In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

The discussion of mathematical knowledge and its relation to the construction of an appropriate diagram in Aristotle's Metaphysics Θ 9. 1051 a21—33 is an important, if compressed, account of Aristotle's most mature thoughts on mathematical knowledge. The discussion of what sort of previous knowledge one must have for understanding a theorem recalls the discussion at An. Post. A 1. 71 a 17–21, where the epistemological point is similar and the examples the same. The first example, that the interior angles of (...) a triangle equal two right angles, appears no less than thirty times in the corpus . The example of the angle inscribed in a semicircle being a right angle also occurs at An. Post. B 11. 94a 27–34, but in a very different context from its two companions. Illustrations of both theorems provided clear stock examples for Aristotle. (shrink)

Political scientists have conventionally assumed that achieving democracy is a one-way ratchet. Only very recently has the question of “democratic backsliding” attracted any research attention. We argue that democratic instability is best understood with tools from complexity science. The explanatory power of complexity science arises from several features of complex systems. Their relevance in the context of democracy is discussed. Several policy recommendations are offered to help stabilize current systems of representative democracy.

These essays constitute a welcome addition to the current re-engagement with the ethical thought of a prominent late Victorian philosopher and reformer. Henry Sidgwick wrote the first professional work of modern moral philosophy, yet one century after his death his thought remains relevant to the present revival of interest in the question of how we should live. -/- How does moral philosophy fit in with the more general use of practical reason? - a still puzzling and deeply contested problem. (...) Which actions are appropriate for an intellectual? - i.e., how should the moral thought of the professional few in the universities be related to the thought and action of the many in the world outside? Sidgwick's solutions to these questions are discussed and criticised by a distinguished group of scholars, providing new insights into these recurring issues of moral philosophy. (shrink)

The philosophy department in Edinburgh is in David Hume tower; the philosophy faculty at Cambridge is in Sidgwick Avenue. In one way, no competition. Everybody has heard of Hume, whereas even the anybody who's anybody may not have heard of Sidgwick. Yet in another way, Sidgwick wins this arcane contest. For if David Hume, contradicting the Humean theory of personal identity, were to return to Edinburgh, he would not recognize the tower. Whereas, if someone with more success in rearousing spirits (...) than Sidgwick himself had could now produce him, Sidgwick would know the avenue. For he planned it; he partially paid for it; and he pushed it past the local opposition. He was its creator. And creator not just of the avenue: if Sidgwick is not quite the only begetter, it was he more than anyone who was responsible for building the school of philosophy in Cambridge which is being celebrated in this series of articles. (shrink)

The philosophy department in Edinburgh is in David Hume tower; the philosophy faculty at Cambridge is in Sidgwick Avenue. In one way, no competition. Everybody has heard of Hume, whereas even the anybody who's anybody may not have heard of Sidgwick. Yet in another way, Sidgwick wins this arcane contest. For if David Hume, contradicting the Humean theory of personal identity, were to return to Edinburgh, he would not recognize the tower. Whereas, if someone with more success in rearousing spirits (...) than Sidgwick himself had could now produce him, Sidgwick would know the avenue. For he planned it; he partially paid for it; and he pushed it past the local opposition. He was its creator. And creator not just of the avenue: if Sidgwick is not quite the only begetter, it was he more than anyone who was responsible for building the school of philosophy in Cambridge which is being celebrated in this series of articles. (shrink)

Plato is a much more experimental philosopher, this book argues, than most commentators acknowledge. Supporting this position, Henry Teloh combines exegesis of particular passages with a synoptic view of Plato's philosophical development through his early, middle, and late dialogues. The result is a study of Plato's ideas with a more ambitious scope than any since W. D. Ross's in 1951,The book chronicles Plato's changing interests through a focus on his ontological commitments—that is, on the types of entities he (...) addresses. It also traces many of the assumptions in Plato's thought back to their sources in pre-Socratic philosophy. By depicting the changes in Plato's thought from one period of dialogue composition to another, and by seeking to explain these changes from textual evidence, this book offers an appealing introduction to Plato for all humanists. (shrink)

This chapter contains sections titled: The Central Idea Bentham's Use of Utility Traditional Interpretation: Mill Reinterpretation (1): The Art of Life Reinterpretation (2): Happiness and Indirect Utilitarianism Mill's Metaphysics and Logic Proof of the Principle of Utility Bentham on Clarification Sidgwick.

