Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

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

I argue that Plato's purpose in the discussion of false belief in the "Theaetetus" is to entertain and then to reject the idea that thinking is a kind of mental grasping. The interpretation allows us to make good sense of Plato's discussion of 'other-judging' (189c-190e), of his remarks about mathematical error (195d-196c), and most importantly, of the initial statement of the puzzle about falsity (188a-c). That puzzle shows that if we insist on conceiving of the relation between thought and its (...) objects on the model of holding or grasping something in our hands, we will be unable to account for the possibility of false identity judgments: For no one who is literally grasping two things in his hands would seriously entertain the idea that one of the things is numerically identical with the other. (shrink)

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

I argue that Plato's purpose in the discussion of false belief in the "Theaetetus" is to entertain and then to reject the idea that thinking is a kind of mental grasping. The interpretation allows us to make good sense of Plato's discussion of 'other-judging' (189c-190e), of his remarks about mathematical error (195d-196c), and most importantly, of the initial statement of the puzzle about falsity (188a-c). That puzzle shows that if we insist on conceiving of the relation between thought and its (...) objects on the model of holding or grasping something in our hands, we will be unable to account for the possibility of false identity judgments: For no one who is literally grasping two things in his hands would seriously entertain the idea that one of the things is numerically identical with the other. (shrink)

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

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

For Slavoj Zizek the empty place or void stands for ‘Drive/Death Drive’: “a drive is not a primordial, positive force but a purely geometrical, topological phenomenon, the name for the curvature of the space of desire.” (Zizek 2005: 361) This paper examines this ‘empty space’ in two recent cultural texts relating to Taiwan: one a multi-media presentation at the Taipei Biennial and the other the movie, Orz Boyz. The connecting topology belongs to the topography of islands found in the rivers (...) of Taipei. Both the film and the multi-media project make explicit use of the islands in ways which this paper relates to the psychoanalytic project of Zizek/Lacan. The possible discourses, besides psychoanalysis emerging from these two cultural objects are outlined, but in particular the notion of childhood and underdevelopment/overdevelopment are discussed. From this vantage point, childhood/drive and the symbolic order this paper examines the current predicament of Taiwan from a psychoanalytic point of view. (shrink)

This collection brings together eleven of Fodor's recent essays about mental content and cognitive processing. All of them have been previously published, save for the title-essays "A Theory of Content I" and "A Theory of Content II.".

This book addresses the challenges of living together after empire in many post-colonial cities. It is organized in two sections. The first section focuses on efforts by people of multiple faiths to live together within their contexts, including such efforts within a neighborhood in urban Manchester; the array of attempts at creating multi-faith spaces for worship across the globe; and initiatives to commemorate divisive conflict together in Northern Ireland. The second section utilizes particular postcolonial methods to illuminate pressing issues within (...) specific contexts—including women’s leadership in an indigenous denomination in the variegated African landscape, and baptism and discipleship among Dalit communities in India. In the context of growing multiculturalism in the West, this volume offers a postcolonial theological resource, challenging the epistemologies in the Western academy. (shrink)

