: Studies of Chinese dialectical materialism have long neglected the important philosophical dimension of Hegelian thought and its influence on Chinese Marxism. This essay examines the work of Zhang Shiying of Beijing University, whose studies of Hegel's works on dialectical logic in the 1950s sought to clarify the nature of Hegel's speculative dialectic and its relation to dialectical materialism. Like Lenin before him, Zhang believed that Hegel's works on logic offered a more profound reflection on materialism than had previously been (...) recognized by Marxist critics of German idealism. Zhang's sensitive reading of both Hegel's Science of Logic and the Encyclopedia Logic highlights the problem of the speculative dialectic and negativity. Examined here is Zhang's analysis of the Hegelian dialectic in light of contemporary accounts of the role of Hegelian negativity in poststructuralist thought. (shrink)

Fundamental movement skill proficiency does not develop solely due to maturation, but also via diverse perceptual-motor experiences across childhood. Practicing gymnastics has been shown to improve postural control. The purpose of the present study was to examine potential changes to postural control of children following a course of educational gymnastics. Two groups of children both completed 20 × 45-min physical education lessons; one group completed educational gymnastics lessons in school delivered by a professional coach, the other group completed their typical (...) PE classes. Unipedal balancing performance was assessed by calculating the percentage of successful trials made. Postural sway dynamics were explored by calculating center-of-pressure sample entropy, 95% ellipse sway area and sway velocity. Measurements were taken before the lessons began and immediately after the lessons were completed. The gymnastics group performed better than the typical PE group at unipedal balancing. Females outperformed males in both groups. Males made different changes to postural control compared to females across 3 months. Educational gymnastics enabled children in a critical period of development to make more rapid improvements to postural performance and control. Novel movement experiences, like those offered by educational gymnastics, may have a positive influence on postural control and importantly, physical literacy. Future work should examine how sex effects the development of postural control strategies in young children. (shrink)

This article explores the neglected idea of fate in Simmel’s thought. It examines the specific definition of fate present in Simmel’s writings and the relation of this definition to tragic drama. The argument operates under the assumption that tragic drama represents the ‘natural habitat’ for the exploration and expression of the fate problematic. In this context, it is argued that Simmel’s rediscovery of the relevance of fate emphasizes the modernity of tragedy. The article explores Simmel’s translation of fate from drama (...) and philosophy into sociology, but into a sociology replete with a distinctly existential and metaphysical consciousness. It is argued that Simmel’s application of fate to modern social life constitutes a sociologization of fate, but that rather than involving a reduction of fate to society, this sociologization actually involves a form of re-enchantment of the social through life. In relation to this sociologization and building on the argument of Peter Baehr, it is argued that the concept of fate is uniquely endowed with a capacity to encourage a sense of pathos conducive to the development of a reflexive and critical sense of collective social responsibility and of shared future. In this regard, the article examines Simmel’s engagement with Naturalist tragedy and the transition from ancient to modern drama. Throughout, it is argued that the experience of modernity, where ‘all that is solid melts into air’, is conducive to a rediscovery of the relevance of fate and tragedy. (shrink)

BABAR, the detector for the SLAC PEP-II asymmetric e+e- B Factory operating at the γ resonance, was designed to allow comprehensive studies of CP-violation in B-meson decays. Charged particle tracks are measured in a multi-layer silicon vertex tracker surrounded by a cylindrical wire drift chamber. Electromagnetic showers from electrons and photons are detected in an array of CsI crystals located just inside the solenoidal coil of a superconducting magnet. Muons and neutral hadrons are identified by arrays of resistive plate chambers (...) inserted into gaps in the steel flux return of the magnet. Charged hadrons are identified by dE/dx measurements in the tracking detectors and by a ring-imaging Cherenkov detector surrounding the drift chamber. The trigger, data acquisition and data-monitoring systems, VME- and network-based, are controlled by custom-designed online software. Details of the layout and performance of the detector components and their associated electronics and software are presented. © 2002 Elsevier Science B.V. All rights reserved. (shrink)