In this incisive political analysis, Kristin Ross thinks through everyday existence across a range of practices-from philosophy to history, from the visual arts to popular fiction-and across the forms taken by collective political action in contemporary struggles. Ross returns to Henri Lefebvre's powerful intuition that ordinary life is both residue and resource, the site of profound alienation and, by the same token, the origin of all emancipatory initiatives and desires.

In a series of recent publications, Alan Sokal has launched a series of stinging attacks against contemporary cultural studies. In Intellectual Impostures, for example, written together with Jean Bricmont, the authors (hereafter S&B) criticise the way in which French poststructuralist critics, such as Julia Kristeva, Jacques Lacan and Gilles Deleuze, have abused the scientific terminology to which, Sokal claims, they exhibit slavish adherence. Many authors, such as Andrew Ross and Stanley Aronowitz, have taken up the cudgels against S&B. But (...) their replies often miss the mark either by arguing at too abstract a level against S&B's project as a whole or employing strategies and principles drawn from the self same body of texts which S&B criticize. In this article, by contrast, I reply to specific criticisms S&B direct against Lacan's use of topological concepts. By showing that S&B miss a perfectly reasonable, mathematically acceptable way of reading Lacan's appropriation of topology, I intend to raise more general doubts about S&B's erudition in connection with the works they criticise. (shrink)

Originally published in 1990, _Psychoanalysis and…_ brings together essays by critics whose work demonstrates the lively interpenetration of psychoanalysis and other disciplines. Andrew Ross investigates psychoanalysis and Marxist thought; Joel Fineman reads the "sound of O" in Othello; Jane Gallop asks "Why does Freud giggle when the women leave the room?"; and Ellie Ragland-Sullivan examines Lacan’s seminars on James Joyce. This stimulating collection of work should still be required reading, especially for students of literature. But _Psychoanalysis and… _demonstrates that (...) psychoanalysis – and theoretical criticism, and feminism, and Lacanian theory, and semiotics, and Marxism, and deconstruction, and literary criticism – was, at the time, a rich and expanding terrain. (shrink)

