The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques (...) for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

Most donated organs in the United States come from brain dead donors, while a small percentage come from patients who die in “controlled,” or expected, circumstances, typically after the family or surrogate makes a decision to withdraw life support. The number of organs available for transplant could be substantially if donations were permitted in “uncontrolled” circumstances–that is, from people who die unexpectedly, often outside the hospital. According to projections from the Institute of Medicine, establishing programs permitting “uncontrolled donation after circulatory (...) determination of death,” or uDCDD, throughout the United States has the potential to provide 22,000 more donation opportunities annually. In contrast, U.S. controlled donation after circulatory determination of death, or cDCDD, cases have increased progressively over the past decade from 87 to 848 donors, but currently account for only 10.6 percent of all deceased donors. Following the IOM recommendations, several projects exploring the feasibility of uDCDD were funded by the federal government, including a grant from the Health Resources and Services Administration that supported a pilot project in New York City in which the authors of this article participated.A key feature of our protocol, and indeed of many uDCDD protocols, is the initiation of preservation methods such as chest compressions and extracorporeal membrane oxygenation shortly after death in order to perfuse and preserve the donor's organs. Critics of uDCDD argue that the means of determining death deviates from generally ascribed principles. They assert that reinstituting circulation in order to preserve organs has the effect of “undoing” the prior determination of death. The result is that cDCDD is widely accepted and practiced routinely even though it only marginally increases the number of organs available for transplantation, and uDCDD is widely considered unacceptable despite being ethically embraced and proven to significantly increase organ donation opportunities in other countries. This article explores the evolution of this counterintuitive state of affairs and calls for a policy that, in line with the IOM report, allows for both cDCDD and uDCDD protocols. (shrink)

Cesario's analysis has three key flaws. First, the focus on whether an effect is “real” overlooks the importance of theory testing. Second, obsession with effects sidelines theoretically informed questions about when and why an effect may arise. Third, failure to take stock of cultural and historical context strips findings of meaning.

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)

Parkinson schreibt, es sei nicht klar, daß Alexander selbst von Geburt an Merkmale oder Zeichen des Ortes seines zukünftigen Todes in sich getragen haben müsse, weil der vollständige Begriff von Alexander den Begriff des in Babylon Sterbens enthält. Die vorliegende Interpretation des Prinzips der Vorherbestimmtheit der Geschichte verdeutlicht dies mit Hilfe der bildlichen Ausdrücke, Pläne und Dispositionen und mit Hilfe einer aristotelischen Unterscheidung zwischen "going to be" und "will be" , fur welche ein formaler chronologischer Apparat ausgearbeitet ist. (...) Die Arbeit gibt ebenfalls Einblick in den Gedanken, daB die Gegenwart schwanger mit der Zukunft ist, und antwortet auf Reschers Kritik, daß Leibniz' Metaphysik von Grund auf statisch sei. (shrink)

This book assesses how Vatican II opened up the Catholic Church to encounter, dialogue, and engagement with other world religions. Opening with a contribution from the President of the Pontifical Council for Interreligious Dialogue, Cardinal Jean-Louis Tauran, it next explores the impact, relevance, and promise of the Declaration Nostra Aetate before turning to consider how Vatican II in general has influenced interfaith dialogue and the intellectual and comparative study of world religions in the postconciliar decades, as well as the contribution (...) of particular past and present thinkers to the formation of current interreligious and comparative theological methods. Additionally, chapters consider interreligious dialogue vis-à-vis theological anthropology in conciliar documents; openness to the spiritual practices of other faith traditions as a way of encouraging positive interreligious encounter; the role of lay and new ecclesial movements in interreligious dialogue; and the development of Monastic Interreligious Dialogue. Finally, it includes a range of perspectives on the fruits and future of Vatican’s II’s opening to particular faiths such as Judaism, Islam, Hinduism, and Buddhism. (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)

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 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)

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.

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.

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)

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.

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.