Intuition—spontaneous, nondeliberative assessment—has long been indispensable in theoretical and practical philosophy alike. Recent research by psychologists and experimental philosophers has challenged our understanding of the nature and authority of moral intuitions by tracing them to “fast,” “automatic,” “button-pushing” responses of the affective system. This view of the affective system contrasts with a growing body of research in affective neuroscience which suggests that it is instead a flexible learning system that generates and updates a multidimensional evaluative landscape to guide decision (...) and action. With this latter view in mind, I revisit some of the classic hypothetical scenarios used in experimental moral psychology. (shrink)

On any given night cable TV news will tell us how polarized American politics is: Republicans are from Mars, Democrats are from Canada. But in fact, writes Peter Wenz in _Beyond Red and Blue_, Americans do not divide neatly into two ideological camps of red/blue, Republican/Democrat, right/left. In real life, as Wenz shows, different ideologies can converge on certain issues; people from the right and left can support the same policy for different reasons. Thus, for example, libertarian-leaning Republicans can (...) oppose the Patriot Act's encroachment on personal freedom and social conservatives can support gay marriage on the grounds that it strengthens the institution of marriage. Wenz maps out twelve political philosophies--ranging from theocracy and free-market conservatism to feminism and cosmopolitanism--on which Americans draw when taking political positions. He then turns his focus to some of America's most controversial issues and shows how ideologically diverse coalitions can emerge on such hot-button topics as extending life by artificial means, the war on drugs, the war on terrorism, affirmative action, abortion, same-sex marriage, health care, immigration, and globalization. Awareness of these twelve political philosophies, Wenz argues, can help activists enlist allies, citizens better understand politics and elections, and all of us define our own political identities. (shrink)

Our ability to rapidly distinguish new from already stored information is important for behavior and decision making, but the underlying processes remain unclear. Here, we tested the hypothesis that contextual cues lead to a preselection of information and, therefore, faster recognition. Specifically, on the basis of previous modeling work, we hypothesized that recognition time depends on the amount of relevant content stored in long-term memory, i.e., set size, and we explored possible age-related changes of this relationship in older humans. In (...) our paradigm, subjects learned by heart four different word lists written in different colors. On the day of testing, a color cue indicated with a probability of 50% that a subsequent word might be from the corresponding list or from a list of new words. The old/new status of the word had to be distinguished via button press. As a main finding, we can show in a sample of n = 49 subjects, including 26 younger and 23 older humans, that response times increased linearly and logarithmically as a function of set size in both age groups. Conversely, corrected hit rates decreased as a function of set size with no statistically significant differences between both age groups. As such, our findings provide empirical evidence that contextual information can lead to a preselection of relevant information stored in long-term memory to promote efficient recognition, possibly by cyclical top-down and bottom-up processing. (shrink)

Tendencies of approach and avoidance seem to be a universal characteristic of humans. Specifically, individuals are faster in avoiding than in approaching negative stimuli and they are faster in approaching than in avoiding positive stimuli. The existence of this automatic approach-avoidance bias has been demonstrated in many studies. Furthermore, this bias is thought to play a key role in psychiatric disorders like drug addiction and phobias. However, its mechanisms are far from clear. Theories of embodied cognition postulate that the nature (...) of gestures plays a key role in this process. To shed light on the role of the involved gesture we employed a 2 × 2 factorial design with two types of stimuli. Participants had either to approach positive and avoid negative stimuli or to avoid positive stimuli and approach negative stimuli. Further, they responded either with a joystick or a button press on a response pad. Participants reacted faster in congruent conditions, i.e., avoiding negative stimuli and approaching positive stimuli, than in incongruent conditions. This replicates the known approach and avoidance bias. However, direct analysis of the button press condition revealed no reaction time advantage for congruent trials compared to incongruent trials. In contrast, in the joystick condition participants were significantly faster performing congruent reactions than incongruent reactions. This interaction, a significant reaction time advantage, when the response is enacted by moving a joystick towards or away from the body provides evidence that approach-avoidance tendencies have a crucial bodily component. (shrink)

