In the wake of the spectacular success of Miranda Fricker's Epistemic Injustice, philosophers have paid a great deal of attention to testimonial injustice. Testimonial injustice occurs when recipients of testimony discount it in virtue of its source: usually, their social identity. The remedy for epistemic injustice is almost always listening better and giving greater weight to the testimony we hear, on most philosophers' implicit or explicit view. But Fricker identifies another kind of epistemic injustice: hermeneutical injustice. This kind of injustice (...) occurs when someone can't articulate their own experience or understand their situation for lack of the hermeneutical tools. There is a possible tension between these kinds of injustice, we suggest: sincere testimony may be misleading (may fail to identify significant harms the testfier is subject, or may fail to register its magnitude, or to categorize it as the kind of harm it is) in virtue of a lack of hermeneutical resources. This tension raises the possibility that there are situations in which experts - those who possess hermeneutical tools - may be able to correct the testimony of those who experience harms in virtue of their identity. In this paper, we identify possible cases in which epistemic injustice might be reduced through such correction: in which an increase in testimonial injustice might serve to decrease it in the longer run, for example. We also suggest how the obvious dangers of a too great readiness to see testimony as in need of expert correction might be mitigated, and how the expert might suggest corrections without ceasing to listen. (shrink)

The following is a transcript of the interview I (Yasuko Kitano) conducted with Neil Levy (The Centre for Applied Philosophy and Public Ethics, CAPPE) on the 23rd in July 2009, while he was in Tokyo to give a series of lectures on neuroethics at The University of Tokyo Center for Philosophy. I edited his words for publication with his approval.

A number of concerns have been raised about the possible future use of pharmaceuticals designed to enhance cognitive, affective, and motivational processes, particularly where the aim is to produce morally better decisions or behavior. In this article, we draw attention to what is arguably a more worrying possibility: that pharmaceuticals currently in widespread therapeutic use are already having unintended effects on these processes, and thus on moral decision making and morally significant behavior. We review current evidence on the moral effects (...) of three widely used drugs or drug types: propranolol, selective serotonin reuptake inhibitors, and drugs that effect oxytocin physiology. This evidence suggests that the alterations to moral decision making and behavior caused by these agents may have important and difficult-to-evaluate consequences, at least at the population level. We argue that the moral effects of these and other widely used pharmaceuticals warrant further empirical research and ethical analysis. (shrink)

Recent work in neuroimaging suggests that some patients diagnosed as being in the persistent vegetative state are actually conscious. In this paper, we critically examine this new evidence. We argue that though it remains open to alternative interpretations, it strongly suggests the presence of consciousness in some patients. However, we argue that its ethical significance is less than many people seem to think. There are several different kinds of consciousness, and though all kinds of consciousness have some ethical significance, different (...) kinds underwrite different kinds of moral value. Demonstrating that patients have phenomenal consciousness — conscious states with some kind of qualitative feel to them — shows that they are moral patients, whose welfare must be taken into consideration. But only if they are subjects of a sophisticated kind of access consciousness — where access consciousness entails global availability of information to cognitive systems — are they persons, in the technical sense of the word employed by philosophers. In this sense, being a person is having the full moral status of ordinary human beings. We call for further research which might settle whether patients who manifest signs of consciousness possess the sophisticated kind of access consciousness required for personhood. (shrink)

Actions performed in a state of automatism are not subject to moral evaluation, while automatic actions often are. Is the asymmetry between automatistic and automatic agency justified? In order to answer this question we need a model or moral accountability that does justice to our intuitions about a range of modes of agency, both pathological and non-pathological. Our aim in this paper is to lay the foundations for such an account.

It is well known that the nature of consciousness is elusive, and that attempts to understand it generate problems in metaphysics, philosophy of mind, psychology, and neuroscience. Less appreciated are the important – even if still elusive – connections between consciousness and issues in ethics. In this chapter we consider three such connections. First, we consider the relevance of consciousness for questions surrounding an entity’s moral status. Second, we consider the relevance of consciousness for questions surrounding moral responsibility for action. (...) Third, we consider the relevance of consciousness for the acquisition of moral knowledge. (shrink)

In this chapter, we argue for three theses: (1) we lack the power to form beliefs at will (i.e., directly); at very least, we lack the power to form at will beliefs of the kind that proponents of doxastic voluntarism have in mind; but (2) we possess a propensity to form beliefs for non-epistemic reasons; and (3) these propensities—once we come to know we have them—entail that we have obligations similar to those we would have were doxastic voluntarism true. Specifically, (...) we will argue that we have obligations to avoid triggering these propensities to form beliefs that are unwarranted or even immoral. (shrink)

