We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...) of language. (shrink)

A long tradition in theology holds that the divine is in some sense incomprehensible, ineffable, or indescribable. This is mirrored in the set-theoretic literature by those who hold that the universe of sets is incomprehensible, ineffable, or indescribable. In this latter field, set theorists often study reflection principles; axioms that posit indescribability properties of the universe. This paper seeks to examine a theological reflection principle, which can be used to deliver a very rich ontology. I argue that in analogy with (...) set-theoretic reflection principles, we should understand theological reflection via schematic commitment. (shrink)

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...) reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

Pereboom’s Four-Case Argument was once considered to be the most powerful of the manipulation arguments against compatibilism. However, because of Demetriou’s :595–617, 2010) response, Pereboom has significantly weakened his argument. Manipulation arguments in general have also been challenged by King : 65–83, 2013). In this paper, I argue that the Four-Case Argument resists both these challenges. One upshot is that Pereboom doesn’t need weaken his argument. Another is that compatibilists still need a response the Four-Case Argument. And another is that (...) we get a much better understanding of the Four-Case Argument, and of manipulation arguments more generally, than is currently available in the literature. (shrink)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a fictional (...) protagonist, Cautious Peacocke, whose coherence I claim shows that Peacocke s proposal cannot be made good. I conclude with the conjecture that similar failure will attend any such semantic-based attempts to ground the epistemology of metaphysical necessity. -/- Dans son livre intitulé Being Known, C. Peacocke se propose de repondre à la question de savoir comment nous en venons a connaitre des nécessités métaphysiques. Il développe une conception sémantique reposant sur des principes comprenant, d’une part, ses Principes de Possibilité — qui fournissent les conditions nécessaires et suffisantes pour un nouveau concept, « l’admissibilité » — et d’autre part des caractérisations de la possibilité et de la nécessité a l’aide de ce nouveau concept. Je me concentre sur une caractéristique structurelle, a savoir l’application récursive a l’œuvre dans la spécification de «l’admissibilité ». Apres avoir esquisse la proposition de Peacocke, j’introduis un personnage fictif, Peacocke-prudent. Je soutiens que la cohérence de ce personnage montre que la proposition de Peacocke ne peut pas être satisfaite. Je conclus en conjecturant qu’un échec similaire se présentera pour toutes les tentatives de fonder l’épistemologie de la nécessité métaphysique sur de telles bases semantiques. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...) I argue, however, that large cardinals are still important axioms of set theory and can play many of their usual foundational roles. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

Permissivism about rationality is the view that there is sometimes more than one rational response to a given body of evidence. In this paper I discuss the relationship between permissivism, deference to rationality, and peer disagreement. I begin by arguing that—contrary to popular opinion—permissivism supports at least a moderate version of conciliationism. I then formulate a worry for permissivism. I show that, given a plausible principle of rational deference, permissive rationality seems to become unstable and to collapse into unique rationality. (...) I conclude with a formulation of a way out of this problem on behalf of the permissivist. (shrink)

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

Crucially, blame can be addressed to its targets, as an implicit demand for recognition. But when we ask whether offenders would actually appreciate this demand, via a sound deliberative route from their existing motivations, we face a puzzle. If they would, their offense reflects a deliberative mistake, and blame’s hostility seems unnecessary. If they wouldn’t, addressing them is futile, and blame’s emotional engagement seems unwarranted. To resolve this puzzle, I develop an account of blame as a proleptic response to indeterminacy (...) in its target’s reasons, yielding attractive accounts of blame’s relation both to internal reasons claims and to free will. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

