In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...) is in good epistemic standing. (shrink)

Euclid’s Elements inspired a number of foundationalist accounts of mathematics, which dominated the epistemology of the discipline for many centuries in the West. Yet surprisingly little has been written by recent philosophers about this conception of mathematical knowledge. The great exception is Imre Lakatos, whose characterisation of the Euclidean Programme in the philosophy of mathematics counts as one of his central contributions. In this essay, we examine Lakatos’s account of the Euclidean Programme with a critical eye, and suggest an alternative (...) picture which builds on his work, but differs in a number of important respects. (shrink)

The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...) even more dramatically, was objects. Curiously, although Benacerraf’s article appeared in the heyday of Quine’s influence, it declined to engage the Quinean position squarely, even seemed to think it was not its business to do so. Despite that, in my experience, most philosophers believe that Benacerraf’s article put paid to the reductionist view that numbers are sets (though perhaps not the view that numbers are objects). My chapter will attempt to overturn this orthodoxy. (shrink)

A focussed issue of The Reasoner on the topic of 'Infinitary Reasoning'. Owen Griffiths and A.C. Paseau were the guest editors.

A brief article introducing *One True Logic*. The book argues that there is one correct foundational logic and that it is highly infinitary.

This short article discusses the fact that the word ‘ancestor’ features in certain arguments that a) are apparently logically valid, b) contain infinitely many premises, and c) are such that none of their finite sub-arguments are logically valid. The article's aim is to motivate, within its brief compass, the study of infinitary logics.

An essay review of Gila Sher's *Logical Consequence*.

The aim of this article is to give students a small sense of what metamathematics is—that is, how one might use mathematics to study mathematics itself. School or college teachers could base a classroom exercise on the letter games I shall describe and use them as a springboard for further exploration. Since I shall presuppose no knowledge of formal logic, the games are less an introduction to Gödel's theorems than an introduction to an introduction to them. Nevertheless, they show, in (...) an accessible way, how metamathematics can be mathematically interesting. (shrink)

Does natural science give us reason to believe that mathematical statements are true? And does natural science give us reason to believe in some particular metaphysics of mathematics? These two questions should be firmly distinguished. My argument in this chapter is that a negative answer to the second question is compatible with an affirmative answer to the first. Loosely put, even if science settles the truth of mathematics, it does not settle its metaphysics.

If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? The paper advances grounds for doubt. [A longer and more detailed sequel to this paper, 'Proving Induction', was published in the Australasian Journal of Logic in 2011.].

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism (...) are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem. (shrink)

The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in ZFC, states that a predictive function M exists with the following property: whatever world we live in, M ncorrectly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On the (...) usual model of time a well-ordered subset is small relative to the set of all times. M’s existence therefore seems to provide a solution to the hard problem. My paper argues for two conclusions. First, the theorem does not solve the hard problem of induction. More positively though, it solves a version of the problem in which the structure of time is given modulo our choice of set theory. (shrink)

From title to back cover, a polemic runs through David Corfield's "Towards a Philosophy of Real Mathematics". Corfield repeatedly complains that philosophers of mathematics have ignored the interesting and important mathematical developments of the past seventy years, ‘filtering’ the details of mathematical practice out of philosophical discussion. His aim is to remedy the discipline’s long-sightedness and, by precept and example, to redirect philosophical attention towards current developments in mathematics. This review discusses some strands of Corfield’s philosophy of real mathematics and (...) briefly assesses some of his objections to orthodox philosophy of mathematics. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and the (...) epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (shrink)

The subtraction argument, originally put forward by Thomas Baldwin (1996), is intended to establish Metaphysical Nihilism, the thesis that there could have been no concrete objects. Some modified versions of the argument have been proposed in order to avoid some difficulties faced by the original argument. In this paper I shall concentrate on two of those versions, the so-called subtraction argument* (presented and defended in Rodriguez-Pereyra 1997, 2000, 2002), and Efird and Stoneham’s recent version of the argument (Efird and Stoneham (...) 2005). I shall defend the subtraction argument* from Alexander Paseau’s (2006) objection that because a crucial premise of the subtraction argument* may have no plausibility independent from Metaphysical Nihilism, the subtraction argument* is not suasive. Although Paseau focuses on the subtraction argument*, I shall point out that Efird and Stoneham could reply to Paseau’s objection in the same way. Thus there are (at least) two suasive versions of the subtraction argument that establish Metaphysical Nihilism. But are those two arguments equally good? I shall argue that the subtraction argument* is preferable to Efird and Stoneham’s argument. (shrink)

Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics and modality, (...) Blackwell, Oxford, 1989) each suggest that a consequence of the empirical methodology of indispensability arguments is that the resulting mathematical objects can only be said to exist (or not exist) contingently. Kristie Miller has argued that this line of thought doesn’t work (Miller in Erkenntnis, 77 (3), 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is. (shrink)

The dispute between realists about color and anti-realists is actually a dispute about the nature of color properties. The disputants do not disagree over what material objects are like. Rather, they disagree over whether any of the uncontroversial facts about material objects--their powers to cause visual experiences, their dispositions to reflect incident light, their atomic makeup, and so on--amount to their having colors. The disagreement is thus about which properties colors are and, in particular, whether colors are any of the (...) properties in a particular set that is acknowledged on both sides to exhaust the properties of material objects. In a previous paper we discussed at length one attempt to identify colors with particular properties of material objects--namely, with their dispositions to cause visual experiences. Here we shall discuss a different and perhaps more influential version of realism, which says that the colors of material objects are microphysical properties of their surfaces. We shall call this theory physicalism about color (physicalism, for short). In order to evaluate this theory, however, we shall first have to clarify some methodological issues. Our hope is that we can bring some further clarity to the question of color realism, whether or not we succeed in our critique of the physicalists' answer. (shrink)

This paper examines the standard view of realization operative incontemporary philosophy of mind, and proposes an alternative, generalperspective on realization. The standard view can be expressed, insummary form, as the conjunction of two theses, the sufficiency thesis andthe constitutivity thesis. Physicalists of both reductionist and anti-reductionist persuasions share a conception of realization wherebyrealizations are determinative of the properties they realize and physically constitutive of the individuals with those properties. Centralto the alternative view that I explore here is the idea that (...) the requisite,metaphysically robust notion of realization is ineliminably context-sensitive. I shall argue that the sufficiency and constitutivity theses aretypically not jointly satisfied by any one candidate realizer, and that goingcontext-sensitive in one's metaphysics is preferable to the standard view.The context-sensitive views developed here are implicit in a range ofcommon views in both the philosophy of mind and the philosophy of biology,even if they have not been explicitly articulated, and even though theyundermine other views that are commonly endorsed. (shrink)

We introduce two notions–the shadows and the shallows of explanation–in opening up explanation to broader, interdisciplinary investigation. The shadows of explanation refer to past philosophical efforts to provide either a conceptual analysis of explanation or in some other way to pinpoint the essence of explanation. The shallows of explanation refer to the phenomenon of having surprisingly limited everyday, individual cognitive abilities when it comes to explanation. Explanations are ubiquitous, but they typically are not accompanied by the depth that we might, (...) prima facie, expect. We explain the existence of the shadows and shallows of explanation in terms of there being a theoretical abyss between explanation and richer, theoretical structures that are often attributed to people. We offer an account of the shallows, in particular, both in terms of shorn-down, internal, mental machinery, and in terms of an enriched, public symbolic environment, relative to the currently dominant ways of thinking about cognition and the world. (shrink)

David Sloan Wilson has recently revived the idea of a group mind as an application of group selectionist thinking to cognition. Central to my discussion of this idea is the distinction between the claim that groups have a psychology and what I call the social manifestation thesis-a thesis about the psychology of individuals. Contemporary work on this topic has confused these two theses. My discussion also points to research questions and issues that Wilson's work raises, as well as their connection (...) to externalist conceptions of the mind familiar since the work of Putnam and Burge. (shrink)

When brief blank fields are placed between alternating displays of an original and a modified scene, a striking failure of perception is induced: the changes become extremely difficult to notice, even when they are large, presented repeatedly, and the observer expects them to occur (Rensink, O'Regan, & Clark, 1997). To determine the mechanisms behind this induced "change blindness", four experiments examine its dependence on initial preview and on the nature of the interruptions used. Results support the proposal that representations at (...) the early stages of visual processing are highly volatile, and that focused attention is needed to stabilize them sufficiently to support the perception of change. (shrink)

(1) Content properties are nonrelational, that is, having a content property does not entail the existence of any contingent object not identical with the thinker or a part of the thinker.2 (2) We have noninferential knowledge of our conscious thoughts, that is, for any of our..

