Theoretically, critical mathematics education (CME) differs markedly from traditional, teacher-centered mathematics teaching approaches. In addition to meeting mathematical goals, a main focus of CME lies on fostering students’ critical consciousness and positioning them as active and informed actors in the classroom and beyond. However, only few empirical studies explicitly focus on how students experience CME instruction and curriculum. In this contribution, we draw on interview data to examine how K-12 students in one Austrian and one American school setting respond to (...) and perceive CME lessons. The analysis revealed that, within both classroom settings, students’ perceptions vary greatly, with some perceiving CME lessons as being completely different from prior experiences in school mathematics to some seeing little-to-no difference. Additionally features of CME instruction that mathematics teachers and researchers might consider to be the most salient are not necessarily the ones that students report attending to. Reasons for that might be manifold, and students might need more time with CME instruction and especially with reflecting on such lessons to identify the rationale behind the instructional approach. Moreover, researchers should be aware that students might not share their understanding of critical instructional reforms and might have diverse or even divergent perceptions. (shrink)

In this theoretical essay, we respond to recent scholarship on decolonizing mathematics that asserts that so-called “Western” mathematics is inherently colonialist – that is, in service of the economic and political control of European or wealthy nations over countries of the Global South. Although generally sympathetic with that literature, we argue against some of its presumptions, in part, by distinguishing “Western” or academic mathematics from its recontextualization for schools. First, we argue that, although colonialist messages and values can be disseminated (...) as part of that recontextualization, it is not clear that academic mathematics is inherently colonialist. Then, we offer a suggestive insight into what it might mean to decolonize school mathematics through a pedagogical approach based on research on native language learning, called the “subordination of teaching to learning.” The approach uses tasks that invite learners to use their indigenous mental powers (or brilliance) through engaging in dialogic interactions with themselves and others about objects and relations among them. To illustrate the subordination of teaching to learning, we present an example of how learners use their learning powers to educate their awareness and build mathematical ideas and reasoning; thereby experiencing the joy of their intellectual efforts. (shrink)

This book, the first to explore religious education and post-modernity in depth, sets out to provide a much needed examination of the problems and possibilities post-modernity raises for religious education.

Decoherence results from the dissipative interaction between a quantum system and its environment. As the system and environment become entangled, the reduced density operator describing the system "decoheres" into a mixture (with the interference terms damped out). This formal result prompts some to exclaim that the measurement problem is solved. I will scrutinize this claim by examining how modal and relative-state interpretations can use decoherence. Although decoherence cannot rescue these interpretations from general metaphysical difficulties, decoherence may help these interpretations to (...) pick out a preferred basis. I will explore whether decoherence solves nagging technical problems associated with selecting a preferred basis. (shrink)

Are the characteristics and relationships among spatio-temporal entities "real" or are they simply conventional terms that note similarities among things in the world but lack any reality of their own? Or if they are real, what sort of reality do they have? Do we live in a world of causes and effects, or is this relation a useful contrivance for our convenience? What is the nature of this "I" that we invoke when referring to ourselves? Is it body? Mind? Both? (...) Neither? And once its nature is understood, what can be said of the choices it makes? Are they really ours, freely made by an independent will? Or is each choice determined more by the internal makeup of the "I" we happen to be and the social/environmental circumstances in which this "I" finds itself, rather than by any act of will? But if each of us "could not have chosen otherwise" than we have, are we no better than the machines we construct? Then again, maybe some of our more advanced machines should be considered conscious entities? Introduction to Metaphysics: The Fundamental Questions presents these and other intriguing questions, many of which have challenged philosophers from antiquity to the present in their efforts to speculate on the nature of what is real. Often filled with twists and turns, dark corners and hidden recesses, this journey of discovery is an exciting excursion into the depths of human understanding. As guides for this intellectual journey editor Andrew Schoedinger has chosen an impressive array of creative and thought-provoking philosophers: Peter Abelard, Aristotle, Renford Bambrough, George Berkeley, Joseph Butler, Rudolf Carnap, Roderick Chisholm, R.G. Collingwood, Arthur Danto, Donald Davidson, Rene Descartes, C.J. Ducasse, Alvin I. Goldman, Keith Gunderson, David Hume, John Locke, Alasdair MacIntyre, A.I. Melden, John Stuart Mill, D.F. Pears, Hilary Putnam, Anthony Quinton, Bertrand Russell, Michael Scriven, Sydney Shoemaker, P. F. Strawson, Richard Taylor, and others. This volume is a unique invitation to join a distinguished group of theorists as they tackle tough questions concerning the existence of universals, the nature of causation, understanding personal identity, the tangled web of free will, and the challenges posed by the advent of artificial intelligence. (shrink)