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)

Scoring rules measure the deviation between a credence assignment and reality. Probabilism holds that only those credence assignments that satisfy the axioms of probability are rationally admissible. Accuracy-based arguments for probabilism observe that given certain conditions on a scoring rule, the score of any non-probability is dominated by the score of a probability. The conditions in the arguments we will consider include propriety: the claim that the expected accuracy of _p_ is not beaten by the expected accuracy of any other (...) credence _c_ by the lights of _p_ if _p_ is a probability. I argue that if we think through how a non-probabilist can respond to pragmatic arguments for probabilism, we will expect the non-probabilist to accept a condition _stronger_ than propriety for the same reasons that the probabilist gives for propriety, but this stronger condition is incompatible with the other conditions that the probabilist needs to run the accuracy argument. This makes it unlikely for the probabilist’s argument to be compelling. (shrink)

Cohesin establishes sister‐chromatid cohesion during S phase to ensure proper chromosome segregation in mitosis. It also facilitates postreplicative homologous recombination repair of DNA double‐strand breaks by promoting local pairing of damaged and intact sister chromatids. In G2 phase, cohesin that is not bound to chromatin is inactivated, but its reactivation can occur in response to DNA damage. Recent papers by Koshland's and Sjögren's groups describe the critical role of the known cohesin cofactor Eco1 (Ctf7) and ATR checkpoint kinase in damage‐induced (...) reactivation of cohesin, revealing an intricate mechanism that regulates sister‐chromatid pairing to maintain genome integrity.1,2 BioEssays 30:5–9, 2008. © 2007 Wiley Periodicals, Inc. (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.

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.

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..

Significant associations have been found between specific human leukocyte antigen (HLA) alleles and organ transplant rejection, autoimmune disease development, and the response to infection. Traditional searches for disease associations have conventionally measured risk associated with the presence of individual HLA alleles. However, given the high level of HLA polymorphism, the pattern of amino acid variability, and the fact that most of the HLA variation occurs at functionally important sites, it may be that a combination of variable amino acid sites shared (...) by several alleles (shared epitopes) are better descriptors of the actual causative genetic variants. Here we describe a novel approach to genetic association analysis in which genes/proteins are broken down into smaller sequence features and then variant types defined for each feature, allowing for independent analysis of disease association with each sequence feature variant type. We have used this approach to analyze a cohort of systemic sclerosis patients and show that a sequence feature composed of specific amino acid residues in peptide binding pockets 4 and 7 of HLA-DRB1 explains much of the molecular determinant of risk for systemic sclerosis. (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)

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)

_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)

Previous research demonstrates that implicitly learned probability information can guide visual attention. We examined whether the probability of an object changing can be implicitly learned and then used to improve change detection performance. In a series of six experiments, participants completed 120–130 training change detection trials. In four of the experiments the object that changed color was the same shape on every trial. Participants were not explicitly aware of this change probability manipulation and change detection performance was not improved for (...) the trained shape versus untrained shapes. In two of the experiments, the object that changed color was always in the same general location . Although participants were not explicitly aware of the change probability, implicit knowledge of it did improve change detection performance in the trained location. These results indicate that improved change detection performance through implicitly learned change probability occurs for location but not shape. (shrink)

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)

ai Diminished gaze fixation is one of the core features of autism and has been proposed to be associated with abnormalities in the neural circuitry of affect. We tested this hypothesis in two separate studies using eye tracking while measuring functional brain activity during facial discrimination tasks in individuals with autism and in typically developing individuals. Activation in the fusiform gyrus and amygdala was strongly and positively correlated with the time spent fixating the eyes in the autistic group in both (...) studies, suggesting that diminished gaze fixation may account for the fusiform hypoactivation to faces commonly reported in autism. In addition, variation in eye fixation within autistic individuals was strongly and positively associated with amygdala activation across both studies, suggesting a heightened emotional response associated with gaze fixation in autism. (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)

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.

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)

We propose using a bi-axial map as a heuristic for categorizing different dynamics involved in the relationship between quality and popularity. The east–west axis represents the degree to which an agent’s decision is influenced by those of other agents. This ranges from the extreme western edge, where an agent learns individually (no outside influence), to the extreme eastern edge, where an agent is influenced by a large number of other agents. The vertical axis represents how easy or difficult it is (...) for an agent to discern the relative quality of available choices. When a case study is located on the map, it becomes easier to select the range of tools to use for understanding and predicting the relation between quality and popularity. (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)