This paper presents a preliminary analysis of the first participatory budgeting experiment in the United States, in Chicago's 49th Ward. There are two avenues of inquiry: First, does participatory budgeting result in different budgetary priorities than standard practices? Second, do projects meet normative social justice outcomes? It is clear that allowing citizens to determine municipal budget projects results in very different outcomes than standard procedures. Importantly, citizens in the 49th Ward consistently choose projects that the research literature classifies as low (...) priority. The results are mixed, however, when it comes to social justice outcomes. While there is no clear pattern in which projects are located only in affluent sections of the ward, there is evidence of geographic clustering. Select areas are awarded projects like community gardens, dog parks, and playgrounds, while others are limited to street resurfacing, sidewalk repairs, bike racks, and bike lanes. Based on our findings, we offer suggestions for future programmatic changes. (shrink)

Public health care interventions—regarding vaccination, obesity, and HIV, for example—standardly take the form of information dissemination across a community. But information networks can vary importantly between different ethnic communities, as can levels of trust in information from different sources. We use data from the Greater Pittsburgh Random Household Health Survey to construct models of information networks for White and Black communities--models which reflect the degree of information contact between individuals, with degrees of trust in information from various sources correlated with (...) positions in that social network. With simple assumptions regarding belief change and social reinforcement, we use those modeled networks to build dynamic agent-based models of how information can be expected to flow and how beliefs can be expected to change across each community. With contrasting information from governmental and religious sources, the results show importantly different dynamic patterns of belief polarization within the two communities. (shrink)

Guthrie contends that religion can best be understood as systematic anthropomorphism - the attribution of human characteristics to nonhuman things and events. Religion, he says, consists of seeing the world as human like. He offers a fascinating array of examples to show how this strategy pervades secular life and how it characterizes religious experience.

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

In this paper, I argue that the cause of morally self-defeating acts at the collective level is greed and, at the individual level, an unrestrained impulse for pleasure beyond Innocent Asouzu’s primordial instinct for self-preservation and ignorance. In investigating why humans act in self-defeating ways, Asouzu came up with two possible factors responsible for self-defeating acts: The primordial instinct for selfpreservation and ignorance. Besides Asouzu’s explanation, I here argue that the problem of self-defeating acts goes beyond the primordial instinct for (...) selfpreservation and ignorance to reveal a flaw characteristic of the human condition. At the collective level, the flaw responsible for self-defeating acts is greed and the unrestrained impulse for pleasure at the individual level. I employ the conversational method to interrogate the different views on self-defeating acts from Socrates to Asouzu and show why my explanation offers a better understanding of the problem. (shrink)

Recently, philosophers have turned their attention to the question, not when a given agent is blameworthy for what she does, but when a further agent has the moral standing to blame her for what she does. Philosophers have proposed at least four conditions on having “moral standing”: -/- 1. One’s blame would not be “hypocritical”. 2. One is not oneself “involved in” the target agent’s wrongdoing. 3. One must be warranted in believing that the target is indeed blameworthy for the (...) wrongdoing. 4. The target’s wrongdoing must some of “one’s business”. -/- These conditions are often proposed as both conditions on one and the same thing, and as marking fundamentally different ways of “losing standing.” Here I call these claims into question. First, I claim that conditions (3) and (4) are simply conditions on different things than are conditions (1) and (2). Second, I argue that condition (2) reduces to condition (1): when “involvement” removes someone’s standing to blame, it does so only by indicating something further about that agent, viz., that he or she lacks commitment to the values that condemn the wrongdoer’s action. The result: after we clarify the nature of the non-hypocrisy condition, we will have a unified account of moral standing to blame. Issues also discussed: whether standing can ever be regained, the relationship between standing and our "moral fragility", the difference between mere inconsistency and hypocrisy, and whether a condition of standing might be derived from deeper facts about the "equality of persons". (shrink)

In the _True Intellectual System_, Cudworth attacks types of atheist position—atomic atheism, hylozoic atheism, etc. He generally uses ancient examples to illustrate those types, but also criticizes some of his contemporaries. We can identify direct criticisms of contemporaries by finding quotations, paraphrases, and accounts of their views in the text. My primary question in this paper is, 'how much of the _True Intellectual System_ is directly about or aimed at Spinoza?' My ultimate answer, contrary to some prominent voices in the (...) existing literature, is 'not very much at all'. (shrink)

