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.

Classical real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value—namely, zero—to cases that are impossible as well as to cases that are possible. There are three non-classical approaches to probability that can avoid this drawback: full conditional probabilities, qualitative probabilities and hyperreal probabilities. These approaches have been criticized for failing to preserve intuitive symmetries that can be preserved by the classical probability framework, but there has not been a systematic study of the (...) conditions under which these symmetries can and cannot be preserved. This paper fills that gap by giving complete characterizations under which symmetries understood in a certain “strong” way can be preserved by these non-classical probabilities, as well as by offering some results to make it plausible that the strong notion of symmetry here is the right one. Philosophical implications are briefly discussed, but the main purpose of the paper is to offer technical results to help make further philosophical discussion more sophisticated. (shrink)

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

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)

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)

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (shrink)

This chapter contains sections titled: Introduction Two Interrelated Problems Lewis's Solution Inductive Paradox Identity versus Counterpart Theory Platonism: The Main Realist Alternative to Lewis An Aristotelian Alternative Leibniz's Account A Combined Account.

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)

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition in the (...) arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (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.

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.

Few studies have examined how trait emotion dysregulation relates to momentary affective experiences and the emotion regulation strategies people use in daily life. In the current study, 112 c...

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.

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.

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.

Let Mm k be the simply connected constant curvature space form of dimension m. • Mm 0 is Rm with euclidean metric • Mm k for k > 0 is an m-sphere of radius k−1/2 • Mm k for k < 0 is m dimensional hyperbolic space modelled on the m-ball of radius (−k)−1/2.

The book takes the reader on a vivid, imaginative journey towards unraveling the mysteries of our existence, roles in society, and personal loyalties. The book melds science with philosophy and theology and highlights the people who dedicated their lives in pursuit of the seven riddles of the universe.

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.

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)

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)

_Laruelle_ is one of the first books in English to undertake in an extended critical survey of the work of the idiosyncratic French thinker François Laruelle, the promulgator of non-standard philosophy. Laruelle, who was born in 1937, has recently gained widespread recognition, and Alexander R. Galloway suggests that readers may benefit from colliding Laruelle’s concept of the One with its binary counterpart, the Zero, to explore more fully the relationship between philosophy and the digital. In _Laruelle_, Galloway argues that (...) the digital is a philosophical concept and not simply a technical one, employing a detailed analysis of Laruelle to build this case while referencing other thinkers in the French and Continental traditions, including Alain Badiou, Gilles Deleuze, Martin Heidegger, and Immanuel Kant. In order to explain clearly Laruelle’s concepts such as the philosophical decision and the principle of sufficient philosophy, Galloway lays a broad foundation with his discussions of “the One” as it has developed in continental philosophy, the standard model of philosophy, and how philosophers view “the digital.” Digital machines dominate today’s world, while so-called digital thinking—that is, binary thinking such as presence and absence or self and world—is often synonymous with what it means to think at all. In examining Laruelle and digitality together, Galloway shows how Laruelle remains a profoundly non-digital thinker—perhaps the only non-digital thinker today—and engages in an extensive discussion on the interconnections between media, philosophy, and technology. (shrink)

I offer a reading of my book One Body on Christian sexual ethics as an application of Inference to Best Explanation based on theological and philosophical data.

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.

P. F. Strawson a critiqué le compte de Leibniz de 1'individuation, en demandant pourquoi il est métaphysiquement impossible pour qu'il y ait des consciences indiscernables mais distincts. L'analogie entre la conscience et la monade est centrale pour Leibniz, et done la critique de Strawson met en question la nécessité métaphysique du principe de l'identité des indiscernables . Par un examen de quelques questions dans le système ontologique de Leibniz, nous défendrons la nécessité métaphysique du PII contre Strawson.

