In providing a good foundation for mathematics, set theorists often aim to develop the strongest theories possible and avoid those theories that place undue restrictions on the capacity to possess strength. For example, adding a measurable cardinal to $ZFC$ is thought to give a stronger theory than adding $V=L$ and the latter is thought to be more restrictive than the former. The two main proponents of this style of account are Penelope Maddy and John Steel. In this paper, I’ll offer (...) a third account that is intended to provide a simple analysis of restrictiveness based on the algebraic concept of retraction in the category of theories. I will also deliver some results and arguments that suggest some plausible alternative approaches to analyzing restrictiveness do not live up to their intuitive motivation. (shrink)

This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and isolate what it would take (...) to remove it while working within his framework. As our goal is to present as coherent and compelling a philosophical and mathematical story as we can, we allow ourselves to augment Steel’s story in places (e.g., in the treatment of Amalgamation) and to depart from it in others (e.g., the removal of ‘meaning’ from the account). The relevant mathematics is laid out in the appendices. (shrink)

This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday (...) mathematical practice. (shrink)

In J Philos Logic 34:155–192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155–192, 2005, we discover that something is missing from Leitgeb’s original definition. Moreover, we (...) show that once the appropriate repairs have been made, the resultant definition is equivalent to a version of the supervaluation definition suggested in J Philos 72:690–716, 1975 and discussed in detail in J Symb Log 51(3):663–681, 1986. The upshot of this is a philosophical justification for the simple supervaluation approach and fresh insight into its workings. (shrink)

The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We (...) argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike. (shrink)

f The purpose of this paper is to investigate categoricity arguments conducted in second order logic and the philosophical conclusions that can be drawn from them. We provide a way of seeing this result, so to speak, through a first order lens divested of its second order garb. Our purpose is to draw into sharper relief exactly what is involved in this kind of categoricity proof and to highlight the fact that we should be reserved before drawing powerful philosophical conclusions (...) from it. (shrink)

Interpretation is commonly used in mathematical logic to compare different theories and identify cases where two theories are for almost all intents and purposes the same. Similar techniques are used in the comparison between alternative logics although the links between these approaches are not transparent. This paper generalizes theoretical comparison techniques to the case of logical comparison using an extremely general approach to semantics that provides a very generous playing field upon which to make our comparisons. In particular, we aim (...) to develop the useful idea that interpretations should determine inner models. (shrink)

This paper critically examines two arguments against the generic multiverse, both of which are due to W. Hugh Woodin. Versions of the first argument have appeared a number of times in print, while the second argument is relatively novel. We shall investigate these arguments through the lens of two different attitudes one may take toward the methodology and metaphysics of set theory; and we shall observe that the impact of these arguments depends significantly on which of these attitudes is upheld. (...) Our examination of the second argument involves the development of a new model for Steel’s multiverse theory, which is delivered in the Appendix. (shrink)

Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on Priest and attempts some fixes and alternative construals to get (...) around some elementary problems. Despite these efforts, the argument remains unconvincing. (shrink)

This paper assembles a unifying framework encompassing a wide variety of mathematical instruments used to compare different theories. The main theme will be the idea that theory comparison techniques are most easily grasped and organized through the lens of category theory. The paper develops a table of different equivalence relations between theories and then answers many of the questions about how those equivalence relations are themselves related to each other. We show that Morita equivalence fits into this framework and provide (...) answers to questions left open in Barrett and Halvorson [4]. We conclude by setting up a diagram of known relationships and leave open some questions for future work. (shrink)

It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can (...) talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched. (shrink)

The purpose of this paper is to propose and explore a general framework within which a wide variety of model construction techniques from contemporary set theory can be subsumed. Taking our inspiration from presheaf constructions in category theory and Boolean ultrapowers, we will show that generic extensions, ultrapowers, extenders and generic ultrapowers can be construed as examples of a single model construction technique. In particular, we will show that Łoś's theorem can be construed as a specific case of Cohen's truth (...) lemma, and we isolate the weakest conditions a filter must satisfy in order for the truth lemma to work. (shrink)

Consistency, interpretability and probability are three key instruments in the mathematical philosopher’s kit when it comes to questions of foundational theory comparison. This paper aims to bring these tools together with a focus on theories capable of providing foundations for mathematics with a particular emphasis on set theory. A number of counterintuitive results emerge which are then addressed by offering a novel framework based on what we call pointwise interpretability. We then investigate a plausible, existing instance of this framework, the (...) generic multiverse, and demonstrate that it can be naturally situated within our pointwise interpretability framework. (shrink)

This paper explores the idea that Descartes’ cogito is a kind of diagonal argument. Using tools from modal logic, it reviews some historical antecedents of this idea from Slezak and Boos and culminates in an orginal result classifying the exact structure of belief frames capable of supporting diagonal arguments and our reconstruction of the cogito.

