The city has featured as a central image in utopian thought. In planning the foundation of the new and ideal city there is a close interconnection between ideas about urban form and the vision of the moral good. The spatial structure of the ideal city in these visions is a framing device that embodies and articulates not only political philosophy but is itself an articulation of moral and cosmological systems. This paper analyses three different utopian moments in three (...) different historical epochs – Tommaso Campanella’s City of the Sun (1602), the Choson dynasty foundation of the city of Seoul (1395) and the modernist utopian urbanism of the controversial Le Corbusier (1887–1965). In this analysis attention is drawn to the cosmological and moral visions articulated in these three ‘images of the city’ (Lynch). The opposition between rationalistic/mechanistic and religious/traditional urban design can prove to be an oversimplification that obscures the complex interrelations between the moral geometry and the natural alignments of the ideal urban form. (shrink)

The literary and critical discourse about characters and characterization in Anglophone drama and fiction since the Renaissance shows a persistent but underrecognized presence of three idioms and vocabularies, two highly developed and one nascent, that either derive from the rhetoric of mathematics in classical antiquity or participate in its modern afterlife. Those discourses—which this article studies in detail—are, first, an explicitly Theophrastan one, in which taxonomies of character are constructed; second, an explicitly Euclidean one, in which characterization is discussed and (...) accomplished in relatively conventional or commonsensical geometric terms; and third, a non- or post-Euclidean one, in which characterization is discussed and inchoately accomplished in the terms of the “new geometries” that emerged during the nineteenth century. What taxonomy in the Aristotelian mode and geometry in the Euclidean mode have in common is that when their vocabularies are applied to characterization, they delimit characters in terms of established categories—whether of ideal shapes or statistically probable types—while discounting whatever features may be unique to individuals. An obliviousness to these three discourses can limit seriously what can be said about, and what can be said on behalf of, the literary and critical texts framed in their terms and also, most importantly, what can be said about the nature of literary characters. (shrink)

Once again, for the first time, Marx and Durkheim join forces while exploring the moral economy of neoliberalism. Resignation and Ecstasy provides a fresh perspective on the immortal vortex of sacred energies pulsating beneath the peculiar logic of modern accumulation. Relying on dialectical methods, classical sociology and psychoanalysis are reconstituted within an Hegelian social ontology to differentiate the ephemeral from the eternal aspects of social life.

This paper examines the ethical and religious dimensions of mathematical practice in the early modern era by offering an interpretation of Antoine Arnauld and Pierre Nicole’s Nouveaux éléments de géométrie. According to these important figures of seventeenth-century French philosophy and theology, mathematics could achieve extra-mathematical or non-mathematical goals; that is, mathematics could foster practices of moral self-improvement, deepen the mathematician’s piety and cultivate epistemic virtues. The Nouveaux éléments de géométrie, which I contend offers the most robust account of the (...) virtues cultivated by mathematics in the period, was envisaged by its authors to cultivate moral, Christian and epistemic virtues that could serve in the fulfilment of moral and Christian obligations. In this paper, I set out the goals of mathematical inquiry for the Port-Royalists and describe the specific virtues they believed a revised edition of the Elements of Euclid could foster. I show that Arnauld and Nicole believed that an acquaintance with mathematics could render a student of Euclid more just, truth-loving, attentive and humble, and better able to discern truth from falsity. (shrink)

Moral desert -- Fault forfeits first -- Desert graphs -- Skylines -- Other shapes -- Placing peaks -- The ratio view -- Similar offense -- Graphing comparative desert -- Variation -- Groups -- Desert taken as a whole -- Reservations.

In the central chapters of Leviathan, Hobbes offers a demonstration of the "true doctrine of the laws of nature," which is identified with the "science of virtue andvice" and the "true moral philosophy." In his deduction of the laws of nature, Hobbes attempts to mimic the science of geometry, which he says is the "only science God had hitherto bestowed on mankind. "In this paper, I discuss some of the problems associated with Hobbes's application of the method of (...) geometry to civil philosophy. After locating the root of these problems in Hobbes's in ability to recognize the distinction between formal and applied sciences, I discuss a possible solution. According to this solution, Hobbes's "science of morality" is considered to be a formal science that is applied to the world by an act of human creation. (shrink)

Cet article a pour but de présenter la première traduction française de deux textes de Helmholtz de 1878. À la lumière du développement des géométries non euclidiennes, il y critique la conception kantienne de l’espace. Par là même, il expose une redéfinition purement empiriste de la construction des déterminations spatiales qui, sous le nom de « géométrie physique », joua un rôle important chez Poincaré (qui la révise) et chez Einstein.

