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The Nothing from Infinity paradox arises when the combination of two infinitudes of point particles meet in a supertask and disappear. Corral-Villate claims that my arguments for disappearance fail and concedes that this failure also produces an extreme kind of indeterminism, which I have called plenitudinous. So my supertask at least poses a dilemma of extreme indeterminism within Newtonian point particle mechanics. Plenitudinous indeterminism might be trivial, although easy attempts to prove it so seem to fail in the face of plausible continuity principles. However, the question of its triviality is here moot, since I show that, except in one case, Corral-Villate’s disproofs fail, and with a correction, the original arguments are unrefuted. Consequently, of the two contenders for the outcome of my supertask, the Nothing from Infinity paradox has won out.

How Moore’s open question argument works, insofar as it does, remains a matter of controversy. The author’s purpose here is to construct an open question argument based on a novel interpretation of how Moore’s argument might work. In order to sidestep exegetical questions, he does not claim to be offering Moore’s own argument. Rather, the author offers a reconstruction, making use of important elements of Moore’s methodology and assumptions that could be reasonable within a Moorean viewpoint. The crucial role within the argument is played by what the author calls the real thought move. He shows that the reconstructed argument is more defensible from some standard objections than the common construction. The author finishes by drawing attention to a neglected objective that would make sense within Moore’s viewpoint, showing that it fits with a major commitment of Bonjour’s moderate rationalism, and showing how the package might be important for the non-naturalist today.

We examine conceptual and methodological problems that arise in the course of the scientific study of possible influences of religious belief on the experience of physical pain. We start by attempting to identify a notion of religious belief that might enter into interesting psychological generalizations involving both religious belief and pain. We argue that it may be useful to think of religious belief as a complex dispositional property that relates believers to a sufficiently thick belief system that encompasses both cognitive and non-cognitive elements. Such a conception of religious belief is more likely to correlate with psychological properties of believers that are both sufficiently shared and sufficiently unique to distinguish their psychology from believers in another religion or from non-believers. If the dispositional psychological property that constitutes religious belief does influence pain, then our analysis suggests that it doesn’t do so directly but rather through one of its occurrent manifestations. We offer a taxonomy of the different ways in which occurrent states of belief or experience may interact with physical pain, and we try to identify those that are more interesting or promising. We then proceed to employ the conceptual framework we developed to some of the existing evidence about the neural and psychological correlates of religious belief and experience, and about the cognitive modulation of physical pain. Finally we turn to analyse two experiments that directly investigated the relation between religious belief and pain. We draw attention to the limitations of existing evidence and end by suggesting directions for future conceptual and empirical inquiry.

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force.

There has been a prolonged debate about the nature of norms that has been conducted in terms of the scope of a modal operator. The purpose of this paper is to suggest that there are better concepts in which to conduct that debate, concepts of normative features to which scope is secondary. These are the features of what I call Normative Focus. They are formal features and it is for that reason that, expressing something of their nature in terms of the logic of modal operators, we have mistakenly thought they can be entirely expressed in those terms.We shall see limitations of scope contrasted with better description in terms of Normative Focus. Some authors have addressed such limitations by extending what they mean by scope. I show that scope is still not doing the work for them; what does it is their elicitation of our tacit knowledge of Normative Focus. Finally, I show that scope cannot capture Normative Focus because scope allows us to make only one distinction where we need to make three. So we should leave scope to the philosophers of language and turn instead to the ontology of Normative Focus.

Neuroscience has recently turned to the study of utilitarian and non-utilitarian moral judgement. Koenigs et al. examine the responses of normal subjects and those with ventromedial-prefrontal-cortex (VMPC) damage to moral scenarios drawn from functional magnetic resonance imaging studies by Greene et al., and claim that patients with VMPC damage have an abnormally "utilitarian" pattern of moral judgement. It is crucial to the claims of Koenigs et al. that the scenarios of Greene et al. pose a conflict between utilitarian consequence and duty: however, many of them do not meet this condition. Because of this methodological problem, it is too early to claim that VMPC patients have a utilitarian bias.

where such models are used to rule out derivations involving irrelevant factors (such as the hexed salt example) that are deemed explanatory by the deductive-nomological model. As I mentioned at the outset, my aim has not been to attack Lange’s general thesis that proofs by mathematical induction are not explanatory, but rather to undercut the argument that Lange provides for this thesis. To defend the contrary claim that certain inductive proofs are explanatory would require providing a worked-out theory of mathematical explanation, something that I have not tried to do here. What I have tried to do is to show that there are plausible ways of thinking about mathematical explanation which are in tension with key steps in Lange’s argument, and to this extent his premises are more ‘controversial’ than he admits.