Everyone agrees that we can’t change the past. But what about the future? Though the thought that we can change the future is familiar from popular discourse, it enjoys virtually no support from philosophers, contemporary or otherwise. In this paper, I argue that the thesis that the future is mutable has far more going for it than anyone has yet realized. The view, I hope to show, gains support from the nature of prevention, can provide a new way of responding (...) to arguments for fatalism, can account for the utility of total knowledge of the future, and can help in providing an account of the semantics of the English progressive. On the view developed, the future is mutable in the following sense: perhaps, once, it was true that you would never come to read a paper defending the mutability of the future. And then the future changed. And now you will. (shrink)

At least since Aristotle's famous discussion of the sea-battle tomorrow in On Interpretation 9, philosophers have been fascinated by a rich set of interconnecte.

This chapter considers Ralph Cudworth as a philosophical critic of Hobbes. Cudworth saw Hobbes as a representative of the three views he was attacking: atheism, determinism, and the denial that morality is eternal and immutable. Moreover, he did not just criticize Hobbes by assuming that a general critique of those views applied to Hobbes’s particular case. Rather, he singled out Hobbes, often by quoting him, and argued against the distinctively Hobbesian positions he had identified. In this chapter I look at (...) Cudworth as a critic of Hobbes in two of the three central areas, atheism and ethics, focusing on passages where we see him explicitly picking out Hobbes. (shrink)

In this article, I argue that Immanuel Kant fails to provide a satisfactory account of ‘moral debt’ in Religion within the Boundaries of Mere Reason. More precisely, he fails to answer the question of why we should assume that a debt exists in the first place. In light of recent scholarship on this area of his thought, I sketch some possible readings of Kant on the nature of moral transformation that suggest how he might account for this debt. I then (...) argue that these accounts fail to justify its existence within Kant's project. (shrink)

Results: We analyzed 1,402 surveys and 15 in-depth interviews. Many (32%) CL participants reported greater difficulty refilling medications and a minority (14%) reported greater difficulty accessing HIV care during the pandemic. Most (99%) Opt4Mamas participants reported no difficulty refilling medications or accessing HIV/pregnancy care. Among the CL participants, older women were less likely (aOR = 0.95, 95% CI: 0.92–0.98) and women with more children were more likely (aOR = 1.13, 95% CI: 1.00–1.28) to report difficulty refilling medications. Only 2% of (...) CL participants reported greater difficulty managing FP and most (95%) reported no change in likelihood of using FP or desire to get pregnant. Qualitative analysis revealed three major themes: (1) adverse organizational/economic implications of the pandemic, (2) increased importance of pregnancy prevention during the pandemic, and (3) fear of contracting COVID-19. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

In his Target Article, Terrence Deacon develops simple models that assist in understanding the role of RNA in the origins of life. However, his models fail to adequately represent an important evolutionary dynamic. Central to this dynamic is the selection that impinges on RNA molecules in the context of their association with proto-metabolisms. This selection shapes the role of RNA in the emergence of life. When this evolutionary dynamic is appropriately taken into account, it predicts a role for RNA that (...) is consistent with the Managed-Metabolism Hypothesis about the origins of life, and inconsistent with Deacon’s account. (shrink)

There is a familiar debate between Russell and Strawson concerning bivalence and ‘the present King of France’. According to the Strawsonian view, ‘The present King of France is bald’ is neither true nor false, whereas, on the Russellian view, that proposition is simply false. In this paper, I develop what I take to be a crucial connection between this debate and a different domain where bivalence has been at stake: future contingents. On the familiar ‘Aristotelian’ view, future contingent propositions are (...) neither true nor false. However, I argue that, just as there is a Russellian alternative to the Strawsonian view concerning ‘the present King of France’, according to which the relevant class of propositions all turn out false, so there is a Russellian alternative to the Aristotelian view, according to which future contingents all turn out false, not neither true nor false. The result: contrary to millennia of philosophical tradition, we can be open futurists without denying bivalence. (shrink)