The right temporo-parietal junction (rTPJ) has been associated with two apparently disparate functional roles: in attention and in social cognition. According to one account, the rTPJ initiates a “circuit-breaking” signal that interrupts ongoing attentional processes, effectively reorienting attention. It is argued this primary function of the rTPJ has been extended beyond attention, through a process of evolutionarily cooption, to play a role in social cognition. We propose an alternative account, according to which the capacity for social cognition depends on a (...) network which is both distinct from and in tension with brain areas involved in focused attention and target detection: the default mode network. Theory characterizing the rTPJ based on the area’s purported role in reorienting may be falsely guided by the co-occurrence of two distinct effects in contiguous regions: activation of the supramarginal gyrus (SMG), associated with its functional role in target detection; and the transient release, during spatial reorienting, of suppression of the angular gyrus (AG) associated with focused attention. Findings based on meta-analysis and resting functional connectivity are presented which support this alternative account. We find distinct regions, possessing anti-correlated patterns of resting connectivity, associated with social reasoning (AG) and target detection (SMG) at the rTPJ. The locus for reorienting was spatially intermediate between the AG and SMG and showed a pattern of connectivity with similarities to social reasoning and target detection seeds. These findings highlight a general methodological concern for brain imaging. Given evidence that certain tasks not only activate some areas but also suppress activity in other areas, it is suggested that researchers need to distinguish two distinct putative mechanisms, either of which may produce an increase in activity in a brain area: functional engagement in the task versus release of suppression. (shrink)

Collected essays consider points of affinity and friction between Walter Benjamin and Martin Heidegger. Despite being contemporaries, Walter Benjamin and Martin Heidegger never directly engaged with one another. Yet, Hannah Arendt, who knew both men, pointed out common ground between the two. Both were concerned with the destruction of metaphysics, the development of a new way of reading and understanding literature and art, and the formulation of radical theories about time and history. On the other hand, their life (...) trajectories and political commitments were radically different. In a 1930 letter, Benjamin told a friend that he had been reading Heidegger and that if the two were to engage with one another, “sparks will fly.” Acknowledging both their affinities and points of conflict, this volume stages that confrontation, focusing in particular on temporality, Romanticism, and politics in their work. (shrink)

In this article, we address a major outstanding question of probabilistic Bayesian epistemology: how should a rational Bayesian agent update their beliefs upon learning an indicative conditional? A number of authors have recently contended that this question is fundamentally underdetermined by Bayesian norms, and hence that there is no single update procedure that rational agents are obliged to follow upon learning an indicative conditional. Here we resist this trend and argue that a core set of widely accepted Bayesian norms is (...) sufficient to identify a normatively privileged updating procedure for this kind of learning. Along the way, we justify a privileged formalization of the notion of ‘epistemic conservativity’, offer a new analysis of the Judy Benjamin problem, and emphasize the distinction between interpreting the content of new evidence and updating one’s beliefs on the basis of that content. (shrink)

Kyle Fritz and Daniel Miller’s reply to my article helpfully clarifies their position and our main points of disagreement. Their view is that those who blame hypocritically lack the right to blame for a violation of some moral norm N in virtue of having an unfair disposition to blame others, but not themselves, for violations of N. This view raises two key questions. First, are there instances of hypocritical blame that do not involve an unfair differential blaming disposition? Second, if (...) the answer to the first question is Yes, do hypocritical blamers of this kind lack the right to blame? In this paper, I argue that the answer to the first question is Yes. Given this, Fritz and Miller’s account faces serious problems regardless of whether the answer to the second question is Yes or No. (shrink)

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

In contemporary free will theory, a significant number of philosophers are once again taking seriously the possibility that human beings do not have free will, and are therefore not morally responsible for their actions. (Free will is understood here as whatever satisfies the control condition of moral responsibility.) Free will theorists commonly assume that giving up the belief that human beings are morally responsible implies giving up all our beliefs about desert. But the consequences of giving up the belief that (...) we are morally responsible are not quite this dramatic. Giving up the belief that we are morally responsible undermines many, and perhaps most, of the desert claims we are pretheoretically inclined to accept. But it does not undermine desert claims based on the sheer fact of personhood. Even in the absence of belief in moral responsibility, personhood-based desert claims require us to respect persons and their rights. So personhood-based desert claims can provide a substantial role for desert in free will skeptics' ethical theories. (shrink)

If you ought to perform a certain act, and some other action is a necessary means for you to perform that act, then you ought to perform that other action as well – or so it seems plausible to say. This transmission principle is of both practical and theoretical significance. The aim of this paper is to defend this principle against a number of recent objections, which (as I show) are all based on core assumptions of the view called actualism. (...) I reject actualism, provide an alternative explanation of its plausible features, and present an independent argument for the transmission principle. (shrink)

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...) & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field. (shrink)