Freedom of speech is a fundamental right that can be defended on consequentialist and deontological grounds. Free speech in bioethics has been under threat for 50 years and is perhaps more vulnerable since the millennium due to the new rhetoric of intolerance and new laws suppressing speech. Nevertheless, it is evident that free speech is a necessity for the proper conduct of bioethics, especially given the ethical challenges that the global diffusion of biotechnology has brought and will continue to bring. That necessity can be defended on the very same grounds that the general liberty can be defended.

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill-posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill-posed problem shows that there are precisely two strategies for resolving the paradox: thedistinction strategyand thewell-posing strategy. The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff's attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well-posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand's original three options can be ruled out but also shows that piecemeal attempts at the well-posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes's use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well-posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff's and Jaynes's solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand's paradox continues to stand in refutation of the principle of indifference.

Dretske proposes a theory of knowledge in terms of a theory of information, but wishes to deny that empirical knowledge settles the large question of scepticism. This leads him to deny the closure of knowledge under known entailment. In a recent paper Jager argues that Dretske’s theory of information entails closure for knowledge, ‘at least for the kind of propositions here at issue’ (Jager 2004:194). If Jager is right, Dretske is seriously embarrassed and must give something up. In this paper I show that there are two flaws in Jager’s argument. The principle of informational closure considered by Jager is incompatible with Dretske’s theory of information, and Jager’s argument that Dretske is committed to a certain kind of substitution instance of that principle of informational closure is invalid. I propose adequacy conditions on signalled information and use them to motivate a formulation of a general closure principle for signalled information. I show that Dretske’s account of information satisfies the adequacy conditions, but in a way which commits him to an instance of the general closure principle. I argue that Dretske is consequently committed to closure for some cases of knowledge for which he wishes to deny closure. Finally, I sketch how, on the basis of the closure principle to which Dretske is committed, Jager’s broader argument may yet go through.

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments.

Benardete presents a version of Zeno’s dichotomy in which\ud an infinite sequence of gods each intends to raise a barrier if a traveller\ud reaches where they intend to raise their barrier. In this paper I exhibit the\ud abstract form of the Benardete Dichotomy. I show that the diagnosis\ud based on that form can do philosophical work not done by earlier papers\ud rejecting Priest’s version of the Benardete Dichotomy, and that the\ud diagnosis extends to a paradox not normally classified as a dichotomy. I\ud show how the form is exploited to generate paradox.

A prevalent assumption is that normativity is a unity. In this paper I argue against this assumption by demonstrating the problems it poses to a well known answer to a well known problem for taking rationality to be normative. John Broome's normative requirement relation does indeed avoid that problem, but insofar as the relation is supposed to offer a general characterisation of the normativity of rationality, it fails. It fails because it cannot capture an important aspect of the normativity of rationality, that it is available to guide us. I show that if we distinguish two kinds of normativity it need not fail in this way.

A paradox is presented that the poses new problems for both the truth norm and the knowledge norm of belief.

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series of expected gains can the paradox be resolved.

In his important recent book Schroeder proposes a Humean theory of reasons that he calls hypotheticalism. His rigourous account of the weight of reasons is crucial to his theory, both as an element of the theory and constituting his defence to powerful standard objections to Humean theories of reasons. In this paper I examine that rigourous account and show it to face problems of vacuity and consonance. There are technical resources that may be brought to bear on the problem of vacuity but implementation is not simple and philosophical motivation a further difficulty. Even supposing vacuity is fixed, the problems of consonance bring to light a different obstruction lying in Schroeder’s path. There is a difference between the general weighing of reasons and the context specificity of the correct placing of weight on them in deliberation and this difference cannot be fixed by the resources in the account. For these reasons we are still waiting for a plausible Humean theory of reasons.