Embodiment approaches to cognition and emotion have put forth the idea that the way we think and talk about affective events often recruits spatial information that stems, to some extent, from our bodily experiences. For example, metaphorical expressions such as “being someone’s right hand” or “leaving something bad behind” convey affectivity associated with the lateral and sagittal dimensions of space. Action tendencies associated with affect such as the directional fluency of hand movements (dominant right hand-side – positive; non-dominant left hand-side (...) – negative) and approach-avoidance behaviors (forward – positive; backwards – negative) might be mechanisms supporting such associations. Against this background, experimental research has investigated whether positive and negative words are freely allocated into space (e.g., close or far from one’s body) or resonate with congruent (vs. incongruent) predefined manual actions usually performed by joysticks or button presses (e.g., positive - right; negative - left, or vice versa). However, to date, it is unclear how the processing of affective concepts resonate with directional actions of the whole body that are performed freely within a context enabling lateral and sagittal movements simultaneously. Accordingly, 67 right-handed participants were to freely step on an 8-response pad (front, back, right, left, front-right, front-left, back-right, or back-left) after being presented in front of them valence-laden personal life-events submitted before the task (e.g., words or sentences such as “graduation” or “birth of a child”). The most revealing finding of this study indicates that approach-avoidance behaviors and space-valence associations across laterality are interwoven during whole body step actions: Positive events induced steps highly biased to front-right whereas negative events induced steps highly biased to back-left. (shrink)

Peter Emberley is one of Canada's leading scholars writing on issues linking education and philosophy. This dense, very erudite work could be seen as the high counterpart to his two more popular books on similar themes, Bankrupt Education: The Decline of Liberal Education in Canada and Zero Tolerance: Hot Button Politics in Canada's Universities.