An account of modality is produced which takes as its foundation the idea that modal concepts are parasitic upon our background theoretical commitments. This position is distinguished from the majority of philosophies of modality, which are either primitivist or reductionist. It is in this sense that our account is less burdened by metaphysics. The primary purpose of the document is to demonstrate that our approach is a coherent one. It supports this claim in three stages. First, we identify the historical (...) lineage of our position and elucidate the main desiderata which must be met if the project is to succeed. Second, we provide a series of logical systems which are designed to meet our requirements. A raft of technical challenges beset this part of the project and this is where the bulk of the result in this thesis are located. Finally, we use the precise formalisation as a means to get a better understanding of what is at stake in the project and to understand the resultant position's relationship with other leading, contemporary philosophies of modality. (shrink)

I provide a tableau system and completeness proof for a revised version of Carnap's semantics for quantified modal logic. For Carnap, a sentence is possible if it is true in some first order model. However, in a similar fashion to second order logic, no sound and complete proof theory can be provided for this semantics. This factor contributed to the ultimate disappearance of Carnapian modal logic from contemporary philosophical discussion. The proof theory I discuss comes close to Carnap's semantic vision (...) and provides an interesting counterpoint to mainstream approaches to modal logic. Despite its historical origins, my intention is to demonstrate that this approach to modal logic is worthy of contemporary attention and that current debate is the poorer for its absence. (shrink)

Why should we decolonise knowledge? One popular rationale is that colonialism has set up a single perspective as epistemically authoritative over many equally legitimate ones, and this is a form of...

Contentless experience involves an absence of mental content such as thought, perception, and mental imagery. In academic work it has been classically treated as including states like those aimed for in Shamatha, Transcendental, and Stillness Meditation. We have used evidence synthesis to select and review 135 expert texts from within the three traditions. In this paper we identify the features of contentless experience referred to in the expert texts and determine whether the experiences are the same or different across the (...) practices with respect to each feature. We identify 65 features reported or implied in one or more practices, with most being reported or implied in all three. While there are broad similarities in the experiences across the traditions, we find that there are differences with respect to four features and possibly many others. The main difference identified is that Shamatha involves substantially greater attentional stability and vividness. Another key finding is that numerous forms of content are present in the experiences, including wakefulness, naturalness, calm, bliss/joy, and freedom. The findings indicate that meditation experiences described as contentless in the academic literature can in fact involve considerable variation, and that in many and perhaps most cases these experiences are not truly contentless. This challenges classical understandings in academic research that in these so-called contentless experiences all content is absent, and that the experiences are therefore an identical state of _pure consciousness_ or consciousness itself. Our assessment is that it remains an open question whether the experiences aimed for in the three practices should be classed as pure consciousness. Implications of our analysis for neuroscientific and clinical studies and for basic understandings of the practices are discussed. (shrink)

As we understand them, dispositions are relatively uncontroversial 'predicatory' properties had by objects disposed in certain ways. By contrast, powers are hypothetical 'ontic' properties posited in order to explain dispositional behaviour. Chapter 1 outlines this distinction in more detail. Chapter 2 offers a summary of the issues surrounding analysis of dispositions and various strategies in contemporary literature to address them, including one of our own. Chapter 3 describes some of the important questions facing the metaphysics of powers including why they're (...) worth positing, and how they might metaphysically explain laws of nature and modality. (shrink)

This book puts forth the concept and practice of hip-hop mindfulness as a way for minoritized communities to take creative risks in the face of cultural oppression within educational institutions. Written for students of social justice and diversity education, foundations of education, and ethnic studies, this book introduces the hip-hop mindset as a professional practice that holds relevance for ambitious leaders in any profession who seek to innovate, trailblaze, and create so much professional magic, that they appear to walk on (...) air. (shrink)

Humanity stands at a precipice. -/- Our species could survive for millions of generations — enough time to end disease, poverty, and injustice; to reach new heights of flourishing. But this vast future is at risk. With the advent of nuclear weapons, humanity entered a new age, gaining the power to destroy ourselves, without the wisdom to ensure we won’t. Since then, these dangers have only multiplied, from climate change to engineered pandemics and unaligned artificial intelligence. If we do not (...) act fast to reach a place of safety, it may soon be too late. -/- The Precipice explores the science behind the risks we face. It puts them in the context of the greater story of humanity: showing how ending these risks is among the most pressing moral issues of our time. And it points the way forward, to the actions and strategies we can take today to safeguard humanity’s future. (shrink)