continent. 2.3 (2012): 218–223 Vijay Prashad. Arab Spring, Libyan Winter . Oakland: AK Press. 2012. 271pp, pbk. $14.95 ISBN-13: 978-1849351126. Nearly a decade ago, I sat in a class entitled, quite simply, “Corporations,” taught by Vijay Prashad at Trinity College. Over the course of the semester, I was amazed at the extent of Prashad’s knowledge, and the complexity and erudition of his style. He has since authored a number of classic books that have gained recognition throughout the world. The Darker (...) Nations , a peoples’ history of the Third World, sent defibrillating shockwaves through an academic world that had almost forgotten the epic scope and historic dignity of the non-aligned movement and post-colonial struggles. In his recent, award-winning work, Arab Spring, Libyan Winter , Prashad delves into his capacious knowledge of the Third World to excavate the discourses and narratives surrounding the upheavals of 2011. “Revolutions have no specific timetable,” states Prashad in the opening line of this exciting and provocative look at contemporary events. Instantly, an atmosphere of suspense emerges. The reader is alerted to the problem of history. Does the making of history then involve a suspension of historical time, or is it a continuous narrative structure into which events must eventually be integrated? Arab Spring, Libyan Winter shows that the answer to the question, “How is history made?” lies just as easily in the asking. The first half of the book works through the events that transpired to bring about the explosive popular uprisings of Arab Spring: Tunisia and Egypt, Yemen and Bahrain. But the events are not put together in a cohesive, chronological fashion. Using an uncommonly gripping style more akin to the folk-story motif of the djeli than to traditionally Orientalist academia, Prashad suspends a given situation, points out its components, and traces back the characters and genealogies that define each link before resuming a narrative. Every moment is an end to itself, and an origin of something different. Thus, the making of history becomes the suspension of its own progress, it’s catastrophic 'stability,' in a process of differentiation through inclusion. Empirically, one might suggest that history is a condition of time, and by extension, of the subject, but history is also an eminent producer of the Subject and her concept of time through memory and narrative. Hence, history is often overdetermined by a dominant narrative of the sovereign. The apparently chaotic composition of Prashad’s historicity is, then, an interstitial morphology of resistance. It illustrates that the time to act for the revolutionary lies in the gaps within the dominant historical realities. It points out the sorties of signifiers constituting nothing in the obliterated ruins of history. Through such illuminations, Arab Spring, Libyan Winter breaks through “the surface of history” to elaborate revolution’s snapping synapses, exploding interruptions and breaches, connecting flows. Messianic Politics It is tempting to think, 'History is either singular, or it is diffuse. It is either one coherent factual narrative, or it is comprised of the aletheia of the multitude.' Yet the reader finds Prashad examining the structure of history on multiple levels. For Prashad, world history is shaped by geographically defined political movements, such as communism or national liberation, with historical agents like the working class for the former and the nationalist militant for the latter. Religion, however, is another matter: “Religion has an unshakable eschatology which a post-utopian secular politics lacks.” Within the telos of religion, there appears on the horizon the image of Benjamin’s thoughts on messianic time—time as “a small fissure in the continuous catastrophe,” a break with history, may contain an ultimate redemption of the human beyond the political power struggle. Succoring the split between geo-political and utopian-religious (messianic) time in the context of Arab Spring, Prashad indicates that the base of “the deep desire and commitment to some form of democracy” is forged by the affinity between eschatological Islamist politics with the People. To think about the Subject of messianic time in the context of the lack of a “coherent timetable” for emancipatory politics, it is perhaps best to return to the modern tradition of Martin Luther King, Jr., whose prefigurative blending of liberation theology and emancipatory politics became most important during his works of 1963, the climactic year of “The Letter from a Birmingham Jail,” the March on Washington, and the bombing of the 16th Street Baptist Church. In “The Letter,” King states the point bluntly: Frankly, I have yet to engage in a direct-action campaign that was “well timed” in view of those who have not suffered unduly from the disease of segregation. For years now I have heard the word “wait!” It rings in the ear of every Negro with piercing familiarity. This “Wait” has almost always meant ‘Never.” We must come to see, with one of our distinguished jurists, that “justice too long delayed is justice denied.” The timing of rebellious action must not be a part of history. It must change history. The kairos appears spontaneous and untimely in its convulsive, shocking presence, yet it is, deeper still, a path, a longue durée , forged through diligent and rigorous praxis. King put a finer point on the path of historic liberation in his declaration in his 1963 speech at Western Michigan University: “[T]ime is neutral.... Somewhere along the way we must see that time will never solve the problem alone but that we must help time. Somewhere we must see that human progress never rolls in on the wheels on inevitability. It comes through the tireless efforts and the persistent work of dedicated individuals who are willing to be co-workers with God. Without this hard work, time itself becomes an ally of the insurgent and primitive forces of irrational emotionalism and social stagnation. We must always help time and realize that the time is always right to do right.” Time, then, exists in “the neutral,” while action must turn to the kairos , not only of taking time, but taking the right time. By turning our relation to time into kairos , we move time from its context within history to a duration between histories—the longue dure?e of Messianic time. The implementation of neutrality in this context suggests a broad space of time to extend through the valley of positive and negative. In Roland Barthes’s lectures from 1978, the neutral takes place in this minimal distance of non-conflict that exists outside of two extremes. It is, in the words of Maurice Blanchot, “the non-general, the non-generic, as well as the non-specific.” For Blanchot, the neutrality of time permeates life as death, impassive and beyond control; such is the neutrality of messianic time, which permeates the charge of history, changing the "I" into the "one." The neutrality of time therefore implicates history in a case against extremism, showing that the work of the radical is not to tend to any particular side, but to have the time to navigate through the terrible terrain of history by altering its course, its patterns and rhythms of movement, connection, sociality. Hence, one does not simply “make history,” one alters the course of history in accordance to “the right time.” The historical path toward emerging power is transmitted as a gesture to the outside of history, against history; a gesture as simple as reaching out. Thus a counterhistory, to use Foucault’s term, is brought forward as the guide of time past a point of no return, a Rubicon, the point where the normal path of history falls to the past. The subject, who must be the only true agent of history, facilitates time through helpfulness, and both the Subject and her history become decentered in relation to one another. Yet history negates the neutrality of time. As Barthes discloses, although the neutral is the “thought and practice of the nonconflictual, it is nevertheless bound to assertion, to conflict, in order to make itself heard.” Engaged with history, time is charged with a destiny, and becomes an opposition. As Prashad insists, “For Arab lands, the events of early 2011 were not the inauguration of a new history, but the continuation of an unfinished struggle that is a hundred years old.” The emergence of the Subject during Arab Spring did not conceive of a new history, but changed the path of history toward a different destiny. “Historical grievances combined with inflationary pressures now met with the subjective sense that victory might be at hand—this was not simply a protest to scream into the wind, but a protest to actually remove autocrats from their positions of authority. The facts of resistance had given way to the expectation of revolutionary change.” The negativity of this charge toward “revolutionary destiny” rendered control, as a positive force, seriously lacking. The lack of control lies in the problem that the Subject is not totally detemporalized or timeless, but untimely in her presence. The Subject is untimely, because her work is visionary, and it is only through such visionary work that the Rubicon can be crossed. Still, the crossing of this border is haunted by anxiety over an impending disaster that lays in wait. It is only through the form of what Benjamin calls divine violence, captivated not with the justice of the means, but the ends—the transformation of history—that a revelation of history’s traumatic foundations can be liberated, and patterns and rhythms of time developed throughout obscured traditions awakened. In this situation, the Subject appears to be outside of right, but setting the state to rights. Because her position is correct, in-so-far as the rebelling subject rebels due to a lack of recognition, her representation appears outside of the norm, which is mistaken as right. Therefore, such visionary work must be carried out through obscured traditions, underground, away from the surveillance of empire. Explaining his method from the start along the lines of Marx’s metaphor of the mole, Prashad insists, “It is the burrowing that is essential, not simply the emergence