I here settle a recent dispute between two rival theories in distributive ethics: Restricted Prioritarianism and the Competing Claims View. Both views mandate that the distribution of benefits and burdens between individuals should be justifiable to each affected party in a way that depends on the strength of each individual’s separately assessed claim to receive a benefit. However, they disagree about what elements constitute the strength of those individuals’ claims. According to restricted prioritarianism, the strength of a claim is determined (...) in ‘prioritarian’ fashion by both what she stands to gain and her absolute level of well-being, while, according to the competing claims view, the strength of a claim is also partly determined by her level of well-being relative to others with conflicting interests. I argue that, suitably modified, the competing claims view is more plausible than restricted prioritarianism. (shrink)

According to Milner and Goodale’s dual visual systems (DVS) theory, a division obtains between visual consciousness and motor action, in that the visual system producing conscious vision (the ventral stream) is distinct from the one guiding action (the dorsal stream). That there would be this division is often taken (by Andy Clark and others) to undermine the folk view on how consciousness and action relate. However, even if this division obtains, this leaves open the possibility that con- scious ventral information (...) is often transmitted to the uncon- scious dorsal stream and then used to guide action, a possibility seeming to preserve a significant role for consciousness in action. This article assesses this possibility. In course of doing so, we will review those arguments recently having been made against the DVS view on how visual consciousness and action relate (ones due to, e.g., Briscoe and Schwenkler, or Schenk and McIntosh). What we will find is that, if we properly analyze the data upon which these arguments are based, we are still left with the impression that the DVS view is largely correct; i.e., it is only rarely that visual experience guides action. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

This entry is composed of three sections. In §1, we survey debates about what structural rationality is, including the emergence of the concept in the contemporary literature, its key characteristics, its relationship to substantive rationality, its paradigm instances, and the questions of whether these instances are unified and, if so, how. In §2, we turn to the debate about structural requirements of rationality – including controversies about whether they are “wide-scope” or “narrow-scope”, synchronic or diachronic, and whether they govern processes (...) or states; as well as examining various forms of skepticism about structural requirements of rationality. In §3, we turn to the debate about the normative significance of structural rationality, surveying central challenges for the view that structural rationality is normatively significant and the theoretical options that arise in light of these challenges. (shrink)

Kant famously insists that free will is a condition of morality. The difficulty of providing a demonstration of freedom has left him vulnerable to devastating criticism: critics charge that Kant's post-Groundwork justification of morality amounts to a dogmatic assertion of morality's authority. My paper rebuts this objection, showing that Kant offers a cogent demonstration of freedom. My central claim is that the demonstration must be understood in practical rather than theoretical terms. A practical demonstration of x works by bringing x (...) into existence, and what the demonstration of freedom brings into existence is a moral will, a will regulated by the moral law and capable of acting in accordance with it. Since to act morally is to act freely, bringing a moral will into existence actualizes our capacity for freedom and demonstrates that we possess it. To confirm the viability of such a demonstration, Kant must establish that agents can regulate their wills by practical principles, and that practical judgments are efficacious of themselves (i.e., that non-Humean motivational internalism is true). Kant, I argue, is successful on both counts. (shrink)

I defend a deontological social contract justification of punishment for free will deniers. Even if nobody has free will, a criminal justice system is fair to the people it targets if we would consent to it in a version of original position deliberation (OPD) where we assumed that we would be targeted by the justice system when the veil is raised. Even if we assumed we would be convicted of a crime, we would consent to the imprisonment of violent criminals (...) if prison conditions were better than the state of nature but deterring enough to prevent the state of nature. And even if we assumed we would be accused of a crime, we would consent to an evidentiary standard low enough to allow a conviction rate sufficient to prevent the state of nature. After explaining this justification, I contrast it with the public health quarantine justification defended by Derk Pereboom and Gregg Caruso, and argue that it provides a stronger response to the using criminals as mere means objection. (shrink)

In the De Anima, Aristotle claims that the five senses are infallible about their proper objects. I contend that this claim means that sight is infallible about its proper object in its most specific form, i. e. sight is infallible about red or green and not merely about color in general. This robust claim is justified by Aristotle’s teleological principle that nature does nothing in vain. Additionally, drawing on Aristotle’s comparison of perception and one’s understanding of the essences, I defend (...) a conception of the senses in which the structure of their contents is simple rather than predicative and show how this coheres better with the rest of my interpretation. (shrink)

