The Principle of Sufficient Reason says that all contingent facts must have explanation. In this 2006 volume, which was the first on the topic in the English language in nearly half a century, Alexander Pruss examines the substantive philosophical issues raised by the Principle Reason. Discussing various forms of the PSR and selected historical episodes, from Parmenides, Leibnez, and Hume, Pruss defends the claim that every true contingent proposition must have an explanation against major objections, including Hume's imaginability argument and (...) Peter van Inwagen's argument that the PSR entails modal fatalism. Pruss also provides a number of positive arguments for the PSR, based on considerations as different as the metaphysics of existence, counterfactuals and modality, negative explanations, and the everyday applicability of the PSR. Moreover, Pruss shows how the PSR would advance the discussion in a number of disparate fields, including meta-ethics and the philosophy of mathematics. (shrink)

We show that infinitesimal probabilities are much too small for modeling the individual outcome of a countably infinite fair lottery.

Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.

Necessary Existence breaks ground on one of the deepest questions anyone ever asks: why is there anything? Pruss and Rasmussen present an original defence of the hypothesis that there is a necessarily existing being capable of providing an ultimate foundation for the existence of all things.

An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of probability. Its use is defensible if there is some sense in which the lottery is physically possible, even if exotic physics is needed. I argue that exotic physics is needed and describe several proposals that fail and at least one that succeeds well enough.

This important philosophical reflection on love and sexuality from a broadly Christian perspective is aimed at philosophers, theologians, and educated Christian readers. Alexander R. Pruss focuses on foundational questions on the nature of romantic love and on controversial questions in sexual ethics on the basis of the fundamental idea that romantic love pursues union of two persons as one body. _One Body_ begins with an account, inspired by St. Thomas Aquinas, of the general nature of love as constituted by components (...) of goodwill, appreciation, and unitiveness. Different forms of love, such as parental, collegial, filial, friendly, fraternal, or romantic, Pruss argues, differ primarily not in terms of goodwill or appreciation but in terms of the kind of union that is sought. Pruss examines romantic love as distinguished from other kinds of love by a focus on a particular kind of union, a deep union as one body achieved through the joint biological striving of the sort involved in reproduction. Taking the account of the union that romantic love seeks as a foundation, the book considers the nature of marriage and applies its account to controversial ethical questions, such as the connection between love, sex, and commitment and the moral issues involving contraception, same-sex activity, and reproductive technology. With philosophical rigor and sophistication, Pruss provides carefully argued answers to controversial questions in Christian sexual ethics. "This is a terrific—really quite extraordinary—work of scholarship. It is quite simply the best work on Christian sexual ethics that I have seen. It will become the text that anyone who ventures into the field will have to grapple with—a kind of touchstone. Moreover, it is filled with arguments with which even secular writers on sexual morality will have to engage and come to terms." —_Robert P. George, Princeton University __ "_One Body_ is an excellent piece of philosophical-theological reflection on the nature of sexuality and marriage. This book has the potential to become a standard go-to text for professors and students working on sex ethics issues, whether in philosophy or theology, both for the richness of its arguments, and the scope of its coverage of cases. " — Christopher Tollefsen, University of South Carolina_ "Alexander Pruss here develops sound and humane answers to the whole range of main questions about human sexual and reproductive choices. His principal argument for the key answers is very different from the one I have articulated over the past fifteen years. But his argumentation is at every point attractively direct, careful, energetic in framing and responding to objections, and admirably attentive to realities and the human goods at stake." —_John Finnis, University of Oxford _. (shrink)

We will give a new cosmological argument for the existence of a being who, although not proved to be the absolutely perfect God of the great Medieval theists, also is capable of playing the role in the lives of working theists of a being that is a suitable object of worship, adoration, love, respect, and obedience. Unlike the absolutely perfect God, the God whose necessary existence is established by our argument will not be shown to essentially have the divine perfections (...) of omnipotence, omniscience, omnibenevolence, and sovereignty. Furthermore, it is not even shown that he is contingently omnipotent and omniscient, just powerful and intelligent enough to be the supernatural designer-creator of the exceedingly complex and wondrous cosmos that in fact.. (shrink)

One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...) the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event. (shrink)

(2013). Incompatibilism proved. Canadian Journal of Philosophy. ???aop.label???