onto the surface of history.” Arab Spring, Libyan Winter is a book on uncharted networks of time, spread out over the 252 pages like an elaborate spider’s web of passages intertwining with and overwhelming the machinery of the state. Although untimely, Arab Spring was not a flash in the pan, or a Facebook or Twitter revolution. Prashad notes that the government’s suspension of these tools led to further radicalism by furthering communications through face-to-face encounters. In existential terms, Arab Spring might be thought of as a revolution of Being over techne , an uprising of the unchartable, infinite potential of the Other. The name of this Other is found in Chance. The faith of the revolution lies in the proper decentering of the subject, its giving to the Other of time, for only with respect to time does history actually appear on the horizon of the subject, rather than as an imposition. This time of historical agency appears as a moment when anything can happen—a revolutionary truth event where everything comes into question while being realized in its Otherness as a community of the people begins anew in the streets amidst discourse, friendship, reconfigurations of hegemony, and a becoming of a constituent power. Throwing a wrench into the gears of the “cobwebbed tradition” of Orientalism, the decentering of history in Arab Spring, Libyan Winter is a defining quality of its impassioned revolutionary cry. But perhaps the most paradigmatic points of the book emerge from the unexpected voices. To make the connection between the particular manifestations of revolutionary demands to the general historic terms of revolution, Prashad quotes an anonymous young Egyptian in Tahrir Square, who reminds us, “[T]he French Revolution took a very long time so the people could eventually get their rights.” Far from timelessness, the historicization of Arab Spring must exist precisely within the most uncanny appearance of time, as something that does not appear to come from the natural state of time as we know it, but in arriving has completely transformed the way that we understand time. Strange Monsters Revolution is never as simple as a revolt from below against a rusting structure of elites trying to remain in power. As with the French Revolution, Arab Spring consisted of complex familial ties, outside interests, and religious factions fighting alongside, often in awkward juxtaposition to, liberals, working class parties, farmers, and students. It is perhaps because of this historically difficult and incongruous composition that the Arabic word for revolution is thawra , referring to the image of the bull, or thawr , which has religious significance as a pagan deity for the Ancient Semitic tribes and Cartheginians. If Daniel Guérin was correct in saying, “Anarchism and Marxism drink from the same spring,” then it is quite a different oasis that drove the thirsty beast of revolution through what Prashad calls, “the Libyan labyrinth.” Recalling Bataille’s Acéphale, the intestinal labyrinth gains significance as the mode of metabolism and rumination in which, “(the Acephale) has lost himself, loses me with him, and in which I discover myself as him, in other words, as a monster.” Unraveling the discourse of the revolution, the flows of power and hegemony—from Qaddafi’s nationalist coup in 1969 to the wars with Chad from 1978 to 1987, the neoliberal reforms of the 1990s to, finally, the War on Terror—we find that the metabolic process of Libyan Winter ends in the production of oil. In a process of what Prashad calls “involution,” Qaddafi’s bellicose policies, along with his attempts to nationalize Islam together with oil, mutated the source of his power, turning his house against itself. Already a divided nation, with its two major cities on opposite geographic sides of the country, Libya became split between two opposed political powers—liberal reformists and staunch nationalists—as Qaddafi’s political disengagement manifested through what can only be described in psychoanalytic terms as a recursive passage a l’act (mysteriously calling Wikipedia “Kleenex,” declaring that opponents drank hallucinogens with their instant coffee, and so on). Prashad declares, “The mercurial style that Qaddafi adopted was not about his personality alone, but also a leader’s natural response to a system that relied upon power brokers whose own loyalty… did not have any ideological commitment to the system.” As in the case of other nations during Arab Spring, the true expression of revolt was an outward exposition of what had inwardly been happening in microcosmic societies throughout the realm—from indigenous tribes to political parties, for a century, the people, partly motivated by (and in resistance to) economic impositions of development, had been changing the traditional social compositions and participating in what Ruth Wilson Gilmore calls, “the relative autonomy of the movement from the leaders.” It was this empowerment of political reconfigurations taking place under the context of new democratic assemblages that shocked the elites and evoked such a powerful response. Unlike Qaddafi’s awkward policy choices and rants, real acts of power from the West were clear and decisive. Prashad sets the stages of war and diplomacy, far removed from the deserts, mountains, and cities that forged the backdrop of popular politics. Taking place under the now-classic architecture of the “four pillars” of US interests—oil, the War on Terror, Israel, and the circumvention of Iranian hegemony—we find elites rubbing elbows in “Heliopolist cocktail parties and hushed conferences in Kasr al-Ittihadiya” as well as the Concorde-Lafayette hotel in Paris, which provides the setting for a meeting of anti-Qaddafi figures consolidating their power. These scenes are buttressed with the careful portraiture of key historical actors. As Prashad brings the stage of history to life, we find the diplomats and liberals like Frank Wisner, whose career has brought him from Enron in the late 1990s to the Obama Administration, under the aegis of which he was meeting with Mubarak about military support during Arab Spring. We spy the provocateurs, for instance, gauche cavalier , Bernard Henri-Levy, who telephones Sarkozy from Benghazi about the need for more NATO air strikes. We follow the rebel military establishment as it suffers mysterious deaths and even more mysterious assents (like that of apparent CIA cohort, Khalifa Hifter). In each of these intriguing characters, we find different representations of the security state biopolitique: an oil-injected reification that drives Arab Spring from the resentment of rising food prices to the brink of implosion in Libyan Winter. Reminiscent of the scenes of Cold War soirées represented in old Bond films, the aristocratic fight for oil against democracy that was Libyan Winter presents a harsh truth that the new global crisis is simply the continuation of the old history: the global exploitation of capitalism waged against the imagination of the people. As Benjamin laments, “The labyrinth is the right path for the person who always arrives early enough at his destination. This destination is the marketplace.” Yet, “(t)he labyrinth is the habitat of… a humanity (a class) which does not want to know where its destiny is taking it.” Thus, the labyrinth leads, like the desert, only further into itself. As Blanchot explains, “The desert is even less certain than the world; it is never anything but the approach to the desert.” Only the visionary can take time out of the involution toward oblivion. It is here, in this approach to and escape from history, that we find ourselves within Benjamin’s Golgotha, Blanchot’s desert: A space of indeterminate uncertainty where we become familiar only with our own exile. Blanchot writes, “For the moderated and moderate man, the room, the desert, and the world are strictly determined places. For the man of the desert and the labyrinth, devoted to the error of a journey necessarily a little longer than his life, the same space will be truly infinite, even if he knows that it is not, all the more so since he knows it.” The desert, as allegory, provides an eschatology, a mortality in the destiny of Arab Spring. But any allegory of nature might lead to a labyrinthine eschatology (for example, in Bachelard, the forest presents "a limitless world"); the prescience of the untimely is always an uncanny acceptance of the infinite within the finite—the outside of what is understood. Transgenerational and occupied with the image of the future, the untimely makes otherness its home as it proceeds toward liberation. In the work of helping time navigate this dangerous passage of history, Prashad illustrates that the more violent break with history may have occurred in the peaceable struggles of Tahrir Square, and not in the military clashes of Qaddafi with his former Generals who defected to the CIA and NATO countries. It might be possible to suggest, then, that in the case of Tunisia and Egypt, the historical subject of the people was drawn together in a Dionysian dance of different rhythms in the marvelous realm of the ancients, while we fear that the case of Libya suggests an Apollonian future where time, itself, may lay dying under the machinic hand of history. The properly Nietzschean inversion would follow: time is dead, for history has killed it. Yet, if time is dead, struck down in Golgotha, exposed in the desert, mauled by the thawra , it is only in the present sense that it is rendered impossible outside of the context into which the untimely has thrown us. Thus, if history becomes an art of revolution, life as being-towards-death (death as the provocation of the neutrality of time) becomes what Benjamin calls “the allegory of resurrection” through the glorious ruins of history. Prashad ends his work with a rousing finale: “The time of the impossible has presented itself. In Egypt, where the appetite for the possibilities of the future are greatest, the people continue to assert themselves into Tahrir Square and other places, pushing to reinvigorate a Revolution that must not die… For them the slogan is simple: Down with the Present. Long live the Future. May it be so.&rdquo. (shrink)