Instead of a ?meditation on first philosophy; (Descartes) or a ?return to first principles; (Kant), Laruelle's work is presented here as a kind of ?meditation on last philosophy; in which the normal structuring conditions of philosophical knowledge are withheld. By superimposing non-philosophy on Kant's two-by-two matrix of a priori/a posteriori and analytic/synthetic, we see a relative enlargement of analytic a priori statements, those itemized by Kant but ultimately deemphasized by him as ?merely; analytic. An analytic statement such as n=n is (...) recast by Laruelle not as a marginally useful tautology but as the identity axiom, the most central axiom in non-philosophy. Likewise, the domain of the a priori is enlarged in Laruelle to encompass the entire universe. What this produces, for Laruelle and non-philosophy, is an ?autistic; rationality, in which normal communicative relations are marginalized in favor of a unidirectional identity with the One. (shrink)

Introduction : the computer as a mode of mediation -- The unworkable interface -- Software and ideology -- Are some things unrepresentable? -- Disingenuous informatics -- Postscript : we are the gold farmers.

          Despite the fact that the strength of argument is clearly on the pro-life side—nobody except a handful of academics would question the grave wrongness of abortion were pregnancy never inconvenient—somehow ordinary intelligent people, like our students, often remain unconvinced. There are many reasons for this, of course. For instance, a number of students have had their children aborted while many know others who have had abortions, and one does not want (...) to condemn oneself or oneÂ’s friends. I am a philosopher, however, and so I will be interested in intellectual reasons, even though these subjective psychological ones are almost surely more important. Specifically, I will be interested in the fact that the ordinary person subscribes to a number of erroneous big-picture ethical beliefs, each of which, to a different degree, does something to block access to the pro-life arguments. I will not talk about all such erroneous beliefs and I would be grateful in the discussion for more examples.           I will talk about eight errors I have identified, largely through teaching. For each one, I will identify the error, show how it impacts the pro-life message and explain why it is tempting to most of us —there is, after all, something right about five of the errors. For each of these errors is one that we might ourselves be tempted by on occasion. I will then suggest some ways of refuting the error. In some cases, the mere identification of the error should do the trick, as these erroneous beliefs are often not explicitly identified by our interlocutors. My suggested refutations will not always be phrased in the way in which I would phrase them for didactic effectiveness: in this talk, I am mainly trying to convey ideas. (shrink)

This chapter contains sections titled: Introduction The PSR Nonlocal CPs Toward a First Cause The Gap Problem Conclusions and Further Research References.

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.

The "Supplement" transmitted as the second book of "On the Soul" by Alexander of Aphrodisias is a collection of short texts on a wide range of topics from psychology, including the general hylomorphic account of soul and its faculties, and the theory of vision; questions in ethics ; and issues relating to responsibility, chance and fate. One of the texts in the collection, "On Intellect", had a major influence on medieval Arabic and Western thought, greater than that of (...) class='Hi'>Alexander's "On the Soul" itself. The treatises may all be by Alexander himself; certainly the majority of them are closely connected with his other works. Many of them, however, consist of collections of arguments on particular issues, collections which probably incorporate material from earlier in the history of the Peripatetic school. This translation is from a new edition of the Greek text based on a collation of all known manuscripts and comparison with medieval Arabic and Latin translations. (shrink)

For two million years, members of Homo sapiens (and the species from which it emerged) have shaped to their purpose almost everything they found in nature. Yet we are still reproducing by sex. This is a poor method of conceiving human beings, because it surrenders many of the future child’s characteristics to luck. Both parents and children are better off the more parents control their children’s genotypes. The emerging technologies that enable this do not reduce free will and will not (...) eliminate human characteristics (such as certain forms of “mental illness”) that are worth preserving; rather, they will match types of children to parents who can appreciate them. Technological reproduction, not reproduction by sex, should be regarded as truly human. It is the application of the power of thought to human reproduction, and, like the application of that power to external objects and to memes, it will enhance our capacities. (shrink)