In her paper, The case for physician assisted suicide: not proven, Bonnie Steinbock argues that the experience with Oregon’s Death with Dignity Act fails to demonstrate that the benefits of legalising physician assisted suicide outweigh its risks. Given that her verdict is based on a small number of highly controversial cases that will most likely occur under any regime of legally implemented safeguards, she renders it virtually impossible to prove the case for physician assisted suicide. In this brief paper, we (...) suggest some ways that may enable us to weigh the risks and benefits of legalisation more fairly and, hopefully, allow us to close the case for physician assisted suicide. (shrink)

Response to commentary. We are grateful to Crockett and Craigie for their interesting remarks on our paper. We accept Crockett’s claim that there is a need for caution in drawing inferences about patient groups from work on healthy volunteers in the laboratory. However, we believe that the evidence we cited established a strong presumption that many of the patients who are routinely taking a medication, including many people properly prescribed the medication for a medical condition, have morally significant aspects of (...) their cognition and behavior modified in a way that is unintended and may sometimes be unwelcome. Crockett notes that in some cases the effects of long-term drug use may differ, sometimes markedly, from the effects of short-term use. However, if acute use of a drug affects a neural system involved in mediating moral cognition or behavior, this nevertheless provides some evidence that chronic use of the drug may affect that same system and thus have morally significant effects. It is also plausible, in some cases, that an acute moral effect would give rise to a chronic moral effect via cognitive mechanisms. ... (shrink)

This project has been supported by the Australian Government through the Australian Research Council (project number CS170100008); the Department of Industry, Innovation and Science; and the Department of Prime Minister and Cabinet. ACOLA collaborates with the Australian Academy of Health and Medical Sciences and the New Zealand Royal Society Te Apārangi to deliver the interdisciplinary Horizon Scanning reports to government. The aims of the project which produced this report are: 1. Examine the transformative role that artificial intelligence may play in (...) different sectors of the economy, including the opportunities, risks and challenges that advancement presents. 2. Examine the ethical, legal and social considerations and frameworks required to enable and support broad development and uptake of artificial intelligence. 3. Assess the future education, skills and infrastructure requirements to manage workforce transition and support thriving and internationally competitive artificial intelligence industries. (shrink)

Most philosophers believe that wrongdoers sometimes deserve to be punished by long prison sentences. They also believe that such punishments are justified by their consequences: they deter crime and incapacitate potential offenders. In this article, I argue that both these claims are false. No one deserves to be punished, I argue, because our actions are shot through with direct or indirect luck. I also argue that there are good reasons to think that punishing fewer people and much less harshly will (...) have better social consequences, at a reduced overall cost, then the long prison sentences that are usually seen as required for social protection. (shrink)

A key source of support for the view that challenging people’s beliefs about free will may undermine moral behavior is two classic studies by Vohs and Schooler (2008). These authors reported that exposure to certain prompts suggesting that free will is an illusion increased cheating behavior. In the present paper, we report several attempts to replicate this influential and widely cited work. Over a series of five studies (sample sizes of N = 162, N = 283, N = 268, N (...) = 804, N = 982) (four preregistered) we tested the relationship between (1) anti-free-will prompts and free will beliefs and (2) free will beliefs and immoral behavior. Our primary task was to closely replicate the findings from Vohs and Schooler (2008) using the same or highly similar manipulations and measurements as the ones used in their original studies. Our efforts were largely unsuccessful. We suggest that manipulating free will beliefs in a robust way is more difficult than has been implied by prior work, and that the proposed link with immoral behavior may not be as consistent as previous work suggests. (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)

In an earlier issue, I argue (2014) that psychology and epistemology should distinguish religious credence from factual belief. These are distinct cognitive attitudes. Levy (2017) rejects this distinction, arguing that both religious and factual “beliefs” are subject to “shifting” on the basis of fluency and “intuitiveness.” Levy’s theory, however, (1) is out of keeping with much research in cognitive science of religion and (2) misrepresents the notion of factual belief employed in my theory. So his claims don’t undermine (...) my distinction. I conclude by suggesting some approaches to empirically testing our views. (shrink)

One purpose for the field of consciousness studies may be to increase general understanding about consciousness and its place in human life, thereby possibly aiding us in living in better harmony within our societies and with our fellow humans. Neil Levy’s new work is a candidate for this latter purpose for the field. Consciousness studies may help us better understand how we function as conscious agents—or what role consciousness plays in our agency—and aid in our more just construction (...) of laws, especially those dealing with culpability. (shrink)