In lieu of an abstract, here is a brief excerpt of the content:Reading Audio BooksWilliam IrwinI hide my audio book habit because most of my colleagues, and even some of my snobbier students, regard audio books as a sign of an impending dark age of mass illiteracy. Feeling uneasy, I wonder: when The Brothers Karamazov comes up in conversation am I obliged to "confess" that I listened to the unabridged audio book, but did not silently read the massive tome? Is (...) there a difference that makes a difference between listening to an audio book and reading a printed book?IPeople read less today, partly because reading silently is not social; we crave the company of loved ones at the end of the day, and so prefer to watch television with them. Silent reading does not fit today's multitasking lifestyle; you can listen to music while you drive or jog, but you cannot read a book. Or, then again, perhaps you can, if listening to an audio book is reading after all. Time does not need to be specifically set aside for an audio book the way it does with a conventional book—the lights don't even have to be on. And surprisingly, it is satisfying to listen to a book ten minutes at a time while running errands. Perhaps this is because getting started is as easy as pressing a button. By contrast, few people read printed books in ten minute blocks, presumably because it takes something for most people to warm up to reading. If they are going to read, then they are going to do it for a sustained time—something longer than a ten-minute block. It is easier to "push through" and finish an audio book. I nearly gave up on Catch-22; it's too thick and over the top with satire for my taste. And I surely would have given up on it if I had been reading the book silently. I stuck with [End Page 358] the audio book, however, largely because it was easy to continue; I just pressed play every time I got in my car.Books on tape have been available for quite some time, but, despite often being abridged, they were too clunky and cumbersome for most people. The availability of books on CD and for MP3 download makes it all much more convenient. Audio books are now the fastest growing segment of the book industry and are likely to become even more common and popular, perhaps some day eclipsing the sale of conventional books, perhaps some day becoming the normal way of "reading" literature. And far from being abridged, some audio books today include extras. For example, the audio version of The Amber Spyglass includes epigrams before each chapter that are not in the print version.IIHarold Bloom says, "Deep reading really demands the inner ear as well as the outer ear. You need the whole cognitive process, that part of you which is open to wisdom. You need the text in front of you."1 Before listening to audio books myself I would have agreed with Bloom; but now I suspect he simply has never listened to an audio book. Skeptical of literature on audio, I started my audio experience with nonfiction. Pleasantly surprised with nonfiction, I tried listening to fiction and found the presentation very different. Nonfiction books are simply read, whereas works of fiction are typically performed—characters get distinct voices and the reader really puts on a show. Most audio book performances of literature are much like a one-man play, taking us back to the days of traveling bards and rhapsodes.In The Performance of Reading Peter Kivy highlights that for most of its history Western literature has been experienced out loud.2 As is well known, Homer's Iliad and Odyssey were performed out loud by bards, as Beowulf was centuries later. But less well known is the fact that even after the invention of the printing press, when books were still scarce and expensive, even people in possession of books generally read them out loud to themselves and to others. So it is odd that along with Harold Bloom, my colleagues and students, look with mistrust at... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Reinventing the Wheel: A Buddhist Response to the Information AgeMichael C. BarnhartReinventing the Wheel: A Buddhist Response to the Information Age. By Peter D. Hershock. Albany: State University of New York Press, 1999. Pp. xi + 308.Perhaps one of the most interesting, paradoxical, and—in Peter Hershock's way of thinking, in Reinventing the Wheel: A Buddhist Response to the Information Age — predictable aspects of the digital (...) "revolution" is the degree to which information technology becomes less a means to an end and more an end in itself. Take, for example, the humble phenomenon of the "techno-bore." Such people, having acquired some new electronic gizmo, spend all their time talking about the thing, especially savoring such conversations with like-minded techno-bores, who go on in equal and endless length about their latest toys. Rather than becoming a tool for organizing one's affairs, the digital assistant becomes one's main affair. Or, consider the case of the Internet. Although the "Web" is supposed to put us in touch with each other, say, by making e-mail possible, we find ourselves either unable to cope with the avalanche of mail that comes over the portal and thus unable to respond to it all (or at all), or we spend much more time on our mail than we ever did, thus making the mail itself a nuisance and consequently much less useful than formerly.Of course, none of this is unique to computers and the digital workplace. The same complaints have been voiced in regard to cars, television (and radio, too), modern medicine, and industrialization—in fact, the whole gamut of innovations that we label "technology." Indeed, although information technology is Hershock's main target, it represents only the perfection of a form that has been developing for some time and which he often refers to with the phrase "technologies of control." That is, cars, televisions, blenders, can openers, and computers are tools that are put to use in order to make our lives easier; they accomplish this purpose by putting some element of the world, some range of things, more directly under our control and, importantly, by limiting our involvement with them as well. We make things more tractable, more subject to our wanting (as distinct, Hershock says, from our desiring, which involves an element of respect for the desired), and thus more an extension of ourselves rather than obdurate and resistant things. For example, insofar as a sledgehammer makes breaking rocks easier, it makes rocks and their sizes and shapes more a function of our will, less a reflection of their nature, and distances us also from the material thing. To touch a rock with one's hands is an entirely different experience, a much more intimate experience than touching it with a hammer. In a curious way, says Hershock, the rock becomes more "iconic." In other words, it becomes more representation—our representation—and less a thing-in-itself. The computer and its screen "icons" simply push this envelope to its logical end, reducing all things to "buttons" that can be pushed at will, as our wants dictate. [End Page 414]The more things become iconic, the more they become an extension of our will. But the more they become an extension of our will, the more they become "us." That is, insofar as I successfully "technologize" my world, the more my world becomes simply a reflection of what I want. The situation is not so different from that of the absolute dictator who purges all dissenting voices from his or her realm. The realm becomes the leader—Stalin's Russia or Hitler's Germany, for example. And as we well know from Orwell, such power corrupts absolutely and completely, corrupts both the ruler and the ruled, reducing citizens and ruler to an infantile level. Two related phenomena attend such a development, Hershock tells us: narcissism and nihilism. We become more narcissistic because we become more obsessed with our wants as a reflection of our world. We become more nihilistic because our world of wants is intrinsically meaningless: it reflects what we want, not why we want it, no larger purpose. In short... (shrink)

We will all have sometimes cried out, while running between the bedroom and the bathroom, in the morning, as did King Peter of Georg Buechner’s Leonce und Lena: “But where is my shirt? and my trousers? Halt, few! Free will is here all open in front of me. Where are morals? Where are my cuffs? The categories are in the most scandalous confusion : two more buttons are sewn on, the snuff-box is stuck in the right pocket; my whole (...) system is in disarray.”. (shrink)