John Barton is convinced that in many areas of ethical enquiry the Old Testament has much to teach us, and he argues his case in this new book, which developed out of lectures given both in Canada and in Oxford. During it he looks again at the Ten Commandments; the narrative about David and his children; the ethical issues of ecology, sexual morality and property; human morality as the express command of God; and the motivation for moral conduct. (...) By the end of the book it is clear that although the Old Testament comes to us from a remote, alien and apparently unsophisticated context, the powerful minds who worked on its books still have things to say which remain evocative and suggestive for our own moral enquiries. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Echoes of Romanticism and Expatriate Englishness in Charlotte Brontë's The ProfessorDavid SiglerCharlotte Brontë's many debts to Romanticism, and especially Lord Byron, are a well-known feature of her fiction. Yet only recently has this become an important part of the discussion surrounding The Professor, her first-written and last-published novel. The novel, written between 1844 and 1846 and published posthumously in 1857, is increasingly seen to be in dialogue with William (...) Wordsworth and Walter Scott, in addition to Byron. Anna Barton, seeing Brontë as "the pupil of Wordsworthian Romanticism" and "a daughter of Romanticism," shows how The Professor develops "intertextual exchanges that perform the failure of the Romantic lyric within the Victorian novel."1 Tanya Llewellyn has argued that the protagonist William Crimsworth, seemingly influenced by Byron's Turkish tales, Orientalizes the women in his life as a way to manage sexual threats.2 Mandy Swann, meanwhile, sees in Brontë's early work an ambivalent response to the Romantic figure of the poet-prophet, as part of the author's general struggle, early in her career, to theorize female creativity.3Yet in other recent accounts, William Crimsworth seems to be as un-Byronic and un-Wordsworthian as possible. Crimsworth has been said to be a "particularly off-putting" narrator, "defensive and humourless," whose "dubious masculinity," passionlessness, and, in one reading, stiflingly repressed homosexuality render him a comically overliteral thinker.4 I will suggest that this incapacity in him for meaningful human engagement is what leads him to fixate on British Romantic poetry as a solution, however backhanded, to his erotic and professional difficulties. [End Page 30] Yet as the echoes of Romanticism that haunt his erotic and professional relations quickly take on lives of their own, they enable the story, and its ethical vision, to exceed William's control. Once the novel directs its protagonist's obsessive personality in the direction of Romantic poetry, it can become an intriguing meditation on ethics, expatriate Englishness, and time.William Crimsworth is a hardworking Englishman living and working in Brussels. The city, which William finds too "cosmopolitan," becomes the site of his zealous self-exploration as he mingles, ever defensively, with the locals.5 Approaching the city like "a morning traveller," as he puts it, William must analyze his foreignness if he is to survive his own residual and aspirational Englishness.6 The phrase "morning traveller" is drawn from Robert Southey's 1798 poem "The Traveller's Return," which describes love as an echo-effect. It is a very auditory poem: Southey's "morning traveller" spends the day listening to unfamiliar sounds, until, in the evening, he hears a "distant sheep-bell," which teaches him that "sweetest is the voice of Love / That welcomes his return."7 A sheep bell is, of course, a tracking mechanism, facilitating the free movement and eventual return of sheep to a shepherd. Southey's speaker learns to grasp the hidden similarity between love and the sheep bell. Just as the sound of the bell goes away and comes back, signifying the wandering and return of livestock, the human "morning traveller" must begin to identify with it. He himself, hearing the sound, gets interpellated by it, once it becomes his objective correlative. Brontë's The Professor, in matters of love, uses Romantic poetry, including Southey's, as a similar tracking device for William. The echo it produces constantly and ambivalently connects the protagonist to England and secures his place within the ideological apparatuses of the state.Judith Butler has observed that "my own foreignness to myself is, paradoxically, the source of my ethical connection with others."8 She explains that because there are aspects of oneself that remain forever baffling and inexplicable, we should suppose that other people—who can also seem foreign and inexplicable—contain similar aporias. If their accounts of themselves are difficult for us to understand, we should recognize, through our inability to sympathize, that we too are surely baffling and that they, like us, are likely also baffling to themselves. Thus, [End Page 31] through the sheer dubiousness of understanding other people, we can achieve a kind of negative shared humanity. We all probably confront an inassimilable kernel... (shrink)

Fr. Frank Oppenheim’s body of work dedicated to the philosophy of Josiah Royce exhibits a degree of objectivity and admiration not evidenced in philosophical circles since Ralph Barton Perry’s magisterial The Thought and Character of William James.1 Royce once derisively referred to his own system Σ as akin to a Boston attic—a “junk heap” in which everything is there, but best of luck in getting anything out! It is helpful to consider the entire body of Oppenheim’s Royce-work as the (...) combination of a “Boston attic” and the most ideal image of the “kitchen sink”—the contents not only all there, but neatly separated, perfectly arranged, and brilliantly displayed. The purpose of this essay is to situate Oppenheim’s... (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)

In this book, which thoroughly revises and greatly expands his classic work Sameness and Substance, David Wiggins retrieves and refurbishes in the light of twentieth-century logic and logical theory certain conceptions of identity, of substance and of persistence through change that philosophy inherits from its past. In this new version, he vindicates the absoluteness, necessity, determinateness and all or nothing character of identity against rival conceptions. He defends a form of essentialism that he calls individuative essentialism, and then a (...) form of realism that he calls conceptualist realism. In a final chapter he advocates a human being-based conception of the identity and individuation of persons, arguing that any satisfactory account of personal memory must make reference to the life of the rememberer himself. This important book will appeal to a wide range of readers in metaphysics, philosophical logic, and analytic philosophy. (shrink)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative (...) principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

A collection of 14 essays honoring the life and work of Oxford philosopher Wiggins touching on topics from ancient philosophy to ethics, metaphysics and the theory of meaning. The contributing scholars debate many of the seminal issues of Wiggins' work, including the determinancy of distinctness, relative identity, naturalism in ethics, logic and truth in moral judgments, and the practical wisdom of Aristotle. The collection uniquely features replies by Wiggins to each of the papers. Annotation copyright by Book News, Inc., Portland, (...) OR. (shrink)

Drawing on work of the past decade, this volume brings together articles from the philosophy, history, and sociology of science, and many other branches of the biological sciences. The volume delves into the latest theoretical controversies as well as burning questions of contemporary social importance. The issues considered include the nature of evolutionary theory, biology and ethics, the challenge from religion, and the social implications of biology today (in particular the Human Genome Project).

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they come out both (...) necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>. (shrink)

Discusses a variety of ways mankind is cruel to animals.