It has often been noted that there is some tension between engaging in decision-making and believing that one’s choices might be predetermined. The possibility that our choices are predetermined forces us to consider, in our decisions, act-state pairs which are inconsistent, and hence to which we cannot assign sensible utilities. But the reasoning which justifies two-boxing in Newcomb’s problem also justifies associating a non-zero causal probability with these inconsistent act-state pairs. Put together these undefined utilities and non-zero probabilities entail that (...) expected utilities are undefined whenever it is a possibility that our choices are predetermined. There are three ways to solve the problem, but all of them suffer serious costs: always assume that, contrary to our evidence, the outcome of our present decision-making is not predetermined; give up the reasoning that justifies unconditional two-boxing in Newcomb’s problem; or allow epistemically impossible outcomes to contribute to expected utility, leading to the wrong results in a series of cases introduced by Ahmed :665–685, 2014a, Evidence, decision and causality, Cambridge University Press, Cambridge, 2014b). However they choose to respond, causal decision theorists cannot remain silent: the intuitive tension between decision-making and the possibility of predetermination can be made precise, and resolving it will require giving up something. Causal decision theorists have a predetermination problem. (shrink)

Plato’s Ion is primarily ethical rather than epistemological, investigating the implications of transgressing one’s own epistemic limits. The figures of Socrates and Ion are juxtaposed in the dialogue, Ion being a laughable, comic, ethically inferior character who cannot recognize his own epistemic limits, Socrates being an elevated, serious, ethically superior character who exhibits disciplined epistemic restraint. The point of the dialogue is to contrast Ion’s laughable state with the serious state of Socrates. In this sense, the dialogue’s central argument is (...) performative rather than demonstrative. (shrink)

Gaia, the grand idea -- Good citizens or selfish genes? -- Life at the edge : lessons from extremophiles -- Temperature paces life -- Icehouse earth -- Given enough time -- Evolutionary innovations and environmental change -- A stable or an unstable world? -- The puzzle of life's long persistence -- Conclusions.

This is a personal development book that teaches a powerful tool for self-inquiry embodied through a practice of yoga. This book solves the problem of feeling stuck, lost, or confused. The solution is a powerful inner navigation technique that will help readers find their way.

Settler colonialism is structured in part according to the principle of civilizational progress yet the roots of this doctrine are not well understood. Disparate ideas of progress and practices related to colonial dispossession and domination can be traced back to the Enlightenment, and as far back as ancient Greece, but there remain unexplored logics and continuities. I argue that civilizational progress and settler colonialism are structured according to the opposition between politics governed by reason or faith and the figure of (...) the child as sinful or bestial. Thus, it is not contingent, but rather necessary that justificatory frameworks of European empire and colonialism depict Indigenous peoples as children. To illustrate how the theoretical link between Indigenous peoples and children emerges not as a simple analogy, but rather, as the source of the premodern/modern and savage/civilized binaries, I trace the various historical iterations of the political/childhood opposition through the classical, medieval, enlightenment, and modern eras. I show how the model of civilizational progress from a premodern and savage state of childhood continues to serve as the model for settler colonial exclusion and domination of Indigenous peoples. (shrink)

The deliberative systems approach is a recent innovation within the tradition of deliberative democratic theory. It signals an important shift in focus from the political legitimacy produced within isolated and formal sites of deliberation (e.g., Parliament or deliberative mini-publics), to the legitimacy produced by a number of diverse interconnected sites. In this respect, the deliberative systems (DS) approach is better equipped to identify and address defects arising from the systemic influences of power and coercion. In this article, I examine one (...) of the least explored and least understood defects: the exclusion of non-speaking political actors generated by the uniform privileging of speech in all sites within a system. Using the examples of prefigurative protest, Indigenous refusal to deliberate, and the non-deliberative agency of disabled citizens, I argue that the DS approach allows theorists to better understand forms of domination related to the imposition of speech on those who are either unwilling or unable to speak. (shrink)

How does sign language compare with gesture, on the one hand, and spoken language on the other? Sign was once viewed as nothing more than a system of pictorial gestures without linguistic structure. More recently, researchers have argued that sign is no different from spoken language, with all of the same linguistic structures. The pendulum is currently swinging back toward the view that sign is gestural, or at least has gestural components. The goal of this review is to elucidate the (...) relationships among sign language, gesture, and spoken language. We do so by taking a close look not only at how sign has been studied over the past 50 years, but also at how the spontaneous gestures that accompany speech have been studied. We conclude that signers gesture just as speakers do. Both produce imagistic gestures along with more categorical signs or words. Because at present it is difficult to tell where sign stops and gesture begins, we suggest that sign should not be compared with speech alone but should be compared with speech-plus-gesture. Although it might be easier to blur the distinction between sign and gesture, we argue that distinguishing between sign and gesture is essential to predict certain types of learning and allows us to understand the conditions under which gesture takes on properties of sign, and speech takes on properties of gesture. We end by calling for new technology that may help us better calibrate the borders between sign and gesture. (shrink)