I offer examples showing that, pace G. E. Moore, it is possible to assert ?Q and I don't believe that Q? sincerely, truly, and without any absurdity. The examples also refute the following principles: (a) justification to assert p entails justification to assert that one believes p (Gareth Evans); (b) the sincerity condition on assertion is that one believes what one says (John Searle); and (c) to assert (to someone) something that one believes to be false is to lie (Don (...) Fallis). (shrink)

An omnipotent being would be a being whose power was unlimited. The power of human beings is limited in two distinct ways: we are limited with respect to our freedom of will, and we are limited in our ability to execute what we have willed. These two distinct sources of limitation suggest a simple definition of omnipotence: an omnipotent being is one that has both perfect freedom of will and perfect efficacy of will. In this paper we further explicate this (...) definition and show that it escapes the standard objections to divine omnipotence. (shrink)

It is often loosely said that Ramsey The foundations of mathematics and other logical essays, Routledge and Kegan Paul, Abingdon, pp 156–198, 1931) and de Finetti Studies in subjective probability, Kreiger Publishing, Huntington, 1937) proved that if your credences are inconsistent, then you will be willing to accept a Dutch Book, a wager portfolio that is sure to result in a loss. Of course, their theorems are true, but the claim about acceptance of Dutch Books assumes a particular method of (...) calculating expected utilities given the inconsistent credences. I will argue that there are better ways of calculating expected utilities given a potentially inconsistent credence assignment, and that for a large class of credences—a class that includes many inconsistent examples—these ways are immune to Dutch Books and single-shot domination failures. The crucial move is to replace Finite Additivity with Monotonicity, then \\le P\)) and then calculate expected utilities for positive U via the formula \\, dy\). This shows that Dutch Book arguments for probabilism, the thesis that one’s credences should be consistent, do not establish their conclusion. Finally, I will consider a modified argument based on multi-step domination failure that does better, but nonetheless is not as compelling as the Dutch Book arguments appeared to be. (shrink)

Plantinga’s Free Will Defense is an argument that, possibly, God cannot actualize a world containing significant creaturely free will and no wrongdoings. I will argue that if standard Molinism is true, there is a pair of worlds w1 and w2 each of which contains a significantly free creature who never chooses wrongly, and that are such that, necessarily, at least one of these worlds is a world that God can actualize.

The classical principle of double effect offers permissibility conditions for actions foreseen to lead to evil outcomes. I shall argue that certain kinds of closeness cases, as well as general heuristic considerations about the order of explanation, lead us to replace the intensional concept of intention with the extensional concept of accomplishment in double effect.

Consider the following three-step dialectics. (1) Even if God (consistently) commanded torture of the innocent, it would still be wrong. Therefore Divine Command Metaethics (DCM) is false. (2) No: for it is impossible for God to command torture of the innocent. (3) Even if it is impossible, there is a non-trivially true per impossibile counterfactual that even if God (consistently) com­manded torture of the innocent, it would still be wrong, and this counterfac­tual is incompatible with DCM. I shall argue that (...) the last step of this dialectics is flawed because it would rule out every substantive metaethical theory. (shrink)

We shall use Gödel’s Second Incompleteness Theorem to show that consistency is not possibility, and then argue that the argument does serious damage to some theories of modality where consistency plays a major but not exclusive role.

A number of philosophers have attempted to solve the problem of null-probability possible events in Bayesian epistemology by proposing that there are infinitesimal probabilities. Hájek and Easwaran have argued that because there is no way to specify a particular hyperreal extension of the real numbers, solutions to the regularity problem involving infinitesimals, or at least hyperreal infinitesimals, involve an unsatisfactory ineffability or arbitrariness. The arguments depend on the alleged impossibility of picking out a particular hyperreal extension of the real numbers (...) and/or of a particular value within such an extension due to the use of the Axiom of Choice. However, it is false that the Axiom of Choice precludes a specification of a hyperreal extension—such an extension can indeed be specified. Moreover, for all we know, it is possible to explicitly specify particular infinitesimals within such an extension. Nonetheless, I prove that because any regular probability measure that has infinitesimal values can be replaced by one that has all the same intuitive features but other infinitesimal values, the heart of the arbitrariness objection remains. (shrink)

This article focuses on the question of whether the doctrine of the real presence of Christ's body and blood, and likewise the doctrine of the real absence of bread and wine, can be defended philosophically. It argues for an affirmative answer, and does so by considering a variety of metaphysical models, including that of Aquinas. It will appear, thus, that transubstantiation is a philosophical possibility. If it is possible for two substances to be in the same place at the same (...) time, consubstantiation will be a philosophical possibility as well. Of course, the question of actuality is a theological one. (shrink)

Assuming S₅, the main controversial premise in modal ontological arguments is the possibility premise, such as that possibly a maximally great being exists. I shall offer a new way of arguing that the possibility premise is probably true.