Philosophy and model theory frequently meet one another. Philosophy and Model Theory aims to understand their interactions -/- Model theory is used in every ‘theoretical’ branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant mathematical results are found only in mathematics textbooks: these are aimed squarely at mathematicians; (...) they typically presuppose that the reader has a significant background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are then scattered across disconnected pockets of papers, separated by decades or more. -/- The first aim of Philosophy and Model Theory, then, is to consider the philosophical uses of model theory. On a technical level, we try to show how philosophically significant results connect to one another, and also to state the best version of a result for philosophical purposes. On a philosophical level, we show how similar dialectical situations arise repeatedly, across fragmented debates in varied philosophical areas. -/- The second aim of Philosophy and Model Theory, though, is to consider the philosophy of model theory. Model theory itself is rarely taken as the subject matter of philosophising (contrast this, say, with the philosophy of biology, or the philosophy of set theory). But model theory is a beautiful part of pure mathematics, and worthy of philosophical study in its own right. (shrink)

Tim Button explores the relationship between minds, words, and world. He argues that the two main strands of scepticism are deeply related and can be overcome, but that there is a limit to how much we can show. We must position ourselves somewhere between internal realism and external realism, and we cannot hope to say exactly where.

The paper discusses al-Kindī's response to doctrines held by contemporary theologians of the Mu‘tazilite school: divine attributes, creation, and freedom. In the first section it is argued that, despite his broadly negative theology, al-Kindī recognizes a special kind of “essential” positive attribute belonging to God. The second section argues that al-Kindī agreed with the Mu‘tazila in holding that something may not yet exist but still be an object of God's knowledge and power. Also it presents a new parallel between al-Kindī (...) and John Philoponus. The third section gives an interpretation of al-Kindī as a compatibilist, in other words as holding that humans may be free even though their actions are necessitated. In all three cases, it is argued, al-Kindī is close to the Mu‘tazilite point of view, though he departs from them in the arguments he gives for that point of view. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Tallant (2007) has challenged my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation 'x is real-as-of y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended no-futurism. I also clarify no-futurism by rejecting a common mis-characterisation of the growing-block theorist. By supplying a semantics for no-futurists, I demonstrate that no-futurism faces no sceptical challenges. I conclude by considering the problem of (...) how to interpret the relation 'x is real-as-of y'. -/- (NB: A correction to this article appears in Analysis 68.1.). (shrink)

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of set theories (...) due to Scott, Montague, Derrick, and Potter. (shrink)

In 'Higher-order quantification and the elimination of abstract objects', Dorr uses sum types to develop a novel higher-orderist account of nominalization in natural languages. Dorr's account is elegant and ingenious, but we argue that it faces some serious problems. Dorr could avoid these particular problems if he replaced sum types with (what we call) union types, but union types would then introduce new problems of their own. Fortunately, our own fictionalist approach to nominalization steers clear of all these difficulties.

In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...) and hence is incomplete. Whilst this might initially seem strange, I show how internal categoricity results for arithmetic and set theory allow us to face up to this Antinomy. This also allows us to understand why “Models are not lost noumenal waifs looking for someone to name them,” but “constructions within our theory itself,” with “names from birth.”. (shrink)

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

In his Axel Hägerström Lectures, given in Sweden in 1991, Dick Hare referred to Hägerström as a pioneer in ethics who had made the most important breakthrough that there had been in ethics during the twentieth century. Although Hägerström's development of a nondescriptivist approach to ethics certainly was pioneering philosophical work, when the history of twentieth century ethics comes to be written, I believe that it is Hare's own work that will be seen as having made the most important contribution.

The present paper tries to trace the particular contours that the problem of theodicy assumes in the Chinese Buddhist text the Awakening of Faith in the Great Vehicle. It analyses the beginning section of the main body of text – the section, that is, that outlines the major theoretical structure of the work – in terms of a problem that has been of particular concern in western theology. I believe that taking such a tack is especially valuable for highlighting the (...) central Problematik around which the text is organized. The paper will thus use the problem of theodicy as a means of exploring some of the philosophical implications of the Awakening of Faith. (shrink)

It was a little over ten years ago, 1967–8, that H. D. Lewis delivered the first series of Gifford lectures, The Elusive Mind, in the University of Edinburgh. It was my privilege that year to be an auditor in the Seminar at King's College that Professor Lewis was conducting with his students in the area of this topic. I had already read the works in which, in the midst of neo-orthodox and existentialist religious movements, he had devoted himself to critical (...) valuation of those doctrines - witness his Morals and the New Theology, and Morals and Revelation. This earlier work prepared for a comprehensive interpretation of religious experience in his book in 1960: Our Experience of God. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Name der Zeitschrift: Klio Jahrgang: 99 Heft: 2 Seiten: 694-697.