In this brief overview paper, we analyse information flow in the brain. Although Shannon’s information concept, in its pure algebraic form, has made a number of valuable contributions to neuroscience, information dynamics within the brain is not fully captured by its classical description. These additional dynamics consist of self-organisation, interplay of stability/instability, timing of sequential processing, coordination of multiple sequential streams, circular causality between bottom-up and top-down operations, and information creation. Importantly, all of these processes are dynamic, hierarchically nested and (...) correspond to continuous brain state change, even if the external environment remains constant. This is where metastable coordination comes into play. In a metastable regime of brain functioning, as a result of the simultaneous co-existence of tendencies for independence and cooperation, information is continuously created, preserved for some time and then dissipated through the formation of dynamical and nested spatio-temporal coalitions among simple neuronal assemblies and larger coupled conglomerates of them—so-called delocalised operational modules. (shrink)

I discuss three elements of Dennis Schulting’s new book on the transcendental deduction of the pure concepts of the understanding, or categories. First, that Schulting gives a detailed account of the role of each individual category. Second, Schulting’s insistence that the categories nevertheless apply ‘en bloc’. Third, Schulting’s defence of Kant’s so-called reciprocity thesis that subjective unity of consciousness and objectivity in the sense of cognition’s objective purport are necessary conditions for the possibility of one another. I endorse these fascinating (...) but unfashionable claims and sketch my own version of what they amount to, which is quite different to Schulting’s own construal. I point to some fundamental limitations and problems for Schulting’s position and argue that his project needs to be reshaped or at least reconceived in the face of them. Even if Schulting’s argument is sound, it does not provide a deduction, properly speaking, of the categories. (shrink)

Field theories have been central to physics over the last 150 years, and there are several theories in contemporary physics in which physical fields play key causal and explanatory roles. This paper proposes a novel field trope-bundle (FTB) ontology on which fields are composed of bundles of particularized property instances, called tropes and goes on to describe some virtues of this ontology. It begins with a critical examination of the dominant view about the ontology of fields, that fields are properties (...) of a substantial substratum. (shrink)

Of all the crew to serve on a starship Enterprise, none has had such a convoluted line of existence as the venerable Mr. Spock. This chapter explores what the various incarnations of Mr. Spock can tell us about the nature of reality, existence, and personal identity. Lewis argues for the metaphysical theory of modal realism: all possible worlds are as real as the actual world. In science fiction parlance, this philosophical concept of world is more often called a universe. Thus, (...) Earth and Vulcan are both part of the same world depicted in Star Trek. The central question Lewis addresses is whether our world is the only real world, or whether other possible worlds could also be considered real. Lewis argues for the metaphysical theory of modal realism, all possible worlds are as real as the actual world. (shrink)

Originally published: Philadelphia: Saunders College Pub., c1990.

Programmed cell death (PCD) in unicellular organisms is in some instances an altruistic trait. When the beneficiaries are clones or close kin, kin selection theory may be used to explain the evolution of the trait, and when the trait evolves in groups of distantly related individuals, group or multilevel selection theory is invoked. In mixed microbial communities, the benefits are also available to unrelated taxa. But the evolutionary ecology of PCD in communities is poorly understood. Few hypotheses have been offered (...) concerning the community role of PCD despite its far-reaching effects. The hypothesis we consider here is that PCD is a black queen. The Black Queen Hypothesis (BQH) outlines how public goods arising from a leaky function are exploited by other taxa in the community. Black Queen (BQ) traits are essential for community survival, but only some members bear the cost of possessing them, while others lose the trait In addition, BQ traits have been defined in terms of adaptive gene loss, and it is unknown whether this has occurred for PCD. Our conclusion is that PCD fulfils the two most important criteria of a BQ (leakiness and costliness), but that more empirical data are needed for assessing the remaining two criteria. In addition, we hold that for viewing PCD as a BQ, the original BQH needs to include social traits. Thus, despite some empirical and conceptual shortcomings, the BQH provides a helpful avenue for investigating PCD in microbial communities. (shrink)

In the aftermath of the ‘Brexit’ referendum two pieces of campaign material used by the successful Leave campaign proved controversial: a slogan on the side of a bus fallaciously implying that leaving the EU would necessarily free up £350 million a week for the NHS; and a poster stating that Britain was at “Breaking Point” – purportedly due to an influx of migrants – that was redolent of Nazi propaganda. This paper analyses and develops some criticisms that were levelled at (...) the Leave campaigners who authorised these from the perspective of political liberalism. It concludes that those behind the Breaking Point poster could justifiably have been subject to non-criminal sanction by institutions such as the Electoral Commission, but that this is not the case for the NHS bus. The Breaking Point poster warrants sanction because it belongs to a category of hateful speech that propagates false and discriminatory beliefs about its targets. Where these are disseminated by those in authority or of high status, such as political campaigns, they can strengthen these beliefs amongst the rest of the population. This can lead to members of the targeted group being unable to deliberate effectively as they are not treated with adequate respect in political discussions, which in turn undermines the process of public justification. As a result, it undermines public justification in a way that false factual claims do not, eventhough in this case the NHS slogan appears to have had a greater effect on the referendum result. (shrink)