This book documents Szilard's energetic attempts to influence public policy on arms control and disarmament issues, both through open political processes and statements and through behindthe-scenes contacts with Washington power sources and a remarkable exercise in personal diplomacy with Nikita Khrushchev. Leo Szilard conceived of the possibility of nuclear fission sustained by a chain reaction years before it was achieved in the laboratory. He was also one of the initiators of the atomic bomb project in the United States. Yet he (...) dedicated his final years to the causes of understanding and sustaining life. The eminent physicist became a biologist and a vital force calling, for the control of nuclear and other weapons. This book documents Szilard's energetic attempts to influence public policy on arms control and disarmament issues, both through open political processes and statements and through behindthe-scenes contacts with Washington power sources and a remarkable exercise in personal diplomacy with Nikita Khrushchev. Many of the issues Szilard deals with in this valuable record of the years 1947-1963 are still crucial today. His opposition to antiballistic missile systems, his proposal for a Washington-Moscow "hot line," his work on the Pugwash conferences that brought together scientists from the East and the West, his pivotal role in the creation of the Council for a Livable World, his advocacy of a nuclear policy of no-first-use and restricted retaliation, and his support of "minimum deterrence" in place of an overwhelming counterforce capability - all these matters are as important in the 1980s as they were in the 1950s and 1960s. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

The typical kind of color realism is reductive: the color properties are identified with properties specified in other terms (as ways of altering light, for instance). If no reductive analysis is available — if the colors are primitive sui generis properties — this is often taken to be a convincing argument for eliminativism. That is, realist primitivism is usually thought to be untenable. The realist preference for reductive theories of color over the last few decades is particularly striking in light (...) of the generally anti-reductionist mood of recent philosophy of mind. The parallels between the mind—body problem and the case of color are substantial enough that the difference in trajectory is surprising. While dualism and non-reductive physicalism are staples, realist primitivism is by and large a recent addition to the color literature. And it remains a minority position, although one that is perhaps gaining support. In this paper, we investigate whether it should be accepted, and conclude it should not be. (shrink)

Although widespread throughout the biomedical sciences, the practice of honorary authorship—the listing of authors who fail to merit inclusion as authors by authorship criteria—has received relatively little sustained attention. Is there something wrong with honorary authorship, or is it only a problem when used in conjunction with other unethical authorship practices like ghostwriting? Numerous sets of authorship guidelines discourage the practice, but its ubiquity throughout biomedicine suggests that there is a need to say more about honorary authorship. Despite its general (...) acceptance among many scientists, honorary authorship is unethical. Even if burdensome, responsible researchers are obligated to forgo honorary authorship. (shrink)

Today’s fast-moving, media lifeworld embodies many of the metaphors of its analog predecessors – including those of warfare and conflict. The metaphor of warfare is used to describe everything from corporate marketing strategies to political campaigns, often with harmful consequences. In one way of exploring the front lines of the resulting war on truth, we describe some lessons learned from the experience of military veterans who have actually endured the liminality of combat, and who emerge with what is increasingly termed (...) moral injuries. We use their experience as an analogy for competing narratives in cyberspace, where objective standards of truth and facticity are apparent casualties, and where fake news is emerging as victorious. We then apply models of social construction, specifically the practical theory of the Coordinated Management of Meaning, and the metaphor of jazz improvisation in the context of Schutz’s lifeworld phenomenology as possibly useful, helpful, and hopeful ways of acting into the complexity of truth together. (shrink)

Near the end of the Amherst Cofloquium on “Nietzsche Today: The Reception of his Work after 1968,” Geoff Waite challenged the underlying historical assumption: “Is 1968 chosen because it marks the approximate date of the publication of the first volume of the splendid critical edition of Nietzsche's work by Colli and Montinari, or rather the approximate date of the until recently wholly apolitical appropriation of Nietzsche by post-structuralism? Do we wish to allude to die year of the Zagreb meeting on (...) Nietzsche of “creative Marxists” trying, as they said, to locate “the theme of human freedom in Nietzsche,” or rather to the year that Jiirgen Habermas delivered himself of the opinion that “Nietzsche is no longer contagious?” For some of us, however, 1968 has to mean also and mainly May '68.”. (shrink)

Cimino's The Deer Hunter is a mass culture product that sells. It is a conventional, manipulative Hollywood movie that moves large U.S. audiences. In trying to identify the ideological function of this film, Leibowitz has compared The Deer Hunter to Nazi ideology or German Romantic nationalist aesthetics. This comparison, however, says little about the film itself. To invoke this German tradition is to do little more than to invoke the roots of the modern culture industry in general. The Nazis are (...) only unique in that they succeeded early in blending propaganda, violence, pornography, religion and a consumer mentality in a mechanism of cultural manipulation. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Although popular, I argue that the International Committee of Medical Journal Editors (ICMJE) account of authorship is flawed. It inadvertently allows for practices that it was designed to prevent. In addition, it creates a new category of authorless papers—orphan papers. The original World Association of Medical Editors (WAME) criterion is preferable.