This paper has two specific goals. The first is to demonstrate that the theorem in MetaphysicsΘ 9, 1051a24-27 is not equiva-lent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I ar-gue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosoph-ical reason for the Aristotelian theorem being shorter (...) than the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theo-rems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amend-ments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.4 (2003) 569-570 [Access article in PDF] Ross Harrison, editor. Henry Sidgwick. New York: Published for The British Academy by Oxford University Press, 2001. Pp. v + 122. Cloth, $24.95. Henry Sidgwick consists of papers by Stefan Collini, John Skorupski, and Ross Harrison, with replies by Jonathan Rée, Onora O'Neill, and Roger Crisp.Collini's rich and witty paper considers two (...) pictures of Victorian intellectuals—the "public moralist," such as John Stuart Mill, and the academic specialist. Sidgwick in the 1880s and 1890s does not fit comfortably into either camp. He champions the academic philosopher over Leslie Stephen or Mathew Arnold; he contributes to Mind rather than writing to newspapers or standing for parliament; he refuses to take a public stand on the Boer war despite opposing it. He would not have been a teledon. But he also exerts influence on university policies (founding Newnham College for women, opposing the Latin and Greek requirement for admission), through Royal Commissions, and through his personal connections to those in power. (He had as brothers-in-law the Prime Minister and the Archbishop of Canterbury.) He represents one solution to the new problem of combining academic specialization with practical concerns. [End Page 569]One quibble: Collini argues that Sidgwick wields his analytic method in order to end public debate; disagreements rest on conceptual confusions. But Sidgwick's late essays do not close with "a thin, dry question to which... the answer is more or less obvious," but with controversial proposals (44): to prevent war, individual cultivation of impartiality is more important than external arbitration; there are no significant differences between moral requirements on states and individuals; the unequal distribution of luxuries is morally defensible if and only if necessary for "aesthetic progress"; sociology is suspect and must be kept distinct from ethics. A second paper on clerical veracity is needed given controversy about the first.Harrison's slightly diffuse paper places Sidgwick in the utilitarian tradition of discussing sanctions for morality. (Crisp argues neatly that Bentham and Mill are closer to Sidgwick than Harrison allows.) Harrison closes by arguing that Sidgwick should not have been bothered by the dualism of practical reason—the view that utilitarianism and egoism conflict and that there are no decisive arguments for choosing between them. He should have ended the Methods with utilitarianism. The conflict between egoism and utilitarianism "should not matter" because "these are truths of practical rather than speculative reason." Conflict shows only that "we are not in the best of all possible worlds" (114). This helps if, with Harrison, Sidgwick's worry is the "theoretical" one that rival properties claim to be right-making (110). But Sidgwick sees the problem as practical: when egoism and utilitarianism conflict, I must decide which to follow.Skorupski also rejects the dualism. There are many true underived claims about reasons for action. Each can be seen as an instance of the "Feeling/Disposition Principle" (F): "If there's a reason to feel f there's reason to do what feeling f characteristically disposes one to do" (74). For example, if there is a reason to feel gratitude, there is a reason to express this gratitude. Egoistic reasons are the products of F when desire is the feeling. Any impartial theory, because it goes beyond the feelings of a particular individual in a particular situation, cannot be a case of F and so counts as a principle of practical reason. True claims about reasons for action are either many or, if restricted to practical reason, one. (Skorupski adds that an impartial theory, since indefeasible, trumps egoism. For example, my reason to express gratitude is defeated by noting that general good is not served by expressing gratitude, but need not be defeated by noting that my own good is not served. This, however, seems mere assertion. I suspect it, and F, are best pursued in Skorupski's Ethical Explorations [Oxford: Oxford University Press, 1999].)Showing that an impartial theory is not a case of F does not, by itself, show that it is a principle of practical reason... (shrink)