As Dworkin puts it: moral scepticism is a moral view. This is in contrast to the more popular idea that the real challenge for moral realism is external scepticism, scepticism which arises because of non-moral considerations about the metaphysics of morality. I, too, do not concur with Dworkin’s strongest conclusions about the viability of external scepticism. But, I think his criticism of error scepticism offers a much needed corrective to more traditional metaethical projects. My aim in this paper is to (...) split the difference between Dworkin’s view and more traditional views, concluding that Dworkin’s work in Justice for Hedgehogs contributes to metaethics for everyone.Resumen:En palabras de Dworkin “el escepticismo moral es una concepción moral”; esto en contraste con la idea más popular de que el verdadero reto para el realismo moral es el escepticismo externo, un escepticismo que proviene de consideraciones no morales sobre la metafísica de la moral. Al igual que otros no comparto las conclusiones más poderosas de Dworkin acerca de la viabilidad del escepticismo externo; sin embargo, considero que su crítica de un “escepticismo equivocado” aporta una muy útil enmienda a los proyectos de metaética más tradicionales. Mi objetivo en este ensayo es separar las diferencias entre la perspectiva de Dworkin y las perspectivas tradicionales, para al final concluir que el trabajo de Dworkin, en Justice for Hedgehogs, contribuye a una metaética para todos. (shrink)

Before the start of the COViD-19 global pandemic, I stumbled across Bryan Hall’s book ‘an ethical guidebook to the zombie apocalypse’. I was instantly drawn to the ‘zombiefied’ image of Rodin’s the Thinker on the cover, and so I made an impulsive purchase on a rainy day. On my return home, I filed it unread on my bookshelf where it lay undiscovered - until the lockdown came. Stories began to emerge of a changing world, a growing sense of pandemic panic (...) and a readjustment to a new world and a new way of life - and I remembered my zombie book. With time on my hands, I began to read - and the echoes between the zombie apocalypse and COViD-19 grew more vivid and more real. It became harder to tell truth from fiction as I read of a virus that was spreading around the world, causing society to implode, law and order to breakdown and a sense of right and wrong to be blurred. So, on our return to school, after our lockdown, I was inspired to use the zombie apocalypse as my tool to inspire my year 10 Philosophy elective class – most of whom were just beginning their Philosophy studies. (shrink)

Guy Austin _Claude Chabrol_ Manchester and New York: Manchester University Press, 1999 ISBN 0 7190 5271 8 (hb); 0 7190 5272 6 (pb) 197 pp.

"I have been using the book in a freshman seminar in which we are exploring college. Most of the texts we are using are academic satire novels, but we are using Delbanco's book to help us talk about the place of college in American culture.

Event synopsis: This conference will explore Friedrich Nietzsche's critical relation to Kantian political philosophy. Taking 'Kantian politics' to include modern and contemporary Kantian theories as well as Kant's own theories, the conference will examine Nietzsche's engagement with such Kantian themes as autonomy and rights, equality and democracy, morality and politics, war and cosmopolitanism, history and anthropology. The speakers are renowned scholars of political philosophy from the United States and Europe, and the format of the conferences involves the pre-circulation of papers (...) among participants and extended sessions, so as to allow much time for discussion. The conference is the sixth in a series examining Nietzsche's relation to Kant and Kantianism, each focusing on specific areas and texts of Kant's philosophy. Previous conferences were held on ethics in Leiden, aesthetics in London, epistemology in Lisbon, religion in Belo Horizonte, and anthropology in Lecce, and another will be held on the transcendental in Galway in March 2014. The conference is organized by Tom Bailey ([email protected]) and funded by John Cabot University. There is no conference fee, but if you plan to attend, please register with Tom Bailey, who will also provide you with practical information and the conference papers. All sessions will take place at the University's Guarini campus, in Via della Lungara 233, Trastevere, Rome. The Friday morning sessions will take place in the Aula Magna Regina, and the following sessions in the Board Room. (shrink)