The evolution of life on Earth has produced an organism that is beginning to model and understand its own evolution and the possible future evolution of life in the universe. These models and associated evidence show that evolution on Earth has a trajectory. The scale over which living processes are organized cooperatively has increased progressively, as has its evolvability. Recent theoretical advances raise the possibility that this trajectory is itself part of a wider developmental process. According to these theories, the (...) developmental process has been shaped by a yet larger evolutionary dynamic that involves the reproduction of universes. This evolutionary dynamic has tuned the key parameters of the universe to increase the likelihood that life will emerge and produce outcomes that are successful in the larger process (e.g. a key outcome may be to produce life and intelligence that intentionally reproduces the universe and tunes the parameters of ‘offspring’ universes). Theory suggests that when life emerges on a planet, it moves along this trajectory of its own accord. However, at a particular point evolution will continue to advance only if organisms emerge that decide to advance the developmental process intentionally. The organisms must be prepared to make this commitment even though the ultimate nature and destination of the process is uncertain, and may forever remain unknown. Organisms that complete this transition to intentional evolution will drive the further development of life and intelligence in the universe. Humanity’s increasing understanding of the evolution of life in the universe is rapidly bringing it to the threshold of this major evolutionary transition. (shrink)

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

We show that cast shadows can have a significant influence on the speed of visual search. In particular, we find that search based on the shape of a region is affected when the region is darker than the background and corresponds to a shadow formed by lighting from above. Results support the proposal that an early-level system rapidly identifies regions as shadows and then discounts them, making their shapes more difficult to access. Several constraints used by this system are mapped (...) out, including constraints on the luminance and texture of the shadow region, and on the nature of the item casting the shadow. Among other things, this system is found to distinguish between line elements (items containing only edges) and surface elements (items containing visible surfaces), with only the latter deemed capable of casting a shadow. (shrink)

In this paper, I articulate an argument for incompatibilism about moral responsibility and determinism. My argument comes in the form of an extended story, modeled loosely on Peter van Inwagen’s “rollback argument” scenario. I thus call it “the replication argument.” As I aim to bring out, though the argument is inspired by so-called “manipulation” and “original design” arguments, the argument is not a version of either such argument—and plausibly has advantages over both. The result, I believe, is a more convincing (...) incompatibilist argument than those we have considered previously. (shrink)

I consider statistical criteria of algorithmic fairness from the perspective of the _ideals_ of fairness to which these criteria are committed. I distinguish and describe three theoretical roles such ideals might play. The usefulness of this program is illustrated by taking Base Rate Tracking and its ratio variant as a case study. I identify and compare the ideals of these two criteria, then consider them in each of the aforementioned three roles for ideals. This ideals program may present a way (...) forward in the normative evaluation of candidate statistical criteria of algorithmic fairness. (shrink)

Nietzsche’s Birth of Tragedy overcomes the opposition between scientific optimism and Schopenhauerian pessimism with the image of a music-making Socrates, who symbolizes the aesthetic affirmation of life. This article shows how the aesthetic ideal is an illusion whose metaphysical solace undermines itself in being recognized as such, thereby ceasing to be comforting. While I agree with recent commentaries that contest the pervasive Schopenhauerian reading of The Birth, most of these commentaries still support the view that Nietzsche wishes to communicate some (...) fundamental truth about nature or meaning in life. By contrast, I argue that he treats any such truth as a cultural fiction that emerges from the poetic staging of reality, leaving us with a contradiction of appearances deprived of any intelligible ground. (shrink)

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle. For consider the following two claims: Trump will be impeached tomorrow; Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of (...) these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~] and the latter claim. However, the viability of this approach has been denied by Thomason, and more recently by MacFarlane and Cariani and Santorio, the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees and as contraries, not contradictories. (shrink)

We suggest that the emerging field of the conservation humanities can play a valuable role in biodiversity protection in Papua New Guinea (PNG), where most land remains under collective customary clan ownership. As a first step to mobilising this scholarly field in PNG and to support capacity development for PNG humanities academics, we conducted a landscape review of PNG humanities teaching and research relating to biodiversity conservation and customary land rights. We conducted a systematic literature review, a PNG teaching programme (...) review, and a series of online workshops between the authors (10 PNG-based, 7 UK-based). We found a small but notable amount of PNG research and teaching focused on biodiversity conservation or customary land rights. This included explicit discussion of these topics in 8 of 156 PNG-authored humanities texts published 2010-2020 and related teaching content in the curricula of several different humanities-based programmes. We discuss current barriers to PNG academic development. The growth of fully fledged in-country conservation humanities will require a joint collaborative effort by PNG researchers, who are best placed to carry out such work, and researchers from abroad who can access resources to support the process. (shrink)