We think we know what healers do: they build on patients' irrational beliefs and treat them in a 'symbolic' way. If they get results, it's thanks to their capacity to listen, rather than any influence on a clinical level. At the same time, we also think we know what modern medicine is: a highly technical and rational process, but one that scarcely listens to patients at all. In this book, ethnopsychiatrist Tobie Nathan and philosopher Isabelle Stengers argue that this commonly (...) posed opposition between traditional and modern medicine is misleading. They show instead that healers are interesting precisely because they don't listen to patients, using techniques of 'divination' rather than 'diagnosis'. Healers construct genuine therapeutic strategies by identifying the origins of symptoms in external forces, outside of the mind of the sufferer, and in this regard African healers are virtuosos. Though it may claim otherwise, modern medicine, for its part, is characterised by empiricism rather than rationality. What appears to be the pursuit of rationality is ultimately only a means to dismiss and exclude other forms of treatment. Blurring the distinctions between traditional and modern practices and drawing on perspectives from across the globe, this ethnopsychiatric manifesto encourages us to think in radically new ways about illness, challenging accepted notions on the relationship between sufferer and symptom. It will be of great interest to those working in medicine and healthcare, as well as anthropologists, social scientists and those in the humanities more broadly. (shrink)

Drawing on theoretical arguments from the psychology discipline, we investigate the implications of employee entitlement in organizational settings. Specifically, we utilize workplace engagement theory to suggest that due to their skewed sense of deservingness, employees high in entitlement are less likely to experience workplace engagement. Furthermore, the negative relationship between employee entitlement and workplace engagement is strengthened when ethical leadership is low, yet mitigated when ethical leadership is high. Finally, we predict that under conditions of low ethical leadership, reductions in (...) engagement explain why employee entitlement results in hindered job performance. This mediated effect does not hold when ethical leadership is high. We tested our theoretical model utilizing field data from employees and their direct supervisors in the financial services industry. Our results support our theoretical model. Theoretical and practical implications are discussed. (shrink)

The fairy tale The Three Princes of Serendip can be taken to be allegorical of not only chance discovery (serendipity) but of other aspects of scientific discovery as well. Just as Horace Walpole coined serendipity, so can the term bahramdipity be derived from the tale and defined as the cruel suppression of a serendipitous discovery. Suppressed, unpublished discoveries are designated nulltiples. Several examples are presented to make the case that bahramdipity is an existent aspect of scientific discovery. Other examples of (...) non-ideal scientific research and discovery are provided in order to contrast and clarify the meaning and use of bahramdipity. Additional allegories of scientific discovery are taken from the tale and a hope for the strengthening of scientific integrity is expressed. (shrink)

A poor understanding of probability may lead people to misinterpret every day coincidences and form anomalistic beliefs. We investigated the relationship between anomalistic beli...

This book argues that it can be both reasonable and appropriate to adopt a certain kind of misanthropy. The author defends a cognitivist version of misanthropy, an attitude whose central feature is the judgment that humanity is morally bad. Misanthropy is often dismissed on moral grounds. Many people hold that malice toward human persons is problematic and vulnerable to moral objections. In this book, the author advocates for cognitivist misanthropy. He defends an Asymmetry Thesis, according to which a morally bad (...) deed carries more weight than a morally good deed, even if the harm of the former is exactly equal to the benefit of the latter. He makes the case that being misanthropic in the cognitivist sense is morally permissible and compatible with a broad range of moral reasons for action. He also considers the role of misanthropy in environmental thought, arguing that charges of misanthropy against certain "non-anthropocentric" views do not have the force they are typically thought to carry. Finally, the author investigates the practical implications of adopting cognitivist misanthropy, asking what living with such an attitude would involve. A Philosophical Defense of Misanthropy will appeal to researchers and advanced students working in ethics and the philosophy of human nature. (shrink)