The publication of John Knox's First Blast of the Trumpet in 1558 had engendered a radical debate about the public role of women and the nature of female authority and obedience. Howard was not the only author who attempted to refute Knox's tract. The Marian exile and future Bishop of London, John Aylmer, the Catholic Bishop of Ross, John Leslie, and the Catholic, Scottish lawyer, David Chambers, all published books disproving Knox's allegations about women's unfitness for rule. Richard Bertie, (...) husband of Catherine, Duchess of Suffolk, also prepared a manuscript refutation which was never published. The published works are moderately well known, and have been discussed elsewhere. This article concentrates on Howard's unpublished contribution to the Knox debate. The tract is important because of its length and detail, its conclusions regarding the potential role of aristocratic women, and because of Howard's personal reputation and aristocratic connections. The �Defense� was both eloquent and persuasive, analysing women's legal, historical and theological status within early modern society. Howard presented alternative interpretations of female stereotypes found in sermons and polemical writings. His commentaries on Genesis, Athalia, Jezebel and Deborah show how traditional biblical stories could be interpreted in radically differing ways, with profound implications for contemporary women. Because of the length of Howard's tract, this article can present only a summary of his main conclusions. His interpretation of the first three chapters of Genesis will be presented in rather more detail as an indication of the complexity of the early modern debate about women, and the dangers of trying to attach simplistic labels to individual attitudes. (shrink)