Our paper ‘A new cosmological argument’ gave an argument for the existence of God making use of the weak Principle of Sufficient Reason (W-PSR) which states that for every proposition p, if p is true, then it is possible that there is an explanation for p. Recently, Graham Oppy, as well as Kevin Davey and Rob Clifton, have criticized the argument. We reply to these criticisms. The most interesting kind of criticism in both papers alleges that the W-PSR can be (...) justifiably denied by the atheist, and constitutes no improvement on the strong Principle of Sufficient Reason (S-PSR) which claims that every true proposition in fact has an explanation. The criticism is predicated on the fact that it can be shown that the W-PSR entails the S-PSR. We argue that the W-PSR's plausibility remains despite the criticisms. From this it can be seen to follow that the entailment relation between the W-PSR and the S-PSR gives one reason to believe the S-PSR. (shrink)

Our aim in this paper is to bring to light two sources of tension for Christian theists who endorse the principle of unrestricted composition, that necessarily, for any objects, the xs, there exists an object, y, such that the xs compose y. In Value, we argue that a composite object made of wholly valuable parts is at least as valuable as its most valuable part, and so the mereological sum of God and a wholly valuable part would be at least (...) as valuable as God; but Christian theism arguably demands that no concrete object other than God can be as valuable as God. And in Creation, we argue that the conjunction of theism and unrestricted composition, together with the claim that every concrete entity that is numerically distinct from God is created by God, implies that God is created by God. We conclude by examining the prospects of restricting the thesis of unrestricted composition to the domain of material or spatiotemporal objects as a way to sidestep the above arguments against the conjunction of Christian theism and unrestricted composition. (shrink)

Consider the reasonable axioms of subjunctive conditionals if p → q1 and p → q2 at some world, then p → at that world, and if p1 → q and p2 → q at some world, then → q at that world, where p → q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably (...) false. I will then show how Lewisian semantics can be modified so as to assure and even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then. (shrink)

Gödel's ontological argument is a formal argument for a being defined in terms of the concept of a positive property. I shall defend several versions of Gödel's argument, using weaker premises than Anderson's (1990) version, and avoiding Oppy's (1996 and 2000) parody refutations.

The Adams Thesis holds for a conditional → and a probability assignment P if and only if P=P whenever P>0. The restriction ensures that P is well defined by the classical formula P=P/P. Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results, any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on (...) how far triviality results can go. (shrink)

I defend a simple argument for why considerations of epistemic probability should lead us away from Open Future views according to which claims about the future are never true.

Plural quantification, often used to evade Russell paradoxes, will lead back to them, given certain assumptions about propositions. This chapter provides a more generalized version of the path to paradox by showing that any theory that makes possible the construction of an appropriate packaging relation falls prey to a Russell paradox. It gives examples of widely-held metaphysical theories that require such a relation. It shows that the paradoxes that can result from plural quantification are more widely damaging, and harder to (...) tame, than has been recognized. It also displays formal requirements that any metaphysical framework with a packaging relation must meet if it is to have a chance of escaping self-contradiction. The chapter first gives the general paradox-generating setup, and then shows how three families of metaphysical assumptions allow one to instantiate it. It concludes by assessing the aftermath of the arguments presented. (shrink)

Sceptical theism claims that we have vast ignorance about the realm of value and the connections, causal and modal, between goods and bads. This ignorance makes it reasonable for a theist to say that God has reasons beyond our ken for allowing the horrendous evils we observe. But if so, then does this not lead to moral paralysis when we need to prevent evils ourselves? For, for aught that we know, there are reasons beyond our ken for us to allow (...) the evils, and so we should not prevent them. This paralysis argument, however, shall be argued to rest on a confusion between probabilities and expected utilities. A connection between this paralysis argument and Lenman's1 discussion of the butterfly effect and chaos will be drawn, and the solution offered will apply in both cases. (shrink)

Eugene Mills has recently argued that human organisms cannot begin to exist at fertilization because the evidence suggests that egg cells persist through fertilization and simply turn into zygotes. He offers two main arguments for this conclusion: that ‘fertilized egg’ commits no conceptual fallacy, and that on the face of it, it looks as though egg cells survive fertilization when the process is watched through a microscope. We refute these arguments and offer several reasons of our own to think that (...) egg cells do not survive fertilization, appealing to various forms of essentialism regarding persons, fission cases, and a detailed discussion of the biological facts relevant to fertilization and genetics. We conclude that it is plausible, therefore, that human organisms begin to exist at fertilization – or, at the very least, that there are grounds for thinking that they existed as zygotes which do not apply to the prior egg cells. While this does not entail that human persons begin to exist at this point, it nevertheless has considerable significance for this latter question. (shrink)

According to David Lewis's extreme modal realism, every waythat a world could be is a way that some concretely existingphysical world really is. But if the worlds are physicalentities, then there should be a set of all worlds, whereasI show that in fact the collection of all possible worlds is nota set. The latter conclusion remains true even outside of theLewisian framework.