Objective chance and morality are rarely discussed together. In this paper, I argue that there is a surprising similarity in the epistemic standing of our beliefs about both objective chance and objective morality. The key similarity is that both of these sorts of belief are undermined -- in a limited, but important way -- by plausible genealogical accounts of the concepts that feature in these beliefs. The paper presents a brief account of Richard Joyce's evolutionary hypothesis of the genealogy of (...) morality, and refines the debunking argument which he consequently mounts against moral beliefs. The evolutionary hypothesis in question suggests that we could easily have failed to believe that moral judgments have a peculiarly categorical force. This aspect of our moral belief, then, is unreliable. The paper then turns to chance, and presents a more speculative hypothesis about the cultural evolution of ideas about chance, as a peculiarly physical and objective form of probability. It is argued that, in the same way that our beliefs about morality could easily have lacked the commitment to inescapable force, our beliefs about chance could easily have lacked various idiosyncratic commitments. By a similar argument then, these aspects of our chance beliefs are unreliable. In the final section of the paper, I review some recent objections to genealogical debunking arguments, due to Roger White and Guy Kahane, showing how the form of argument developed in this paper is immune to these criticisms. (shrink)

Shamatha, Transcendental, and Stillness Meditation are said to aim for “contentless” experiences, where mental content such as thoughts, perceptions, and mental images is absent. Silence is understood to be a central feature of those experiences. The main source of information about the experiences is texts by experts from within the three traditions. Previous research has tended not to use an explicit scientific method for selecting and reviewing expert texts on meditation. We have identified evidence synthesis as a robust and transparent (...) method that is suitable for this purpose. In this paper we use evidence synthesis based on expert texts to examine silence/quietness as a feature of the contentless experiences in the three practices. Objective criteria were used to select a sample of 135 expert texts. A database containing the expert descriptions of the meditation techniques and experiences was produced by extracting the relevant material from the publications and coding that material to differentiate individual features. The database, which forms part of the supplementary material for this paper, identifies each feature of the contentless experiences referred to in the expert texts, including silence/quietness. Our key finding is that the experts indicate silence/quietness has a particular connection with stillness, and the absence of concepts, mental activity/noise, thoughts, and disturbance. Further analysis leads to the following insights. The silence/quietness reflects the absence of thoughts and sounds, and this fits neatly with a conception of silence/quietness as the absence of internal and external noise. In some cases the terms silence and quietness may also reflect the absence of other disturbances such as non-auditory perceptions, mental images, and negative feelings. That would fit with a conception of silence/quietness as complete calm or absence of disturbance. It is not clear from the expert texts how silence/quietness is distinct from other features such as stillness that also reflect the absence of disturbances. As a separate matter, silence/quietness has connections with all the other features of the contentless experiences, but the closeness of the connections varies. Our work uncovers fine distinctions and ambiguities which lead to new research questions that can be explored in future studies. (shrink)

The binary between the figure of the child and the fully human being is invoked with regularity in analyses of race, yet its centrality to the conception of race has never been fully explored. For most commentators, the figure of the child operates as a metaphoric or rhetorical trope, a non-essential strategic tool in the perpetuation of White supremacy. As I show in the following, the child/human binary does not present a contingent or merely rhetorical construction but, rather, a central (...) feature of racialization. Where Black peoples are situated as objects of violence it is often precisely because Blackness has been identified with childhood and childhood is historically identified as the archetypal site of naturalized violence and servitude. I proceed by offering a historical account of how Black peoples came to inherit the subordination and dehumanization of European childhood and how White youth were subsequently spared through their partial categorization as adults. (shrink)

In this article, I outline the major themes of ‘anti-theodicy’. Anti-theodicy is characterised as a reaction, as rejection, against traditional solutions to the problem of evil and against the traditional formulations of the problem of evil to which those solutions respond. I detail numerous ‘moral’ anti-theodical objections to theodicy, illustrating the central claim of anti-theodicy: Theodicy is morally objectionable. I also detail some ‘non-moral’ anti-theodical objections, illustrating the second major claim of anti-theodicy: Traditional formulations of the problem of evil are (...) conceptually misguided. My focus remains on the analytic philosophical tradition throughout, but I briefly allude to the rich theological tradition of anti-theodicy. Although we should recognise the significant degree of diversity amongst anti-theodical arguments and the philosophical views of their proponents, this article should serve to illustrate the general theme: ‘Theodicies mediate a praxis that sanctions evil.’. (shrink)

It is often claimed that from the moment of conception embryos have the same moral status as adult humans. This claim plays a central role in many arguments against abortion, in vitro fertilization, and stem cell research. In what follows, I show that this claim leads directly to an unexpected and unwelcome conclusion: that natural embryo loss is one of the greatest problems of our time and that we must do almost everything in our power to prevent it. I examine (...) the responses available to those who hold that embryos have full moral status and conclude that they cannot avoid the force of this argument without giving up this key claim. (shrink)