In recent years, and especially in the wake of Barack Obama's reelection, projections that whites will soon become a minority have proliferated. In this essay, I will argue that such predictions are misleading at best, as they rest on questionable philosophical presuppositions, including the presupposition that racial concepts like ‘whiteness’ are static and unchanging rather than fluid and continually being reconstructed. If I am right about these fundamental inaccuracies, one must wonder why the myth of the white minority persists. I (...) will argue that by reenvisioning whites as a minority culture struggling against a hostile dominant group, and by promoting white solidarity as a response to a crisis, such predictions actually serve to defend and legitimize white supremacy. (shrink)

First Published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

A signal development in contemporary physics is the widespread use, in explanatory contexts, of highly idealized models. This paper argues that some highly idealized models in physics have genuine explanatory power, and it extends the explanatory role for such idealizations beyond the scope of previous philosophical work. It focuses on idealizations of nonlinear oscillator systems.

The early publication history of the very short Breviarium of Guillaume Budé's De asse et partibus eius is analysed and clarified, and the earliest versions are dated to c. 1520. Though short, it was an influential little work, and in particular its links with Cuthbert Tunstall's De arte supputandi are explored. It is argued that Bude himself was the author of the Brevianum, and that it may have a relevance to the Budé/Porzio controversy about the 'sestertius' and 'sestertium'.

This essay reviews John Gardner’s recent books, From Personal Life to Private Law, and Torts and Other Wrongs. Both books offer profound insights into private law’s concerns with justice and our reasons for action. The essay focuses on Gardner’s continuity thesis, and in particular on his idea that a third party may act on behalf of a wrongdoer as her delegee. Three settings are considered. First, I will discuss settings in which the state or another third party acts to remedy (...) a wrong without the wrongdoer’s consent. Second, I will review settings in which the legal remedies at issue – e.g., general damages or punitive damages – may not fit well with the idea that the state is acting on behalf of a wrongdoer. Third, I will analyze settings in which the state may be acting on behalf of right holders, yet still be concerned with the continuity thesis. Assessing each of these contexts offers further insights into the purpose of private law remedies. (shrink)

The liar paradox in its simplest form is the following argument. Consider the sentence 'this sentence is false'; call that the "liar sentence". Suppose the liar sentence is true. Then, since it says it is false, the liar sentence is false. So our supposition that it is true was mistaken, and the liar sentence must be false. But that's precisely what the liar sentence says, so it is true after all. The liar sentence is, therefore, both true and false---an absurd (...) result. ;Hans Herzberger has argued that several solutions to the Grelling paradox exhibit a common pattern: the very devices we introduce in order to avoid one version of the paradox are integral components of new versions of the paradox. Herzberger suggests that this is typical of semantic paradox in general. Chapters 1, 2, and 3 of this dissertation examine several possible solutions to the liar---especially appeals to language levels and to contexts---and attempt to locate these possible solutions in Herzberger's pattern. ;There is some reason to think that this pattern is inescapable---that is, that the liar paradox is ultimately unsolvable---so the remaining two chapters of this dissertation explore what follows from the claim that it is unsolvable. Chapter 4 develops an argument from the claim that the liar is unsolvable to the claim that we cannot understand ourselves. Chapter 5, then, attempts to make sense of this circumstance by invoking a Nietzschean view of thinking and truth---perspectivalism, which holds that all thinking concerns interpretation and that there are no uninterpreted facts. Given some perspectivalist assumptions, we can see how it is inevitable that we will be unable to understand ourselves---and how we can nevetherless attain a certain limited kind of understanding. Perspectivalism also recommends a certain intellectual humility: if everything is interpretation, then no view of mine can be a comprehensive and accurate view of the way the world really is. This by itself is not a surprising claim; the surprising claim is that the liar paradox is the basis of it. (shrink)

Broad comparisons of international relations across time—of the prospects for peace and of the possibilities for a new ethics for a connected world—typically focus on two dimensions: economic globalization and integration on the one hand, and the character of major interstate relations on the other. One of the most striking features of the pre-1914 world was precisely the coincidence of intensified globalization with a dramatic deterioration in major power relations, the downfall of concert-style approaches to international order, and the descent (...) into total war and ideological confrontation—what T. S. Eliot termed “the panorama of futility and anarchy which is contemporary history.” Today's optimists stress the degree to which globalization appears much more firmly institutionalized than it was a hundred years ago, the rather striking success of global economic governance in responding to the financial crisis of 2007–2008, and the longer-term trend within international society to move away from major-power war. Pessimists are less sure. They worry that we have had to re-learn just how unstable global capitalism can be, both in terms of the wrenching societal changes produced by economic success and of the political strains produced by slowdown and recession. And they point to the abiding or resurgent power of nationalism in all of the core countries in the system, the return of balance-of-power thinking, and the renewed salience of major power politics. (shrink)