Highlights ► We investigated the role of two personality traits in moral judgment using fMRI. ► Psychoticism and need for cognition correlated with number of utilitarian decisions. ► Only psychoticism was associated with reduced activation in the subgenual ACC. ► Our data suggest that utilitarian judgments can reflect a reduced aversion to harm. ► They offer little support to a tie between utilitarian judgment and greater deliberation., Recent research on moral decision-making has suggested that many common moral judgments are based on immediate intuitions. However, some individuals arrive at highly counterintuitive utilitarian conclusions about when it is permissible to harm other individuals. Such utilitarian judgments have been attributed to effortful reasoning that has overcome our natural emotional aversion to harming others. Recent studies, however, suggest that such utilitarian judgments might also result from a decreased aversion to harming others, due to a deficit in empathic concern and social emotion. The present study investigated the neural basis of such indifference to harming using functional neuroimaging during engagement in moral dilemmas. A tendency to counterintuitive utilitarian judgment was associated both with ‘psychoticism’, a trait associated with a lack of empathic concern and antisocial tendencies, and with ‘need for cognition’, a trait reflecting preference for effortful cognition. Importantly, only psychoticism was also negatively correlated with activation in the subgenual cingulate cortex (SCC), a brain area implicated in empathic concern and social emotions such as guilt, during counterintuitive utilitarian judgments. Our findings suggest that when individuals reach highly counterintuitive utilitarian conclusions, this need not reflect greater engagement in explicit moral deliberation. It may rather reflect a lack of empathic concern, and diminished aversion to harming others.

Neuroimaging studies on moral decision-making have thus far largely focused on differences between moral judgments with opposing utilitarian (well-being maximizing) and deontological (duty-based) content. However, these studies have investigated moral dilemmas involving extreme situations, and did not control for two distinct dimensions of moral judgment: whether or not it is intuitive (immediately compelling to most people) and whether it is utilitarian or deontological in content. By contrasting dilemmas where utilitarian judgments are counterintuitive with dilemmas in which they are intuitive, we were able to use functional magnetic resonances imaging to identify the neural correlates of intuitive and counterintuitive judgments across a range of moral situations. Irrespective of content (utilitarian/deontological), counterintuitive moral judgments were associated with greater difficulty and with activation in the rostral anterior cingulate cortex, suggesting that such judgments may involve emotional conflict; intuitive judgments were linked to activation in the visual and premotor cortex. In addition, we obtained evidence that neural differences in moral judgment in such dilemmas are largely due to whether they are intuitive and not, as previously assumed, to differences between utilitarian and deontological judgments. Our findings therefore do not support theories that have generally associated utilitarian and deontological judgments with distinct neural systems.

Neuroscience and psychology have recently turned their attention to the study of the subpersonal underpinnings of moral judgment. In this article we critically examine an influential strand of research originating in Greene's neuroimaging studies of 'utilitarian' and 'non-utilitarian' moral judgement. We argue that given that the explananda of this research are specific personal-level states-moral judgments with certain propositional contents-its methodology has to be sensitive to criteria for ascribing states with such contents to subjects. We argue that current research has often failed to meet this constraint by failing to correctly 'fix' key aspects of moral judgment, criticism we support by detailed examples from the scientific literature.

Although religious belief is often claimed to help with physical ailments including pain, it is unclear what psychological and neural mechanisms underlie the influence of religious belief on pain. By analogy to other top-down processes of pain modulation we hypothesized that religious belief helps believers reinterpret the emotional significance of pain, leading to emotional detachment from it. Recent findings on emotion regulation support a role for the right ventrolateral prefrontal cortex (VLPFC), a region also important for driving top-down pain inhibitory circuits. Using functional magnetic resonance imaging in practicing Catholics and avowed atheists and agnostics during painful stimulation, here we show the existence of a context-dependent form of analgesia that was triggered by the presentation of an image with a religious content but not by the presentation of a non-religious image. As confirmed by behavioral data, contemplation of the religious image eneabled the religious group to detach themselves from the experience of pain. Critically, this context-dependent modulation of pain specifically engaged the right VLPFC, whereas group-specific preferential liking of one of the pictures was associated with activation in the ventral midbrain. We suggest that religious belief might provide a framework that allows individuals to engage known pain-regulatory brain processes.