This article is concerned with a puzzle that arises from three initially plausible assumptions that form an inconsistent triad: (1) Epistemic reasons are normative reasons (normativism); (2) reasons are normative only if conformity with them is good (the reasons/value-link); (3) conformity with epistemic reasons need not be good (the nihilist assumption). I start by defending the reasons/value-link, arguing that normativists need to reject the nihilist assumption. I then argue that the most familiar view that denies the nihilist assumption – epistemic (...) teleology – is untenable. Finally, I consider two alternative ways of accounting for the goodness of conformity with epistemic reasons: it may be good because it accords with the virtue of reasons-responsiveness, and it may be good because it is good to conform with normative reasons as such. I argue that both of these conceptions avoid the problems of epistemic teleology and merit serious consideration as potential solutions to the puzzle. (shrink)

Partiality is the special concern that we display for ourselves and other people with whom we stand in some special personal relationship. It is a central theme in moral philosophy, both ancient and modern. Questions about the justification of partiality arise in the context of enquiry into several moral topics, including the good life and the role in it of our personal commitments; the demands of impartial morality, equality, and other moral ideals; and commonsense ideas about supererogation. This paper provides (...) an overview of the debate on the ethics of partiality through the lens of the domains of permissible and required partiality. After outlining the conceptual space, I first discuss agent-centred moral options that concern permissions not to do what would be impartially optimal. I then focus on required partiality, which concerns associative duties that go beyond our general duties to others and require us to give special priority to people who are close to us. I discuss some notable features of associative duties and the two main objections that have been raised against them: the Voluntarist and the Distributive objections. I then turn to the justification of partiality, focusing on underivative approaches and reasons-based frameworks. I discuss the reductionism and non-reductionism debate: the question whether partiality is derivative or fundamental. I survey arguments for ‘the big three’, according to which partiality is justified by appeal to the special value of either projects, personal relationships, or individuals. I conclude by discussing four newly emerging areas in the debate: normative transitions of various personal relationships, relationships with AI, epistemic partiality, and negative partiality, which concerns the negative analogue of our positive personal relationships. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinisim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

According to a widely held view, epistemic reasons are normative reasons for belief – much like prudential or moral reasons are normative reasons for action. In recent years, however, an increasing number of authors have questioned the assumption that epistemic reasons are normative. In this article, I discuss an important challenge for anti-normativism about epistemic reasons and present a number of arguments in support of normativism. The challenge for anti-normativism is to say what kind of reasons epistemic reasons are if (...) they are not normative reasons. I discuss various answers to this challenge and find them all wanting. The arguments for normativism each stress a certain analogy between epistemic reasons and normative reasons for action. Just like normative reasons for action, epistemic reasons provide partial justification; they provide premises for correct reasoning; they constitute good bases for the responses they are reasons for; and they are reasons for which agents can show these responses without committing a mistake. In each case, I argue that the relevant condition is plausibly sufficient for the normativity of a reason, and that normativism is in any case in a much better position to explain the analogy than anti-normativism. (shrink)

According to an attractive and widely held view, all practical reasons are explained in terms of the (instrumental or final) value of the action supported by the reason. I argue that this theory is incompatible with plausible assumptions about the practical reasons that correspond to certain moral rights, including the right to a promised action and the right to an exclusive use of one’s property. The argument is an explanatory rather than extensional one: while the actions supported by the relevant (...) reasons (e.g. keeping a valid promise or respecting property) can be argued to have a certain kind of value, I argue that this value presupposes a moral right, and therefore cannot explain the reason. Reflection on such cases suggest the conclusion that reasons that are subject to normative powers are generally not value-based. This also has important implications for the dialectic between ‘value-first’ and ‘reasons-first’ approaches to normativity. (shrink)

