The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age, very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of (...) mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga. (shrink)

In this article, we propose the Fair Priority Model for COVID-19 vaccine distribution, and emphasize three fundamental values we believe should be considered when distributing a COVID-19 vaccine among countries: Benefiting people and limiting harm, prioritizing the disadvantaged, and equal moral concern for all individuals. The Priority Model addresses these values by focusing on mitigating three types of harms caused by COVID-19: death and permanent organ damage, indirect health consequences, such as health care system strain and stress, as well as (...) economic destruction. It proposes proceeding in three phases: the first addresses premature death, the second long-term health issues and economic harms, and the third aims to contain viral transmission fully and restore pre-pandemic activity. -/- To those who may deem an ethical framework irrelevant because of the belief that many countries will pursue "vaccine nationalism," we argue such a framework still has broad relevance. Reasonable national partiality would permit countries to focus on vaccine distribution within their borders up until the rate of transmission is below 1, at which point there would not be sufficient vaccine-preventable harm to justify retaining a vaccine. When a government reaches the limit of national partiality, it should release vaccines for other countries. -/- We also argue against two other recent proposals. Distributing a vaccine proportional to a country's population mistakenly assumes that equality requires treating differently situated countries identically. Prioritizing countries according to the number of front-line health care workers, the proportion of the population over 65, and the number of people with comorbidities within each country may exacerbate disadvantage and end up giving the vaccine in large part to wealthy nations. (shrink)

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle's mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature. Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, (...) surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address 'problems' that Aristotle posed but couldn't answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics. (shrink)

“S ought (not) to see to it that p at t” is true iff an intention on the part of S to see to it that p at t is (in) correct. From this truth condition follows an understanding of the conceptual role of ought-claims in practical inference: ought-claims are interchangeable with intentions having the same content. From this conceptual role, it is quite clear why first-person, present-tense ought-judgments, and just those, motivate: failure to be motivated is a failure of (...) rationality. The point and purpose of 'ought' is mainly to express the results of practical reasoning performed on premises held hypothetically, an exercise of which there are many varieties. Our capacity for normative thought and language is a consequence of, and intimately related to, our capacity for practical thought. (shrink)

This thesis explores, thematically and chronologically, the substantial concordance between the work of Martin Heidegger and T.S. Eliot. The introduction traces Eliot's ideas of the 'objective correlative' and 'situatedness' to a familiarity with German Idealism. Heidegger shared this familiarity, suggesting a reason for the similarity of their thought. Chapter one explores the 'authenticity' developed in Being and Time, as well as associated themes like temporality, the 'they' (Das Man), inauthenticity, idle talk and angst, and applies them to interpreting Eliot's poem, (...) 'The Love Song of J. Alfred Prufrock'. Both texts depict a bleak Modernist view of the early twentieth-century Western human condition, characterized as a dispiriting nihilism and homelessness. Chapter two traces the chronological development of Ereignis in Heidegger's thinking, showing the term's two discernible but related meanings: first our nature as the 'site of the open' where Being can manifest, and second individual 'Events' of 'appropriation and revelation'. The world is always happening as 'event', but only through our appropriation by the Ereignis event can we become aware of this. Heidegger finds poetry, the essential example of language as the 'house of Being', to be the purest manifestation of Ereignis, taking as his examples Hölderlin and Rilke. A detailed analysis of Eliot's late work Four Quartets reveals how Ereignis, both as an ineluctable and an epiphanic condition of human existence, is central to his poetry, confirming, in Heidegger's words, 'what poets are for in a destitute time', namely to re-found and restore the wonder of the world and existence itself. This restoration results from what Eliot calls 'raid[s] on the inarticulate', the poet's continual striving to enact that openness to Being through which human language and the human world continually come to be. The final chapter shows how both Eliot and Heidegger value a genuine relationship with place as enabling human flourishing. Both distrust technological materialism, which destroys our sense of the world as dwelling place, and both are essentially committed to a genuinely authentic life, not the angstful authenticity of Being and Time, but a richer belonging which affirms our relationship with the earth, each other and our gods. (shrink)

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature. Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, (...) surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address ‘problems’ that Aristotle posed but couldn’t answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics. (shrink)