How are we able to perceive the world veridically? If we ask this question as a part of the scientific investigation of perception, then we are not asking for a transcendental guarantee that our perceptions are by and large veridical; we presuppose that they are. Unless we assumed that we perceived the world for the most part veridically, we would not be in a position to investigate our perceptual abilities empirically. We are interested, then, not in how it is possible (...) in general for us to perceive the world veridically, but instead in what the relation is between our environment and its properties, of which we have knowledge, on the one hand, and our perceptual mechanisms, on the other, that results in very many, even most of our perceptions being veridical in everyday life. (shrink)

Several studies (e.g., Becklen & Cervone, 1983; Mack & Rock, 1998; Neisser & Becklen, 1975) have found that observers attending to a particular object or event often fail to report the presence of unexpected items. This has been interpreted as inattentional blindness (IB), a failure to see unattended items (Mack & Rock, 1998). Meanwhile, other studies (e.g., Pashler, 1988; Phillips, 1974; Rensink et al., 1997; Simons, 1996) have found that observers often fail to report the presence of large changes in (...) a display when these changes occur simultaneously with a transient such as an eye movement or flash of the display. This has been interpreted as change blindness (CB), a failure to see unattended changes (Rensink et al., 1997). In both cases there is a striking failure to report an object or event that would be quite visible under other circumstances. And in both cases there is a widespread (although not universal) belief that the underlying cause has to do with the absence of attention. The question then arises as to how these effects might be related. Is CB the same thing as IB? If not, what is the relation between them? And given that these phenomena deal with failures of subjective perception, what can they teach us about the nature of our visual experience? In particular, what can they teach us about the role played by visual attention? (shrink)

Review of Fodor: Concepts: Where Cognitive Science Went Wrong -/- The cover of Fodor’s book proudly claims that this is his most irritating book in years, guaranteed to exasperate all those who read it. The book lives up to this promise. Although leavened by moments of wit and humour, Fodor misses no opportunity for the one-liner put-down, be it about lexical semantics, empiricism, cognitive neuropsychology or the psychology of cognitive development. He even writes a whole chapter on Prototypes without referring (...) to Rosch except in a footnote, where her name is consistently mis-spelled for good measure. Those looking to see how his ideas relate to current work in psychology and linguistics on lexical concepts will be disappointed. (shrink)

Individualists claim that wide explanations in psychology are problematic. I argue that wide psychological explanations sometimes have greater explanatory power than individualistic explanations. The aspects of explanatory power I focus on are causal depth and theoretical appropriateness. Reflection on the depth and appropriateness of other wide explanations of behavior, such as evolutionary explanations, clarifies why wide psychological explanations sometimes have more causal depth and theoretical appropriateness than narrow psychological explanations. I also argue for the rejection of eliminative materialism.

The paper rejects the claim that phenomena such as change and inattentional blindness show that perceptual representations are inaccurate or that a radical overhaul of our traditional picture of perception is required. The paper rejects in particular the sensorimotor theory of perception, which denies that there are any perceptual representations. It further argues that the degree of resolution of perceptual experience relevant to assessing its accuracy is determined by our use of it in standard conditions, and that the integration of (...) behavior with perceptual representation shows that it is by and large as accurate as its degree of resolution requires. (shrink)

At the beginning of the first book of Posterior Analytics, Aristotle‟s feature of demonstrative knowledge involves a certain concept of “necessity”. The traditional interpretation tends to associate this concept with modal necessity, which is found in the Prior Analytics and De interpretatione. The present article aims to show in which way the sixth chapter of book A of Posterior Analytics presupposes a set of essentialist theses that claims to base the necessity of scientific knowledge on predicative relations of essential character. (...) To acknowledge this essentialist background and simultaneously support a modal interpretation of scientific necessity urges us to attribute serious drawbacks to Aristotle‟s theory of demonstration, forcing us to reassess this interpretative tendency. (shrink)

This paper points to some problems for the position that D.M. Walsh calls "alternative individualism," and argues that in defending this view Walsh has omitted an important part of what separates individualists and externalists in psychology. Walsh's example of Hox gene complexes is discussed in detail to show why some sort of externalism about scientific taxonomy more generally is a more plausible view than any extant version of individualism.