Wittgenstein n'a eu de cesse de critiquer la distinction entre géométrie pure et géométrie appliquée. Cette distinction a été notoirement défendue par les positivistes logiques qui, dans le cadre d'une théorie renouvelée de l'a priori, entendaient marquer une séparation nette entre les mathématiques (systèmes formels non interprétés) et la physique (systèmes interprétés, dotés d'une signification factuelle ou empirique). Les raisons de ce partage perdent leur évidence si l'on envisage la géométrie en action, comme une pratique où les règles ne peuvent (...) pas être considérées indépendamment des « coups » qu'elles règlent effectivement. Cette conception « syntaxique » de la géométrie éclaire la signification réelle du « conventionnalisme géométrique » attribué à Poincaré ; elle fait comprendre du même coup les distorsions introduites par les interprétations qui se sont appuyées de façon implicite ou explicite sur la distinction entre le pur et l'appliqué. (shrink)

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used (...) to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann’s principle of classical statistical thermodynamics. A new expression for a general nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics. (shrink)

In The Geometry of Desert I used graphs to explore two common ideas about moral desert, namely, that people differ in terms of how deserving they are, and that it is a good thing if people get what they deserve. I argued that desert is a more complex value than we normally recognize, and I laid out a number of alternative possible views, defending some of them. In a pair of critical discussions published in this journal, Victor Tadros (...) and Kasper Lippert-Rasmussen offer a variety of objections to several of the ideas I have put forward. In this essay I welcome their criticisms and respond to some of the main points they raise. (shrink)

I extract some philosophical morals from some aspects of Lagrangian mechanics. One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels---``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian mechanics provides an introduction to the subject for philosophers, and is (...) technically elementary. In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. (shrink)

John Rawls was the most influential political philosopher of the 20th century. His magnum opus, A Theory of Justice, revolutionised moral and political philosophy by offering a deductive way out of the intellectually unsatisfying reliance on brute intuitionism while avoiding the pitfall of irrelevance by implausibility that had plagued other contract arguments. Rawls’s elegant, novel and innovative approach provided a parsimonious solution to the problem of distributive justice by using, mutatis mutandis, the familiar device of the social contract. His (...) was an ambitious project that attempted to “provide a deductive basis for the principles that account for [our considered] judgements” (1971: p. 185). Indeed, Rawls stated categorically that his argument was meant to be “strictly deductive,” going as far as to say “we should strive for a kind of moral geometry with all the rigor which this name connotes” (p. 121). Rawls’ grand ambitions, however, did not long survive: under intellectual pressure from several directions he retreated into a somewhat relativistic intuitionism, saying he no longer wanted to discover universal moral principles, but rather principles ‘appropriate’ to modern democracies. I will not attempt engage with or summarize the vast literature of responses to A Theory of Justice that led Rawls down this path. Instead, I will diverge from the later Rawls and defend his original conclusion – i.e. his principles of justice – while modifying parts of his argument. Specifically, I will argue that it is crucial to notice that the veil of ignorance screens out two different types of particular information: information about individuals and information about society. A veil that screens out only the first type of information is a “thin” veil, while one that screens out both the first and second types is a “thick” veil. I will conclude that Rawls’ own methodological commitments – particularly, pure procedural justice – are compatible only with a thin veil of ignorance but, despite this, that broadly Rawlsian principles still emerge from the original position. (shrink)

IN BOTH THE EUDEMIAN ETHICS AND THE NICOMACHEAN ETHICS, Aristotle says that the aim of ethical inquiry is a practical one; we want to know what virtue is so that we may become good ourselves and thereby do well and be happy. By classifying ethical inquiry as a practical endeavor, Aristotle is rejecting a view that he attributes to Socrates according to which ethics is a kind of theoretical science. In theoretical sciences, such as geometry or astronomy, the knowledge (...) of a particular subject matter is sought as an end in itself, and the possession of such knowledge is sufficient to make one a geometer or an astronomer. In rejecting this model Aristotle argues that the knowledge of virtue is sought not solely for itself but in order to inform praxis and in order that we become virtuous and good, not by knowing what the virtues are but by cultivating them in practice. (shrink)