In a recent paper Tom Stoneham (2007) offered a reductio of coherentism. In this paper I defend Stoneham from a criticism made by Darrell Rowbottom (2007) and I offer two proofs. The first is of an early step in Stoneham’s argument, a step which is not (in my opinion) adequately argued by Stoneham; the second is that holistic coherentism is logically equivalent to the symmetry and quasi-transitivity1 of epistemic support and a condition on justified beliefs. I rebut Rowbottom partly because my proof uses the premiss he is criticising. I offer the proofs because I think the results are a matter of independent interest. For example, Thagard (2000) takes symmetry as an axiom, but perhaps he need not, or perhaps it, together with his view of explanation, commits him to holism. My proofs are independent of the criticisms of Stoneham made by Christoph Jager (2007) and Paul Noordhof (2007). Stoneham’s first premiss is his characterization of coherentism

Many of the philosophical doctrines purveyed by postmodernists have been roundly refuted, yet people continue to be taken in by the dishonest devices used in proselytizing for postmodernism. I exhibit, name, and analyse five favourite rhetorical manoeuvres: Troll's Truisms, Motte and Bailey Doctrines, Equivocating Fulcra, the Postmodernist Fox Trot, and Rankly Relativising Fields. Anyone familiar with postmodernist writing will recognise their pervasive hold on the dialectic of postmodernism and come to judge that dialectic as it ought to be judged.

Freedom of speech is a fundamental liberty that imposes a stringent duty of tolerance. Tolerance is limited by direct incitements to violence. False notions and bad laws on speech have obscured our view of this freedom. Hence, perhaps, the self-righteous intolerance, incitements and threats in response to Giubilini and Minerva. Those who disagree have the right to argue back but their attempts to shut us up are morally wrong.

In this chapter I show how challenges to our ability to tame the uncertainty of a pandemic leaves us vulnerable to uncertainty phobia. This is because, contrary to what we might hope, not all the uncertainty that matters can be tamed by our knowledge of the relevant probabilities. Unrelievable wild uncertainty is a hard burden to bear, especially so when we must act in the face of it. We are tempted to retreat into uncertainty phobia, leading to fixed definite opinions precisely when acting on sound judgement requires our opinions to be hedged and mobile. Coping with a pandemic requires us to bear the burden rather than give in to temptation: it requires us to practise the virtue of epistemic forbearance.

It is of the nature of the two-envelope paradox when fully developed that not only are there several plausible ways of evaluating swapping, but that there are intricate semi-dependencies between those ways. Consequently a certain amount of complexity has to be marshalled in order to be sure of both covering the full extent of the problem and eliminating those parts which are inessential or not paradoxical. Finite two-envelope cases are ones in which there is an upper bound on the amount of money in an envelope. Everybody agrees that the finite cases are solved by the considerations we give in section 1 of our paper. The expectations in infinite two-envelope cases are identical to infinite sums, which mathematicians call 'series'. So, to speak of an expectation, such as E(B-A), in these cases, is to speak of a series. Series are identified by the infinite sequence of their terms; rearranging the terms of a series gives you a different series. The sum of a series is defined to be the limit of the sequence of its partial sums. So when we speak of the behaviour of expectations in the infinite cases we are speaking of the behaviour of series, which is defined in terms of the behaviour of sequences. These are among the fruits of the nineteenth century demand for rigour in that part of mathematics called 'analysis'. In our Appendix (pp. 430 ff.l) we make use of those fruits in analysing the infinite two-envelope cases. We consider 'five different series which may be held to give the average expected gain on swapping' (p. 430). On the basis of showing how they depend on the behaviour of