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)

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)

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)

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)

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)

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)

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.".

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)

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)

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)

Oxford Philosophical Texts Series Editor: John Cottingham The Oxford Philosophical Texts series consists of authoritative teaching editions of canonical texts in the history of philosophy from the ancient world down to modern times. Each volume provides a clear, well laid out text together with a comprehensive introduction by a leading specialist, giving the student detailed critical guidance on the intellectual context of the work and the structure and philosophical importance of the main arguments. Endnotes are supplied which provide further commentary (...) on the arguments and explain unfamiliar references and terminology, and a full bibliography and index are also included. The series aims to build up a definitive corpus of key texts in the Western philosophical tradition, which will form a reliable and enduring resource for students and teachers alike. David Hume's aim in writing An Enquiry concerning Human Understanding was to introduce his philosophy to a European culture in which many educated people read original works of philosophy. He gives an elegant and accessible presentation of strikingly original and challenging views about the limited powers of human understanding, the attractions of scepticism, the compatibility of free will and determinism, and weaknesses in the foundations of religion. Hume's philosophy was highly controversial in the eighteenth century and remains so today. The text printed in this edition is that of the Clarendon critical edition of Hume's works. A substantial introduction by the editor explains the intellectual background to the work and surveys its main themes. The volume also includes detailed explanatory notes on the text, a glossary of terms, a full list of references, and a section of supplementary readings. (shrink)

Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make (...) some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous. (shrink)

Discusses a variety of ways mankind is cruel to animals.

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

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

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

From religion to philosophy to science, all human systems of definition are formed by human brains. The nature and limits of the human brain are the nature and limits of those systems. This essay shows how the human brain works normally then unusually, and what this reveals about the limits of human knowledge. There are many conditions and instances where the brain processes information unusually, including mental disorders, physical events, and drug use. This essay focuses on the neurological events called (...) mystical experiences. (shrink)

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)

One of the most lasting contributions of Marr's posthumous book is his articulation of the different “levels of analysis” that are needed to understand vision. Although a variety of work has examined how these different levels are related, there is comparatively little examination of the assumptions on which his proposed levels rest, or the plausibility of the approach Marr articulated given those assumptions. Marr placed particular significance on computational level theory, which specifies the “goal” of a computation, its appropriateness for (...) solving a particular problem, and the logic by which it can be carried out. The structure of computational level theory is inherently teleological: What the brain does is described in terms of its purpose. I argue that computational level theory, and the reverse-engineering approach it inspires, requires understanding the historical trajectory that gave rise to functional capacities that can be meaningfully attributed with some sense of purpose or goal, that is, a reconstruction of the fitness function on which natural selection acted in shaping our visual abilities. I argue that this reconstruction is required to distinguish abilities shaped by natural selection—“natural tasks” —from evolutionary “by-products”, rather than merely demonstrating that computational goals can be embedded in a Bayesian model that renders a particular behavior or process rational. (shrink)

This short peer-reviewed text is a concise look at the psychology of how human beings make decisions, including how they form their worldviews and make arguments.

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

Although written consent forms are standard in clinical research, there is little regulatory or empirical guidance regarding how to most effectively review consent forms with potential participants. We developed an algorithm for embedding five questions with corrective feedback while reading consent forms with potential participants, and then applied it in the context of seven clinical research studies. A substantial proportion of participants within each protocol displayed initially inadequate responses to at least one question, but after the protocol elements were explained (...) again, most people demonstrated adequate understanding of them. These data illustrate the need for more attention not just to the content of consent forms, but also to the manner in which the forms are incorporated into the consent process. Embedding explicit inquiries about key protocol elements during consent form review and giving corrective feedback appears to be a simple yet effective way to foster better understanding of disclosed information. (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)

Various U.S. laws, such as the Clean Air Act and the Food Quality Protection Act, require additional protections for susceptible subpopulations who face greater environmental health risks. The main ethical rationale for providing these protections is to ensure that environmental health risks are distributed fairly. In this article, we (1) consider how several influential theories of justice deal with issues related to the distribution of environmental health risks; (2) show that these theories often fail to provide specific guidance concerning policy (...) choices; and (3) argue that an approach to public decision making known as accountability for reasonableness can complement theories of justice in establishing acceptable environmental health risks for the general population and susceptible subpopulations. Since accountability for reasonableness focuses on the fairness of the decision-making process, not the outcome, it does not guarantee that susceptible subpopulations will receive a maximum level of protection, regardless of costs or other morally relevant considerations. (shrink)

Part of the appeal of the biological approach to personal identity is that it does not have to countenance spatially coincident entities. But if the termination thesis is correct and the organism ceases to exist at death, then it appears that the corpse is a dead body that earlier was a living body and distinct from but spatially coincident with the organism. If the organism is identified with the body, then the unwelcome spatial coincidence could perhaps be avoided. It is (...) argued that such an identification would be a mistake. A living organism has a different part/whole relationship and persistence conditions than the alleged body. A case will be made that the concept ‘human body’ is a conceptual mess, vague in an unprincipled manner, and that an eliminativist stance towards dead bodies is the appropriate response. CiteULike Connotea Del.icio.us What's this? (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.