Intellectual Impostures , for example, written together with Jean Bricmont, the authors (hereafter S&B) criticise the way in which French poststructuralist critics, such as Julia Kristeva, Jacques Lacan and Gilles Deleuze, have abused the scientific terminology to which, Sokal claims, they exhibit slavish adherence. Many authors, such as Andrew Ross and Stanley Aronowitz, have taken up the cudgels against S&B. But their replies often miss the mark either by arguing at too abstract a level against S&B's project as a (...) whole or employing strategies and principles drawn from the self same body of texts which S&B criticize. In this article, by contrast, I reply to specific criticisms S&B direct against Lacan's use of topological concepts. By showing that S&B miss a perfectly reasonable, mathematically acceptable way of reading Lacan's appropriation of topology, I intend to raise more general doubts about S&B's erudition in connection with the works they criticise. (shrink)

Of all the developments in twentieth century physics, none has given rise to more heated debates than the changes in our understanding of science precipitated by the quantum revolution''. In this revolution, Niels Bohr's dramatically non-classical theory of the atom proved to be the springboard from which the new atomic physics drew it's momentum. Furthermore, Bohr's contribution was crucial not only because his interpretation of quantum mechanics became the most widely accepted view but also because in his role as educator (...) and spokesman for atomic physics Bohr was very much the patron spirit of the entire quantum revolution. The conceptual framework which he proposed to provide a new viewpoint for understanding the quantum theoretical description of atomic systems became for most of this century the dominant outlook of countless productive experimental and theoretical physicists. He called this new framework complementarity''. (shrink)

Following the practice of human beings everywhere historians distinguish the real or most significant cause of an occurrence or state of affairs from ‘less important considerations’, ‘precipitating circumstances’, or ‘mere conditions’. I shall term claims that some phenomenon is most basically to be attributed to some one of the factors causally necessary for its occurrence attributive causal explanations or causal attributions and discuss here the extent to which moral convictions are constitutive of them.

The career of Oxford philosopher Roger Crisp has produced a wonderfully rich yield of elegant, lucid philosophizing that combines in a rare mix historical erudition and brilliant, creative, and highly interdisciplinary ethical argument. Crisp is steeped in Aristotle and Mill, W. D. Ross and Derek Parfit, but his deepest source of inspiration is by his own admission the Victorian era Cambridge philosopher Henry Sidgwick, author of the famous Methods of Ethics. Although Sidgwick has been regarded as a kind (...) of master of those who know by everyone from Brand Blanshard and C. D. Broad to John Rawls and Peter Singer, his star has been on an especially dramatic ascent in recent decades, in very... (shrink)