Always connect—that is the imperative of today’s media. But what about those moments when media cease to function properly, when messages go beyond the sender and receiver to become excluded from the world of communication itself—those messages that state: “There will be no more messages”? In this book, Alexander R. Galloway, Eugene Thacker, and McKenzie Wark turn our usual understanding of media and mediation on its head by arguing that these moments reveal the ways the impossibility of communication is (...) integral to communication itself—instances they call excommunication. In three linked essays, _Excommunication_ pursues this elusive topic by looking at mediation in the face of banishment, exclusion, and heresy, and by contemplating the possibilities of communication with the great beyond. First, Galloway proposes an original theory of mediation based on classical literature and philosophy, using Hermes, Iris, and the Furies to map out three of the most prevalent modes of mediation today—mediation as exchange, as illumination, and as network. Then, Thacker goes boldly beyond Galloway’s classification scheme by examining the concept of excommunication through the secret link between the modern horror genre and medieval mysticism. Charting a trajectory of examples from H. P. Lovecraft to Meister Eckhart, Thacker explores those instances when one communicates or connects with the inaccessible, dubbing such modes of mediation “haunted” or “weird” to underscore their inaccessibility. Finally, Wark evokes the poetics of the infuriated swarm as a queer politics of heresy that deviates from both media theory and the traditional left. He posits a critical theory that celebrates heresy and that is distinct from those that now venerate Saint Paul. Reexamining commonplace definitions of media, mediation, and communication, _Excommunication_ offers a glimpse into the realm of the nonhuman to find a theory of mediation adequate to our present condition. (shrink)

Louis Pojman has argued that Christian faith does not entail belief, or even assigning a probability of 1/2 to the claims of Christianity. However, this conclusion fails in many cases because of its ethical consequences. A Christian is committed by his faith to acting in accordance with Christian teaching. However, there are circumstances when it is morally impermissible to act in accordance to beliefs to which one assigns epistemic probability smaller than 1/2, namely when the action is prohibited by ethical (...) claims that one takes to be more probable. It is argued that in most cases such considerations preclude a person who assigns a probability of less 1/2 from being both committed both to Christianity and to the moral life. Matters are particularly clear in the paradigmatic faith-action of Abraham’s sacrifice of Isaac: this action would clearly be immoral if Abraham assigned a probability less than 1/2, or in fact any probability not very close to 1, to the existence of God. A moral version of Pascal’s wager is also discussed. (shrink)

Bayesian epistemology has struggled with the problem of regularity: how to deal with events that in classical probability have zero probability. While the cases most discussed in the literature, such as infinite sequences of coin tosses or continuous spinners, do not actually come up in scientific practice, there are cases that do come up in science. I shall argue that these cases can be resolved without leaving the realm of classical probability, by choosing a probability measure that preserves “enough” regularity. (...) This approach also provides a resolution to the McGrew, McGrew and Vestrum normalization problem for the fine-tuning argument. (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)

Digital and analog: What do these terms mean today? The use and meaning of such terms change through time. The analog, in particular, seems to go through various phases of popularity and disuse, its appeal pegged most frequently to nostalgic longings for nontechnical or romantic modes of art and culture. The definition of the digital vacillates as well, its precise definition often eclipsed by a kind of fever-pitched industrial bonanza around the latest technologies and the latest commercial ventures. One common (...) response to the question of the digital is to make reference to things like Twitter, Playstation, or computers in general. Here one might be correct, but only coincidentally, for the basic order of digitality (the digitality of digitality) has not yet been demonstrated through mere denotation. And the second question—the question of the analog—is harder still, with responses often also consisting of mere denotations of things: sound waves, the phonograph needle, magnetic tape, a sundial. At least denotation itself is analogical. This article will aim to define the analog explicitly and argue, perhaps counterintuitively, that the golden age of analog thinking was not a few decades past, prior to the wide-spread adoption of the computer. In fact, the fields of structuralism and poststructuralism that emerged in the middle to late twentieth century, concurrent with the deployment of the digital computer, were characteristically digital, what with their focus on the symbolic order and logical economies. If anything, the golden age of analog is happening today, all around us, as evidenced by the proliferation of characteristically analog concerns: sensation, materiality, experience, affect, ethics, and aesthetics. (shrink)

In simplified form, the argument that I am defending holds that the incompatibility of our freedom with determinism follows from the conjunction of (1) a plausible supervenience claim which says that whether a human agent is free depends only on what happens during the agent’s life and (2) a freedom-cancellation principle of Richard Gale which says that an agent is not free if all of her actions are intentionally brought about by another agent. Improved versions of (1) and (2) are (...) also considered. (shrink)