "Schriften über die Wahrscheinlichkeitsrechnung" (vg. WL II, p. 190), korrigiert aber dort, wo es ihm nötig erscheint (vgl. WL II, pp. 187–191), und leistet so im Grunde eine Reformulierung des elementaren Teils der Wahrscheinlichkeitslehre seiner Zeit innerhalb seiner logischen Theorie von den Sätzen an sich. — Ich bezwecke hier keine historische Studie über Bolzanos Wahrscheinlichkeitslehre, obwohl es von Interesse sein mag, herauszuschälen, worin Bolzano mit welchen Wahrscheinlichkeitstheoretikern seiner Zeit übereinstimmt, und worin nicht, insbesondere welche Schwächen von Bolzanos Wahrscheinlichkeitslehre Schwächen aller damaligen Wahrscheinlichkeitslehren waren. Eine wichtige systematische Studie über Bolzanos Wahrscheinlichkeitslehre bestünde — wie von Berg (1962, pp. 148-149) ansatzweise begonnen — in einer exakten Rekonstruktion seiner Wahrscheinlichkeitslehre innerhalb eines konsistenten logischen Systems der Sätze an sich. Ich werde im folgenden etwas bei weitem Bescheideneres, doch möglicherweise durchaus Fruchtbares versuchen, nämlich die Lehrsätze von Bolzanos Wahrscheinlichkeitslehre in die Sprache einer heutigen Wahrscheinlichkeitstheorie zu übersetzen und die übersetzten Lehrsätze dort herzuleiten, soweit dies möglich ist. Man könnte dann in einem zweiten Schritt, der hier nicht mehr unternommen wird, untersuchen, inwieweit jene Thesen, die den Herleitungstest überstanden haben, jenen Zweck erfüllen, den Bolzano ihnen ursprünglich zugedacht hat: als mathematisches Rüstzeug für seine Argumentationen gegen die Auffassung zu dienen, Wundererzählungen könnten nicht glaubwürdig sein. (shrink)

Does postulating skeptical theism undermine the claim that evil strongly confirms atheism over theism? According to Perrine and Wykstra, it does undermine the claim, because evil is no more likely on atheism than on skeptical theism. According to Draper, it does not undermine the claim, because evil is much more likely on atheism than on theism in general. I show that the probability facts alone do not resolve their disagreement, which ultimately rests on which updating procedure – conditionalizing or updating (...) on a conditional – fits both the evidence and how we ought to take that evidence into account. (shrink)

In this essay, I investigate the implications for the discussion of theism in philosophy of religion for the beliefs of ordinary Christians and conclude that, in light of its historical development, those implications are minimal.

This paper provides an account of what it is to have faith in a proposition p, in both religious and mundane contexts. It is argued that faith in p doesn’t require adopting a degree of belief that isn’t supported by one’s evidence but rather it requires terminating one’s search for further evidence and acting on the supposition that p. It is then shown, by responding to a formal result due to I.J. Good, that doing so can be rational in a (...) number of circumstances. If expected utility theory is the correct account of practical rationality, then having faith can be both epistemically and practically rational if the costs associated with gathering further evidence or postponing the decision are high. If a more permissive framework is adopted, then having faith can be rational even when there are no costs associated with gathering further evidence. (shrink)

In “Can it be rational to have faith?”, it was argued that to have faith in some proposition consists, roughly speaking, in stopping one’s search for evidence and committing to act on that proposition without further evidence. That paper also outlined when and why stopping the search for evidence and acting is rationally required. Because the framework of that paper was that of formal decision theory, it primarily considered the relationship between faith and degrees of belief, rather than between faith (...) and belief full stop. This paper explores the relationship between rational faith and justified belief, by considering four prominent proposals about the relationship between belief and degrees of belief, and by examining what follows about faith and belief according to each of these proposals. It is argued that we cannot reach consensus concerning the relationship between faith and belief at present because of the more general epistemological lack of consensus over how belief relates to rationality: in particular, over how belief relates to the degrees of belief it is rational to have given one’s evidence. (shrink)

In his essay, "Fine-Tuning and Multiple Universes", Roger White examines the extent to which a multiple-universe hypothesis lessens the ’surprisingness’ that our universe should be life-sustaining. White offers two main conclusions. His first conclusion -- that the existence of our world is not itself evidence for the existence of multiple universes -- is sound. However, his second conclusion is that, on the hypothesis that multiple universes exist, the further hypothesis of an intelligent designer does not lesson the surprisingness that our (...) universe should be life-permitting. This second conclusion, which would undercut most design arguments, is shown to rest on a mistake. (shrink)

How are inferences to design affected when one makes the (plausible) assumption that the universe is spatially infinite? I will show that arguments for the existence of God based on the improbable development of life don’t go through. I will also show that the model of design inferences promulgated by William Dembski is flawed. My model for design inferences has the (desirable) consequence that there are circumstances where a seeming miracle can count as evidence for the existence of God, even (...) if one would expect that type of event to naturalistically occur in a spatially infinite universe. (shrink)

There seems to be a widespread conviction — evidenced, for example, in the work of Mackie, Dawkins and Sober — that it is Darwinian rather than Humean considerations which deal the fatal logical blow to arguments for intelligent design. I argue that this conviction cannot be well-founded. If there are current logically decisive objections to design arguments, they must be Humean — for Darwinian considerations count not at all against design arguments based upon apparent cosmological fine-tuning. I argue, further, that (...) there are good Humean reasons for atheists and agnostics to resist the suggestion that apparent design — apparent biological design and/or apparent cosmological fine-tuning — establishes (or even strongly supports) the hypothesis of intelligent design. (shrink)