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

Necessitists about set theory think that the pure sets exists, and are the way they are, as a matter of necessity. They cannot explain why the sets (de rebus) are all the sets. This constitutes the Ur-Objection against necessitism; it is the primary motivation cited by potentialists about set theory. -/- At least three families of potentialism draw motivation from the Ur-Objection. Contingentists think that any things could form a set even if they actually did not. Prioritists think that sets (...) hyperintensionally depend upon their members. Structural-potentialists think that any possible set-hierarchy could be extended. However, once we have disentangled these three versions of potentialism, we see that the Ur-Objection should not motivate anyone. (shrink)

Potentialists think that the concept of set is importantly modal. Using tensed language as an heuristic, the following bar-bones story introduces the idea of a potential hierarchy of sets: 'Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets.' Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with (...) Level Theory, as developed in Part 1. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a natural (...) extension of BLT is definitionally equivalent with ZF. (shrink)

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same (...) relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

No-futurists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David Braddon-Mitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that no-futurists should treat 'x is real-as-of y' as a nonsymmetric relation. Then different moments are real-as-of different times. (...) This reunites privilege with indexicality, but entails that no-futurists must believe in ineliminably tensed facts. (shrink)

This book provides a sustained and penetrating critique of a wide range of views in modern cognitive science and philosophy of the mind, from Turing's famous test for intelligence in machines to recent work in computational linguistic theory. While discussing many of the key arguments and topics, the authors also develop a distinctive analytic approach. Drawing on the methods of conceptual analysis first elaborated by Wittgenstein and Ryle, the authors seek to show that these methods still have a great deal (...) to offer in the field of the cognitive theory and the philosophy of mind, providing a powerful alternative to many of the positions put forward in the contemporary literature. Amoung the many issues discussed in the book are the following: the Cartesian roots of modern conceptions of mind; Searle's 'Chinese Room' thought experiment; Fodor's 'language of thought' hypothesis; the place of 'folk psychology' in cognitivist thought; and the question of whether any machine may be said to 'think' or 'understand' in the ordinary senses of these words. Wide ranging, up-to-date and forcefully argued, this book represents a major intervention in contemporary debates about the status of cognitive science an the nature of mind. It will be of particular interest to students and scholars in philosophy, psychology, linguistics and computing sciences. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way (...) of fleshing out this idea is synonymous with a ZF-like theory. This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a simpler model-theoretic (...) result. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...) of the Church–Turing Thesis is unaffected by SAD computation. (shrink)

Over the past several decades, scholars of liberal and democratic theory have shown a heightened interest in the role that various virtues might play in promoting the good/free society. Yet within this recent “return” to the virtues, one quality that has been almost entirely left out of the discussion is humility. In this essay, I critically address this lacuna and offer a defense of a particular form of humility, what I call democratic humility. After considering a range of moral and (...) political objections to the concept of humility, I provide an account that seeks to address some of these long-standing difficulties while arguing that the idea of humility, recuperated as an ethos of civic attentiveness, may be one of the most important virtues for late-modern societies marked by ethical and cultural pluralism. (shrink)

Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is self-stultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’.

Minimalists, such as Paul Horwich, claim that the notions of truth, reference and satisfaction are exhausted by some very simple schemes. Unfortunately, there are subtle difficulties with treating these as schemes, in the ordinary sense. So instead, minimalists regard them as illustrating one-place functions, into which we can input propositions (when considering truth) or propositional constituents (when considering reference and satisfaction). However, Bertrand Russell's Gray's Elegy argument teaches us some important lessons about propositions and propositional constituents. When applied to minimalism, (...) these lessons show us why we should abandon it. (shrink)

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.