Substantive theories of diachronic identity have been offered for different kinds of entities. The kind of entity whose diachronic identity has received the most attention in the literature is person, where such theories as the psychological theory, the body theory, the soul theory, and animalism have been defended. At the same time, Wittgenstein's remark that ?to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say (...) nothing at all? suggests that the idea of further analysing identity is mistaken at root. I shall offer a simple, deflationary theory that reduces diachronic identity to quantification, synchronic identity and existence at a spacetime location (or at a time, for non-spatial entities). On logical grounds, the theory is guaranteed to have no counterexamples. Because the theory is guaranteed to have no counterexamples, all the imaginative examples offered as intuitive support for theories of personal identity are going to be either incorrect or compatible with the theory. I shall argue that the deflationary theory is preferable on simplicity grounds to typical substantive theories, and that various problems that are commonly thought to concern diachronic identity are better seen as about something else. (shrink)

Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the (...) Popper function to be rotationally invariant and defined on pairs of sets from some algebra that contains at least all countable subsets. Then it turns out that the Popper function trivializes for all finite sets: P=1 for all A ) if B is finite. Likewise, Popper functions invariant under all sequence reflections can’t be defined in a way that models a bidirectionally infinite sequence of independent coin tosses. (shrink)

This paper argues that if creatures are to have significant free will, then God's essential omni-benevolence and essential omnipotence cannot logically preclude Him from creating a world containing a moral evil. The paper maintains that this traditional conclusion does not need to rest on reliance on subjunctive conditionals of free will. It can be grounded in several independent ways based on premises that many will accept.

God is omnirational: whenever he does anything, he does it for all and only the unexcluded reasons that favor the action, and he always acts for reasons. Thisdoctrine has two unexpected consequences: it gives an account of why it is that unification is a genuine form of scientific explanation, and it answers the question of when the occurrence of E after a petitionary prayer for E is an answer to the prayer.

While it might seem prima facie plausible that divine foreknowledge is all that is needed for prophecy, this seems incorrect. To issue a prophecy, God hasto know not just how someone will act, but how someone would act were the prophecy issued. This makes some think that Middle Knowledge is required.I argue that Thomas Flint’s two Middle Knowledge based accounts of prophecy are unsatisfactory, but one of them can be repaired. However the resources needed for repair also yield a sketch (...) of a foreknowledge-only account of prophecy. (shrink)

The Principle of Sufficient Reason (PSR) says that, necessarily, every contingently true proposition has an explanation. The PSR is the most controversial premise in the cosmological argument for the existence of God. It is likely that one reason why a number of philosophers reject the PSR is that they think there are conceptual counter-examples to it. For instance, they may think, with Peter van Inwagen, that the conjunction of all contingent propositions cannot have an explanation, or they may believe that (...) quantum mechanical phenomena cannot be explained. It may, however, be that these philosophers would be open to accepting a restricted version of the PSR as long as it was not ad hoc. I present a natural restricted version of the PSR that avoids all conceptual counter-examples, and yet that is strong enough to ground a cosmological argument. The restricted PSR says that all explainable true propositions have explanations. (Published Online April 21 2004). (shrink)

Assuming S5, the main controversial premise in modal ontological arguments is the possibility premise, such as that possibly a maximally great being exists. I shall offer a new way of arguing that the possibility premise is probably true.

The free-will defence (FWD) holds that the value of significant free will is so great that God is justified in creating significantly free creatures even if there is a risk or certainty that these creatures will sin. A difficulty for the FWD, developed carefully by Quentin Smith, is that God is unable to do evil, and yet surely lacks no genuinely valuable kind of freedom. Smith argues that the kind of freedom that God has can be had by creatures, without (...) a risk of creatures doing evil. I shall show that Smith's argument fails – the case of God is disanalogous to the case of creatures precisely because creatures are creatures. (shrink)

McGrew, McGrew and Vestrup (MMV) have argued that the fine-tuning anthropic principle argument for the existence of God fails because no probabilities can be assigned to the likelihood that physical constants fall in some finite interval. In particular, the fine-tuning argument that, say, some constant must lie in the range (1.000,1.001) in order for intelligent life to be possible is no better than a seemingly absurd coarse-tuning argument based on the need for that constant to lie in the range (0.001, (...) 10000000). The author of this piece defends the coarse tuning argument as a rational piece of reasoning, and, further, argues that the countable additivity assumption in the MMV paper can be dropped in favor of finite additivity. (shrink)

Some, notably Peter van Inwagen, in order to avoid problems with free will and omniscience, replace the condition that an omniscient being knows all true propositions with a version of the apparently weaker condition that an omniscient being knows all knowable true propositions. I shall show that the apparently weaker condition, when conjoined with uncontroversial claims and the logical closure of an omniscient being's knowledge, still yields the claim that an omniscient being knows all true propositions.