Parents play a critical role in their child’s personal development and day-to-day experiences. However, as digital technologies are increasingly embedded in most New Zealand children’s everyday life activities parents face the task of ensuring their child’s online safety. To do so, they need to understand the way their child engages with and through these tools and make sense of the rapidly changing, and more technically complex, nature of digital devices. This presents a digital parenting dilemma: maximising children’s online opportunities while (...) minimising online risks and potential harm. This factsheet presents evidence about digital parenting in New Zealand based on nationally representative data collected from parents, caregivers and whānau and their children aged 9-17. It uses measures from the Global Kids Online project to explore the prevalence of different practices used by New Zealand parents to influence or mediate children’s internet use. (shrink)

Nietzsche takes moral judgments to be false beliefs, and encourages us to pursue subjective nonmoral value arising from our passions. His view that strong and unified passions make one virtuous is mathematically derivable from this subjectivism and a conceptual analysis of virtue, explaining his evaluations of character and the nature of the Overman.

We can infer moral conclusions from nonmoral evidence using a three-step procedure. First, we distinguish the processes generating belief so that their reliability in generating true belief is statistically predictable. Second, we assess the processes’ reliability, perhaps by observing how frequently they generate true nonmoral belief or logically inconsistent beliefs. Third, we adjust our credence in moral propositions in light of the truth ratios of the processes generating beliefs in them. This inferential route involves empirically discovering truths of the form (...) “Process P, which generates belief in moral proposition M, has truth ratio T", and using them to discover probabilities for moral propositions. The inferential route is noncircular, and progress along it is driven fundamentally by induction. (shrink)

This essay presents an ideal for modern Western romantic love.The basic ideas are the following: people want to form a distinctive sort of plural subject with another, what Nozick has called a "We", they want to be loved for properties of certain kinds, and they want this love to establish and sustain a special sort of commitment to them over time.

This factsheet presents findings from a quantitative study looking at adults’ experiences of sending and sharing potentially harmful digital communications in New Zealand. Typically research into harmful digital communications focuses on the experiences of those on the receiving end – the victims. However, to better address the distress and harm caused, information is needed about the people sending and sharing potentially harmful messages and posts. In this study we asked adult New Zealanders whether they had sent potentially harmful digital communications (...) in the previous year and if so, how often they had done this, who they were sent to, the channel(s) they used, and the reason for doing this. (shrink)

Moral realism is often taken to have common sense and initial appearances on its side. Indeed, by some lights, common sense and initial appearances underlie all the central positive arguments for moral realism. We offer a kind of debunking argument, taking aim at realism’s common sense standing. Our argument differs from familiar debunking moves both in its empirical assumptions and in how it targets the realist position. We argue that if natural selection explains the objective phenomenology of moral deliberation and (...) judgement, then this undermines arguments from that phenomenology. This results in a simpler, and in some ways more direct, challenge to realism. It is also less vulnerable to the main objections that have been leveled against such arguments. If accepted, our conclusion should make a real difference to the dialectic in this area. It means that neither realism nor its denial is the default, to-be-refuted, position. (shrink)

Disputes over territory are a major contributing factor to the disruption of international relations. We believe that a cumulative, integrated, and continuously updated resource providing information about such disputes in an easily accessible form would be of benefit to intelligence analysts, military strategists, political scientists, and also to historians and others concerned with international disputes. We propose an ontology-based strategy for creating such a resource. The resource will contain information about territorial disputes, arguments for and against claims pertaining to sovereignty, (...) proffered evidence for such claims, political and military motives (overt or hidden), and associated conflicts. Our approach is designed to address several issues surrounding the representation of geopolitical conflict, including the tracking and individuation of disputes and the validation of disseminated information. (shrink)

How does valuing something for its own sake differ from valuing an entity for the sake of other things? Although numerous answers come to mind, many of them rule out substantive views about what is valuable for its own sake. I therefore seek to provide a more neutral way to distinguish the two valuing attitudes. Drawing from existing accounts of valuing, I argue that the two can be distinguished in terms of a conative-volitional feature. Focusing first on “non-final valuing”—i.e. valuing_ (...) x_ for the sake of something else—I argue that it involves adopting certain reasons on account of a desire for _x_ to contribute to other things. I then show how this contrasts final valuing. The result, I argue, is a plausible account of how the two modes of valuing differ that leaves open substantive views about what all can be valued for its own sake. This is helpful because it develops a popular methodology used to explore the value of a wide range of things, including natural entities, family heirlooms, and artworks, as well as, more broadly, entities that might have “extrinsic final value.”. (shrink)

In Thus Spoke Zarathustra, Nietzsche presents passion as constituting human agency. He encountered this Humean view in Schopenhauer, and recognized its explanatory advantages over Platonic and Kantian rationalism. Zarathustra's poetic speeches anticipate and address contemporary objections to the view that passion constitutes agency. "On the Despisers of the Body" explains why understanding the self as constituted by passion provides better explanations of reasoning, value judgment, and the unity of the self than Christine Korsgaard's neo-Kantian view. "On Enjoying and Suffering the (...) Passions" explains why understanding virtues as constituted by passions provides a better explanation of moral phenomenology than John McDowell's rationalism. (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.