According to Richard Gelwick, one of the fundamental implications of Polanyi’s epistemology is that all intellectual disciplines are inherently heuristic. This article draws out the implications of a heuristic vision of theology latent in Polanyi’s thought by placing contemporary theologian David Brown’s dynamic understanding of tradition, imagination, and revelation in the context of a Polanyian-inspired vision of reality. Consequently, such a theology will follow the example of science, reimagining its task as one of discovery rather than mere reflection on a (...) timeless body of divine revelation. The ongoing development of a theological tradition thus involves the attempt to bring one’s understanding of the question of God to bear on the whole of the human experience. The pursuit of theology as a heuristic endeavor is a bold attempt to construct an integrated vision of nothing less than the entirety of all that is, without absolutizing one’s vision, and without giving up on the question of truth. (shrink)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

Can a human society be constrained in such a way that self-organization will thereafter tend to produce outcomes that advance the goals of the society? Such a society would be self-organizing in the sense that individuals who pursue only their own interests would none-the-less act in the interests of the society as a whole, irrespective of any intention to do so. The paper sketches an agent-based model that identifies the conditions that must be met if such a self-organizing society is (...) to emerge. The model draws heavily on an understanding of how self-organizing societies have emerged repeatedly during the evolution of life on Earth. The model demonstrates that the key enabling requirement for a self-organizing society is ‘consequence-capture’. Broadly this means that all agents in the society must capture sufficient of the beneficial consequences of their actions for the goals of the society. ‘Consequence-capture’ can be organized in a society by appropriate management that suppresses free riders and supports pro-social actions. In human societies these constraints include institutions such as systems of governance and social norms. If a self-organizing society is to emerge, consequence-capture must apply to all agents in the society, including those involved in the establishment and adaptation of institutions. If this is achieved, the result will be a fully self-organizing society in which the interests of all agents are aligned with the interests of the society as a whole. (shrink)

The precautionary principle is invoked in a number of important personal and policy decision contexts. Peterson shows that certain ways of making the principle precise are inconsistent with other criteria of decision-making. Some object that the results do not apply to cases of deep uncertainty or value incommensurability which are alleged to be in the principle’s wheelhouse. First, I show that Peterson’s impossibility results can be generalized considerably to cover cases of both deep uncertainty and incommensurability. Second, I contrast an (...) alternative way of giving voice to the precautionary impulse. (shrink)

Thomas Hobbes often includes powers and abilities in his descriptions of the world. Meanwhile, Hobbes’s philosophical picture of the world appears quite reductive, and he seems sometimes to say that nothing exists but bodies in motion. In more extreme versions of such a picture, there would be no room for powers. Hobbes is not an eliminativist about powers, but his view does tend toward ontological minimalism. It would be good to have an account of what Hobbes thinks powers are, and (...) how they fit into his understanding of the world. In this chapter, I investigate Hobbes’s account of the metaphysics of powers and abilities. Section 1 considers three important aspects of Hobbes’s account of powers: the connection between powers and causes; the modal aspects of powers; and the connection between powers and motions. Sections 2 and 3 then consider interpretive arguments about whether Hobbes identifies powers with underlying corporeal features. (shrink)

Conspiracy theories are rather a popular topic these days, and a lot has been written on things like the meaning of _conspiracy theory_, whether it’s ever rational to believe conspiracy theories, and on the psychology and demographics of people who believe conspiracy theories. But very little has been said about why people might be led to posit conspiracy theories in the first place. This paper aims to fill this lacuna. In particular, I shall argue that, in open democratic societies, citizens (...) justifiably presuppose that the epistemic authorities—journalists, academics, scientists, and so on—are engaged in a good faith pursuit of the truth. This presupposition generates certain normative expectations on the behaviors of the epistemic authorities—they ought to be open to new evidence, possess a healthy degree of skepticism, be willing to engage with opponents, and so on. So, when an epistemic authority is presented with some putatively anomalous data or an alternative hypothesis for some event or phenomena, people expect the epistemic authority to respond in a way that is consonant with these norms. In some instances, however, the epistemic authorities do not respond in this way and instead are dogmatic, dismissive, and engage in _ad hominem_. From the point of view of the citizen, there’s a tension here between how the epistemic authorities ought to behave and how they have, in fact, behaved which is best resolved either by taking the epistemic authorities less seriously or by positing a conspiracy theory. Put another way, the failure of the epistemic authorities to adhere to the norms by which we take them to be governed when presented with apparent anomalies or alternative hypotheses is one reason for which one might initially posit a conspiracy theory. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