This paper surveys some recent work on realization in the philosophy of mind and the philosophy of science.

Surprisingly little has been written about hedged assertion. Linguists often focus on semantic or syntactic theorizing about, for example, grammatical evidentials or epistemic modals, but pay far less attention to what hedging does at the level of action. By contrast, philosophers have focused extensively on normative issues regarding what epistemic position is required for proper assertion, yet they have almost exclusively considered unqualified declaratives. This essay considers the linguistic and normative issues side-by-side. We aim to bring some order and clarity (...) to thinking about hedging, so as to illuminate aspects of interest to both linguists and philosophers. In particular, we consider three broad questions. 1) The structural question: when one hedges, what is the speaker’s commitment weakened from? 2) The functional question: what is the best way to understand how a hedge weakens? And 3) the taxonomic question: are hedged assertions genuine assertions, another speech act, or what? (shrink)

Friedrich Engels’ dialectical assessment of modern science resulted from his fascination with the natural sciences in combination with his resurging interest in the work of “old Hegel.” Engels became especially interested in what he saw as the molecular essence of life, namely proteins or, more specifically, albumin, seeing life as the mode of existence of these enigmatic substances. Hegelian dialectics is crucial for a dialectical materialist understanding of contemporary technoscience. The dialectical materialist understanding of technoscience as a research practice builds (...) on Engels, but also on later authors who were inspired by his writings, e.g., life scientists such as Haldane and Bernal. Considering the criticism raised against Engels’ dialectics by 20th-century Marxists, a dialectical diagnostic of contemporary technoscience can be achieved, which shifts the focus from artificial albumin as “living matter” to contemporary research on synthetic cells. (shrink)

This paper subjects Dan Brown’s most recent novel Origin to a philosophical reading. Origin is regarded as a literary window into contemporary technoscience, inviting us to explore its transformative momentum and disruptive impact, focusing on the cultural significance of artificial intelligence and computer science: on the way in which established world-views are challenged by the incessant wave of scientific discoveries made possible by super-computation. While initially focusing on the tension between science and religion, the novel’s attention gradually shifts to the (...) increased dependence of human beings on smart technologies and artificial intelligence. Origin’s message, I will argue, reverberates with Oswald Spengler’s The Decline of the West, which aims to outline a morphology of world civilizations. Although the novel starts with a series of oppositions, most notably between religion and science, the eventual tendency is towards convergence, synthesis and sublation, exemplified by Sagrada Família as a monumental symptom of this transition. Three instances of convergence will be highlighted, namely the convergence between science and religion, between humanity and technology and between the natural sciences and the humanities. (shrink)

Recent epistemology has focused almost exclusively on propositional knowledge. This paper considers an underexplored area of epistemology, namely knowledge of persons: if propositional knowledge is a state of mind, consisting in a subject's attitude to a (true) proposition, the account developed here thinks of interpersonal knowledge as a state of minds, involving a subject's attitude to another (existing) subject. This kind of knowledge is distinct from propositional knowledge, but it exhibits a gradability characteristic of context-sensitivity, and admits of shifty thresholds. (...) It is supported by a wide range of unexplored linguistic data and intuitive cases; and it promises to illuminate debates within epistemology, philosophy of religion, and ethics. (shrink)

Some philosophers oppose recent arguments for the Knowledge Norm of Assertion by claiming that assertion, being an act much like any other, will be subject to norms governing acts generally, such as those articulated by Grice for the purpose of successful, cooperative endeavours. But in fact, Grice is a traitor to their cause; or rather, they are his dissenters, not his disciples. Drawing on Grice's unpublished papers, I show that he thought of asserting as a special linguistic act in need (...) of its own norm, and he tied his maxim of Quality to knowledge. I also develop a simple Gricean-inspired argument showing that the Quality maxim is not dependent on the Cooperative Principle. If it is not thus dependent, then the Cooperative Principle cannot be the explanation of, or source of normativity for, the Quality maxim. Thus, leveraging the insights informing the maxim of Quality actually provides the resources for a distinctive positive case that knowledge is the constitutive norm of assertion. (shrink)

