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

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.

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)

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.

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)

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)

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

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)

There is an important sense in which one can be sure without being certain, i.e., without assigning unit probability. I will offer an explication of this sense of sureness, connecting it with the level of credence that a rational agent would need to have to be confident that she won’t ever lose her confidence. A simple formal result then gives us an explicit formula connecting the threshold α for credence needed for confidence with the threshold needed for being sure: one (...) needs 1−(1−α) to be sure. I then suggest that stepping between α and 1−(1−α) gives a procedure that generates an interesting hierarchy of credential thresholds. (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.

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)

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)

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)

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)

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)

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.

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)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (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.

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)

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.

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.

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.

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.

We introduce three arguments for the thesis that time cannot exist prior to an original creation event. In the first argument, we seek to show that if time doesn’t depend upon creation, then time is infinite in the backwards direction, which is incompatible with arguments for a finite past. In the second and third arguments, we allow for the possibility of backwards-infinite time but argue that God could not have a sufficiently good reason to refrain from creating for infinitely many (...) moments—either in a world void of created things or in the actual world prior to creation. Our end goal is to help clarify connections between time and divine action. (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)

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)

I shall argue that, appearances to the contrary notwithstanding, current biological science does not rule out the possibility of miraculous intervention in the evolutionary history of human beings. This shows that it is possible to reconcile evolutionary science with the claim that we are designed by God.

In this article I respond to a number of powerful criticisms of my book One Body.

David Lewis (1979) has argued that according to his possible worlds analysis of counterfactuals, “backtracking” counterfactuals of the form “If event A were to happen at tA, then event B would happen at tB” where tB precedes tA, are usually false if B does not actually happen at tB. On the other..

A recombinationist like the earlier Armstrong (1989) claims that logically possible worlds are recombinations of items found in the actual world, with some items reduplicated if need be and others deleted. An immediate consequence of this is that if an alien property is a property that could only be defined in terms of fundamental properties that are actually uninstantiated, then it is logically impossible that an alien property be instantiated as no recombination of the items in the actual world can (...) yield a world with an entity having such a property. Recombinationism immediately implies that S5 is false. To see this, suppose for simplicity, as I will throughout this paper, that electric charge is a fundamental property--otherwise, a different example would have to be used. Then, let w be a possible world lacking any charged objects. At w, then, it is true that it is logically impossible that there be a charged particle since no recombination of the entities in w yields a charged particle. Therefore, contrary to S5, what is possible at w differs from what is possible at the actual world, since charged particles are actual and hence logically possible at the actual world. While this argument may make one sceptical of recombinationism, the recombinationist will say that it is not surprising that if we follow out the Aristotelian intuition that possibility is to be grounded in actually existing entities, then what is possible will depend on what is actual. Henceforth I will no longer assume S5, and so logical possibilities will have to be relativized to worlds if recombinationism is true: it is logically possible at the actual world for charged particles to exist, but at a world at which there are no charged particles it is logically impossible for charged particles to exist... (shrink)

“Ex nihilo nihil fit,” goes the classic adage: nothing comes from nothing. Parmenides used the Principle of Sufficient Reason to argue that there was no such thing as change: If there was change, why did it happen when it happened rather than earlier or later? “Nothing happens in vain, but everything for a reason and under necessitation,” claimed Leucippus. Saint Thomas insisted in the.

I argue that it is possible for a human animal to survive the loss of all bodily parts other than the brain.

The free-will defence 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)

The A-theory of time says that it is an objective, non-perspectival fact about the world that some events are present, while others were present or will be present. I shall argue that the A-theory has some implausible consequences for inductive reasoning. In particular, the presentist version of the A-theory, which holds that the difference between the present and the non-present consists in the present events being the only ones that exist, is very much in trouble.

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.