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.

Nietzsche and Hume agree that desire drives all human action and practical reasoning. This shared view helps them appreciate continuities between human and animal motivation and sets them against a long tradition of rationalist rivals including Kant and Plato. In responding to Kant, Nietzsche further developed the Humean views that Kant himself was responding to. Kantians like Christine Korsgaard argue that reflective endorsement and rejection of options presented by desire demonstrates reason’s ability to independently drive reasoning and action. In Daybreak (...) 109, Nietzsche provides a simpler Humean explanation: reflective endorsement and rejection involve reflecting on one desire from the viewpoint of another, with desire as the only motivational force. This explains the attentional and hedonic phenomenology of reflective endorsement without ascribing any motivational force to rational processes independent of desire. (shrink)

John McDowell claims that virtuous people recognize moral reasons using a perceptual capacity that doesn't include desire. I show that the phenomena he cites are better explained if desire makes us see considerations favoring its satisfaction as reasons. The salience of moral considerations to the virtuous, like the salience of food to the hungry, exemplifies the emotional and attentional effects of desire. I offer a desire-based account of how we can follow uncodifiable rules of common-sense morality and how some reasons (...) can be silenced in deliberation. I conclude by arguing that animals can be virtuous by having the right desires. (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)

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.

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)

This article addresses two areas of continuing controversy about consent in clinical research: the question of when consent to low risk research is necessary, and the question of when consent to research is valid. The article identifies a number of considerations relevant to determining whether consent is necessary, chief of which is whether the study would involve subjects in ways that would (otherwise) infringe their rights. When consent is necessary, there is a further question of under what conditions consent is (...) valid or successful in waiving a right. The most influential account of validity conditions is non-moralized, in the sense that the conditions make no essential reference to whether the researcher soliciting consent has obtained it in a way that wrongs the subject. The article examines the implications of this account, and compares it with recent accounts that moralize some of the validity conditions. -/- . (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)

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)

Philosophers from Hart to Lewis, Johnston and Bennett have expressed various degrees of reservation concerning the doctrine of double effect. A common concern is that, with regard to many activities that double effect is traditionally thought to prohibit, what might at first look to be a directly intended bad effect is really, on closer examination, a directly intended neutral effect that is closely connected to a foreseen bad effect. This essay examines the extent to which the commonsense concept of intention (...) supports a reasonably consistent and coherent application of double effect. Two important conclusions are these: (1) a number of traditionally proscribed activities involve a kind of “targeting” of innocents that can be taken to exhibit a direct intention to harm them; (2) a direct intention to harm need not involve a desire to harm in any ordinary sense of the latter expression. (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)

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)

I argue that the three strongest arguments against metaphysical libertarianism—the randomness objection, the constitutive luck objection, and the physicalist objection—are actually unsuccessful and therefore that metaphysical libertarianism is more plausible than the common philosophical wisdom allows. My more positive thesis, what I will refer to as “Agent Exceptionalism,” is that, when making decisions and performing actions, human beings can indeed satisfy the four conditions of metaphysical libertarianism: the control condition, the rationality condition, the ultimacy condition, and the physicalism condition.

This essay argues that there are theoretical benefits to keeping distinct—more pervasively than the literature has done so far—the psychological states of imagining that p versus believing that in-the-story p, when it comes to cognition of fiction and other forms of narrative. Positing both in the minds of a story’s audience helps explain the full range of reactions characteristic of story consumption. This distinction also has interesting conceptual and explanatory dimensions that haven’t been carefully observed, and the two mental state (...) types make distinct contributions to generating emotional responses to stories. Finally, the differences between the mental states illuminate how a given story can be both shared with others and at the same time experienced as personal. (shrink)

Epistemic akrasia can be rational. I consider a lonely pragmatist who believes that her imaginary friend doesn’t exist, and also believes on pragmatic grounds that she should believe in him. She rationally believes that her imaginary friend doesn’t exist, rationally follows various sources of evidence to the view that she should believe in him to end her loneliness, and rationally holds these attitudes simultaneously. Evidentialism suggests that her ambivalent epistemic state is rational, as considerations grounded in the value of truth (...) justify her beliefs. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...) the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (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)

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.

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)

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)