This dissertation addresses the ontological significance of poetry in the thought of Martin Heidegger. It gives an account of both his earlier and later thinking. The central argument of the dissertation is that poetry, as conceptualised by Heidegger, is beneficial and necessary for the living of an authentic life. The poetry of T. S Eliot features as a sustaining voice throughout the dissertation to validate Heidegger's ideas and also to demonstrate some interesting similarities in their ideas. Chapter one demonstrates how (...) effectively certain concepts from Heidegger's 'Being and Time' can be applied in an analysis of T.S. Eliots celebrated poem 'The Love Song of J. Alfred Prufrock'. The reading involves concepts such as angst, authenticity, inauthenticity, the they and idle talk as they appear in 'Being and Time' and then relates these to aspects of T.S Eliot's poem. Chapter two is an exegesis of Heideggers essay 'The Origin of the Work of Art' in order to understand the meaning of poetry as he describes it. The essay centres on the interpretation of a painting by Vincent van Gogh, and what the experience of the painting reveals to someone authentically engaging with the artwork. Heidegger attempts to establish what the essence of a thing is (the artwork as thing), for the 'origin' of the artwork resides in its 'thingliness'. He creates an important distinction between equipment and the artwork, as well as earth and the world in order to justify the unique, originary position that the artwork occupies. This leads Heidegger to create a new understanding of poetry (which is expanded to encompass all art forms) and to emphasise the importance of the human agent in both the creation and preservation of the artwork. Chapter three is an exploration of language in both the Heidegger of 'Being and Time' and the later Heidegger's thought. The aim is to explore the ontological effect that Heidegger's conception of language has for our existence. He places language within a primordial role arguing that it is not us who speak language, but language that speaks us. This conception has important consequences for our relationship with Being, and the way in which we understand our existence. The final chapter unifies the various themes of the dissertation into a cohesive argument. The chapter begins with a discussion on the meaning of our existence following the later Heidegger. This is nothing less than the guardianship of Being which can only be understood in its relation to our dwelling within the fourfold. In conclusion it is through the measure of the language of poetry that we can realise the possibility of authentic dwelling. (shrink)

Aldo Leopold was a pragmatist in the vernacular sense of the word. Bryan G. Norton claims that Leopold was also heavily influenced by American Pragmatism, a formal school of philosophy. As evidence, Norton offers Leopold's misquotation of a definition of right (as truth) by political economist, A.T. Hadley, who was an admirer of the philosophy of William James. A search of Leopold's digitised literary remains reveals no other evidence that Leopold was directly influenced by any actual American Pragmatist or by (...) Pragmatism (although he may have been indirectly influenced by Pragmatism early in his career). A 1923 reference, by Leopold, to Hadley and Hadley's putative definition of truth, cited by Norton, is dripping with irony. Leopold, as he matured philosophically, regarded a profound cultural shift from anthropocentric dominionism and consumerism to an evolutionary-ecological worldview and an associated non-anthropocentric 'land ethic' to be necessary for successful and sustainable conservation. Hadley espoused a brutal form of Social Darwinism and his philosophy, as expressed in the book of Hadley's that Norton cites, is politically reactionary, militaristic and unconcerned with conservation. Leopold's mature philosophy and Hadley's – far from consonant, as Norton claims – are diametrically opposed. (shrink)

A recent resurgence of interest in the thought of the Scottish thinker, Adam Ferguson (1723-1816), still leaves nagging questions, especially regarding works other than his celebrated An Essay on t...

Né dans le sillage d’un « significant renewal of interest in Bergsonism and a greater recognition of his influence on twentieth-century philosophy » (p. 1), ce livre ne pouvait que poser des questions sur le temps, ramenant également à la philosophie de Heidegger, à qui l’on doit l’une des pensées les plus originales à ce sujet. Aussi Heath Massey s’emploie-t-il lire les textes de Bergson qui tentent de repenser la notion traditionnelle de temps à côté de ceux de Heidegger, (...) mettant plus particulièrement en lumière l’influence de celui-là sur celui-ci, une influence largement passée inaperçue. L’importance de cette œuvre tient dans la façon dont l’A. conteste la philosophie du temps que Heidegger attribue à Bergson. Notre guide considère la lecture bergsonienne de Heidegger comme une « oversimplication » (p. 84) et vise à éclaircir comment, malgré les propos du penseur allemand, le philosophe français a été capable de radicalement repenser le temps d’un point de vue ontologique. Dès lors, l’ouvrage s’achève sur un goût de soupçon, celui-ci faisant dire que Heidegger a essayé de se distinguer de Bergson pour ne pas admettre ce dont il lui est redevable. (shrink)

Introduction -- Instrumental rationality -- Social order -- Deontic constraint -- Intentional states -- Preference noncognitivism -- A naturalistic perspective -- Transcendental necessity -- Weakness of will -- Normative ethics.