Wright's _Truth and Objectivity_ seeks to systematise a variety of anti-realist positions. I argue that many objections to the system are avoided by transposing its talk of truth into talk of warrant. However, a problem remains about debates involving 'direction-of-fit'. -/- Dummett introduced 'anti-realism' as a philosophical view informed by mathematical intuitionism. Subsequently, the term has been associated with many debates, ancient and modern. _Truth and Objectivity_ proposes that truth admits of different characteristics; these various debates then concern which characteristics (...) truth has, in a given area. This pluralism of truth is at odds with deflationism. I find fault with Wright's argument against deflationism. However, transmission of warrant across the Disquotational Schema suffices to ground Wright's proposal, which survives as a pluralism of classes of warrant. -/- The two main debates concern whether truths are always knowable (Epistemic Constraint) and whether disagreements in an area must be down to some fault of one of those involved (Cognitive Command). I introduce Assertoric Constraint, relating to Epistemic Constraint, where truths cannot outstrip the availability of warrant for their assertion. I solve a structural problem by a comparison with a constitutive analysis of Moore's Paradox. The relativism of blameless disagreement is problematic. Wright's response invokes a sort of ignorance which he calls `Quandary'. I criticise this before proposing an alternative. -/- I agree with Wright that Dummett's original anti-realism does not belong among the positions which Wright seeks to systematise. However, two candidates show that the proposal suffers a weakness. Wright thinks Expressivism misguided, and implicitly rules out his earlier non-cognitivism about necessity. I argue that Expressivism has promise, and I endorse Wright's Cautious Man argument for non-cognitivism about necessity; both involve play with `direction-of-fit'. I conclude that this sort of anti-realist debate needs to be accommodated by the proposal. (shrink)

Hypocrisy is widely thought to be morally objectionable in a way that undermines the hypocrite’s moral standing to blame others. To wit, we seem to intuitively accept the “Nonhypocrisy Condition:” R has the standing to blame S for some violation of a moral norm N only if R’s blaming S is not hypocritical. This claim has been the subject of intensifying philosophical investigation in recent years. However, we can only understand why hypocrisy is morally objectionable and has an effect on (...) standing to blame if we can correctly characterize hypocrisy itself. Unfortunately, some recent discussions fail to do this, which fatally undermines subsequent arguments concerning the effect of hypocrisy on the standing to blame. This paper’s central aim is to develop and defend a better account of hypocrisy. The hope is that with such an account in hand, we can explain and perhaps justify our moral aversion to hypocrisy in general as well as the Nonhypocrisy Condition in particular. (shrink)

In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truth-functional connectives.

The principle of indifference states that in the absence of any relevant evidence, a rational agent will distribute their credence equally among all the possible outcomes under consideration. Despite its intuitive plausibility, PI famously falls prey to paradox, and so is widely rejected as a principle of ideal rationality. In this article, I present a novel rehabilitation of PI in terms of the epistemology of comparative confidence judgments. In particular, I consider two natural comparative reformulations of PI and argue that (...) while one of them prescribes the adoption of patently irrational epistemic states, the other provides a consistent formulation of PI that overcomes the most salient limitations of existing formulations. (shrink)

When viewing a circular coin rotated in depth, it fills an elliptical region of the distal scene. For some, this appears to generate a two-fold experience, in which one sees the coin as simultaneously circular (in light of its 3D shape) and elliptical (in light of its 2D ‘perspectival shape’ or ‘p-shape’). An energetic philosophical debate asks whether the latter p-shapes are genuinely presented in perceptual experience (as ‘perspectivalists’ argue) or if, instead, this appearance is somehow derived or inferred from (...) experience (as ‘anti-perspectivalists’ argue). This debate, however, has largely turned on introspection. In a recent study, Morales, Bax, and Firestone (2020) aim to provide the first empirical test of this question. They asked subjects to find an elliptical coin seen face-on from a search array that also included a circular coin seen either face-on or at an angle. They found that subjects reacted more slowly when the distracting circle was seen at an angle, such that it’s p-shape matched that of the target ellipse. From this, they concluded that the similar p-shape between the ellipse and circle constituted a phenomenal similarity between the two, and thus that perspectivalism is true. We show that these results can also be explained by pre-attentive guidance by unconscious representations (in what follows, just “unconscious pre-attentive guidance”) and that this explanation is at least as plausible as one from phenomenal similarity. Thus, we conclude that the experiment does not support perspectivalism over anti-perspectivalism. (shrink)