In this paper, I discuss how Nietzsche’s critique of nihilism concerns the complicity between Christian morality and modern atheism. I unpack in what sense Schopenhauer’s ascetic denial of the will signifies a return to nothingness, what he calls the nihil negativum. I argue that Nietzsche’s formulation of nihilism specifically targets Schopenhauer’s pessimism as the culmination of the Western metaphysical tradition, the crucial stage of its intellectual history in which the scientific pursuit of truth finally unveils the ascetic will to nothingness (...) that motivates it. I contend that Nietzsche’s critique of Schopenhauer anticipates current scholarly debates around the significance of the nihil negativum and offers a compelling objection against contemporary proponents of philosophical nihilism such as Eugene Thacker and Ray Brassier. (shrink)

P.F. Strawson’s (1962) “Freedom and Resentment” has provoked a wide range of responses, both positive and negative, and an equally wide range of interpretations. In particular, beginning with Gary Watson, some have seen Strawson as suggesting a point about the “order of explanation” concerning moral responsibility: it is not that it is appropriate to hold agents responsible because they are morally responsible, rather, it is ... well, something else. Such claims are often developed in different ways, but one thing remains (...) constant: they meant to be incompatible with libertarian theories of moral responsibility. The overarching theme of this paper is that extant developments of “the reversal” face a dilemma: in order to make the proposals plausibly anti-libertarian, they must be made to be implausible on other grounds. I canvas different attempts to articulate a “Strawsonian reversal”, and argue that none is fit for the purposes for which it is intended. I conclude by suggesting a way of clarifying the intended thesis: an analogy with the concept of funniness. The result: proponents of the “reversal” need to accept the difficult result that if we blamed small children, they would be blameworthy, or instead explain how their view escapes this result, while still being a view on which our blaming practices “fix the facts” of moral responsibility. (shrink)

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction?

In his Enquiry concerning the Principles of Morals David Hume said that a group of earlier modern philosophers, beginning with Malebranche, held that morality was founded on relations. In this paper I follow up on that suggestion by investigating pre-Humean views in moral philosophy according to which morality is founded on relations. I do that by looking at the work of Nicolas Malebranche, John Locke, and Samuel Clarke. Each of them talked prominently about relations in their accounts of basic aspects (...) of morality. Beyond that, each of them turns out to have held both metaphysical and epistemological views that might be described as founding morality on relations. Despite the definite differences between the three philosophers’ approaches, Hume does seem to have noticed a genuine connection here—even though he himself tended to ignore significant versions of this approach when criticizing it. (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of (...) theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically impure (...) (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for a (...) wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...) we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

It has previously been argued that Schopenhauer is a distinctive type of virtue ethicist (Hassan, 2019). The Aristotelian version of virtue ethics has traditionally been accused of being fundamentally egoistic insofar as the possession of virtues is beneficial to the possessor, and serve as the ultimate justification for obtaining them. Indeed, Schopenhauer himself makes a version of this complaint. In this chapter, I investigate whether Schopenhauer’s moral framework nevertheless suffers from this same objection of egoism in light of how he (...) conceives of the relationship between morality and ascetic 'salvation'. Drawing upon his published works and letters, I argue that Schopenhauer has the resources to avoid the objection. Because of his idiosyncratic metaphysics, I argue that Schopenhauer can also avoid the problem of self-effacement which may result from the way in which he avoids the egoism objection. The discussion thus intends to establish further nuance to Schopenhauer’s conception of virtue and its value. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

Our purpose in this article is to draw attention to a connection that obtains between two dilemmas from two separate spheres: sports and the law. It is our contention that umpires in the game of cricket may face a dilemma that is similar to a dilemma confronted by legal decision makers and that comparing the nature of the dilemmas, and the arguments advanced to solve them, will serve to advance our understanding of both the law and games.

This paper discusses the materialist views of Margaret Cavendish, focusing on the relationships between her views and those of two of her contemporaries, Thomas Hobbes and Henry More. It argues for two main claims. First, Cavendish's views sit, often rather neatly, between those of Hobbes and More. She agreed with Hobbes on some issues and More on others, while carving out a distinctive alternative view. Secondly, the exchange between Hobbes, More, and Cavendish illustrates a more general puzzle about just what (...) divided materialists from their opponents. Seemingly straightforward disagreements about whether incorporeal substances exist turn out to be more complex ones in which the nature of those things is disputed at the same time as their existence. (shrink)