In this paper, we argue that, barring a few important exceptions, the phenomenon we refer to using the expression “being moved” is a distinct type of emotion. In this paper’s first section, we motivate this hypothesis by reflecting on our linguistic use of this expression. In section two, pursuing a methodology that is both conceptual and empirical, we try to show that the phenomenon satisfies the five most commonly used criteria in philosophy and psychology for thinking that some affective episode (...) is a distinct emotion. Indeed, being moved, we claim, is the experience of a positive core value (particular object) perceived by the moved subject as standing out (formal object) in the circumstances triggering the emotion. Drawing on numerous examples, we describe the distinctively rich phenomenology characteristic of the experience as well as the far-reaching action-tendencies and functions associated with it. Having thus shown that the candidate emotion seem to satisfy the five criteria, we go on, in section three, to compare it with sadness and joy, arguing that it should not be confused with either. Finally, in section four, we illustrate the explanatory power of our account of “being moved” by showing how it can shed light on, and maybe even justify, the widespread distrust we feel towards the exhibition of ‘sentimentality’. On the whole and if we are right, we have uncovered an emotion which, though never or rarely talked about, is of great interest and no small importance. (shrink)

The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...) conception of evidence and the knowledge-first view of evidence. (shrink)

Advances in neuroscience implicate reentrant signaling as the predominant form of communication between brain areas. This principle was used in a series of masking experiments that defy explanation by feed-forward theories. The masking occurs when a brief display of target plus mask is continued with the mask alone. Two masking processes were found: an early process affected by physical factors such as adapting luminance and a later process affected by attentional factors such as set size. This later process is called (...) masking by object substitution, because it occurs whenever there is a mismatch between the reentrant visual representation and the ongoing lower level activity. Iterative reentrant processing was formalized in a computational model that provides an excellent fit to the data. The model provides a more comprehensive account of all forms of visual masking than do the long-held feed-forward views based on inhibitory contour interactions. (shrink)

This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

Recent epistemology offers an account of what it is to know other persons. Such views hold promise for illuminating several issues in philosophy of religion, and for advancing a distinctive approach to religious epistemology. This paper develops an account of interpersonal knowledge, and clarifies its relation to propositional and qualitative knowledge. I then turn to our knowledge of God and God's knowledge of us, and compare my account of interpersonal knowledge with important work by Eleonore Stump on "Franciscan" knowledge. I (...) examine how interpersonal knowledge may figure in liturgical practice, in diffusing the problem of divine hiddenness, and in motivating a novel understanding of divine love. I also explore the possibility of epistemic injustice arising from dismissal or neglect of our religious testimony to one another, or of divine testimony to humanity, focusing specifically on the import of interpersonal knowledge. (shrink)

Hope is an attitude with a distinctive epistemological dimension: it is incompatible with knowledge. This chapter examines hope as it relates to knowledge but also to probability and inductive considerations. Such epistemic constraints can make hope either impossible, or, when hope remains possible, they affect how one’s epistemic situation can make hope rational rather than irrational. Such issues are especially relevant to when hopefulness may permissibly figure in practical deliberation over a course of action. So I consider cases of second-order (...) inductive reflection on when one should, or should not, be hopeful for an outcome with which one has a long record of experience: in other words, what is the epistemology behind when one should, if ever, stop hoping for outcomes which have failed one many times in the past? (shrink)

Frankfurt cases are supposed to provide us with counterexamples to the principle of alternative possibilities. Among the most well known responses to these cases is what John Fischer has dubbed the flicker of freedom strategy. Here we revisit a version of this strategy, which we refer to as the fine-grained response. Although a number of philosophers, including some who are otherwise unsympathetic to Frankfurt’s argument, have dismissed the fine grained response, we believe there is a good deal to be said (...) on its behalf. We argue, in particular, that reflection on certain cases involving omissions undermines the main objections to the response and also provides the groundwork for an argument in support of it. (shrink)

This chapter covers contemporary work on disagreement, detailing both the conceptual and normative issues in play in the debates in mainstream analytic epistemology, and how these relate to religious diversity and disagreement. §1 examines several sorts of disagreement, and considers several epistemological issues: in particular, what range of attitudes a body of evidence can support, how to understand higher-order evidence, and who counts as an epistemic “peer”. §2 considers how these questions surface when considering disagreements over religion, including debates over (...) the nature of evidence and truth in religion, epistemic humility, concerns about irrelevant influences and about divine hiddenness, and arguments over exclusivism, inclusivism, and pluralism. Finally, §3 summarizes the contributors’ essays in this volume. (shrink)