In contrast to the Nietzschean conception of Übermensch as signifying, hitherto, a supermanhood in moral terms alone, the principle of the latter lies in its being antithetical to the present human status, and in its thus proving altogether superior both ontologically and physically. With this premise the notions of Sixth Force and Photonic Frame are now associated. Set forth after a qualitative fashion, while the former is related to the thus far known elemental constituents of matter, as well as (...) to forces and interactions between matter particles, and under this form deemed to intangibly account for all the chaos, indeterminacy and otherwise imperfection or limit found so peculiar to man, the latter refers to an ultimate trait in the actual Overman touching a most luminous and unparalleled corporeality. An original conception of geometry in photonic terms is also propounded. Illustrations meeting at length with a semiotic process and literary hints add to the suggestion. (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal (...) analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Leibniz’s Political and Moral Philosophy in the Novissima Sinica, 1699–1999Patrick RileyThe Preface to Leibniz’s Novissima Sinica 1 contains an important but highly compressed and abbreviated quintessence of his theory of justice or jurisprudence universelle—a version so compressed and abbreviated that one must have a broader and fuller understanding of this universal jurisprudence before one can entirely appreciate what Leibniz has to say about Christian charity, Platonism, and (...) class='Hi'>geometry in the Novissima Sinica itself. Above all, one wants to know why Leibniz, in the key paragraph of the Preface to Novissima Sinica, should describe the Chinese emperor as just and charitable and as a (more or less) “Platonic” geometer who is as wise as he is charitable. And why should Leibniz contrast this “wisely charitable” Chinese ruler with the Pontius Pilate who irresponsibly asked, “What is truth?” and then permitted the judicial murder of the very Christ who did most to make charity and justice coextensive by saying, “A new law I give unto you, that ye love one another”? 2 The wise course, therefore, is to throw enough light on Leibnizian universal jurisprudence in general to make his moral-political utterances in Novissima Sinica intelligible in particular.In 1693, four years before the publication of Novissima Sinica, Leibniz revealed the outlines of his jurisprudence universelle in the Codex Iuris Gentium:a good man is one who loves everybody, so far as reason permits. Justice, then, which is the virtue which regulates that affection which [End Page 217] the Greeks call philanthropy, will be most conveniently defined... as the charity of the wise man, that is, charity which follows the dictates of wisdom... Charity is a universal benevolence, and benevolence the habit of loving or of willing the good. Love then signifies rejoicing in the happiness of another..., the happiness of those whose happiness pleases us turns into our own happiness, since things which please us are desired for their own sakes. 3Slightly later, in La véritable piété, Leibniz indicated what this view of justice entails:those who... reduce justice to [mere] rigor, and who fail altogether to understand that one cannot be just without being benevolent... in a word, not only those who look for their profit, pleasure, and glory in the misery of others, but also those who are not at all anxious to procure the common good and to lift out of misery those who are in their care, and generally those who show themselves to be without enlightenment and without charity, boast in vain of piety which they do not know at all, whatever appearance they create. 4The central idea of Leibniz’s “universal jurisprudence,” which aims to find quasi-geometrical, eternal moral verities equally valid for all rational beings, human or divine, is that justice is “the charity of the wise” (caritas sapientis), 5 that it is not mere conformity to sovereign-ordained “positive” law given ex plenitudo potestatis (in the manner of Hobbes); nor is it mere “refraining from harm” or even “rendering what is due” (the neminem laedere and suum cuique tribuere of Roman law). 6 The equal stress on “charity” and on “wisdom” suggests that Leibniz’s practical thought is a kind of fusing of Platonism—in which the wise know the eternal truths such as absolute goodness (Phaedo 75d), which the gods themselves also know and love (Euthyphro 93-10e) and which therefore deserve to rule (Republic 443d-e) 7 —and of Pauline Christianity, whose key moral idea is that charity or love is the first of the virtues (“though I speak [End Page 218] with the tongues of men and of angels, and have not charity, I am become as sounding brass or a tinkling cymbal”). 8 Historically, there is nothing remarkable in trying to fuse Platonism and Christianity. Augustine’s thought (particularly the early De Libero Arbitrio) is just such a fusion. 9 But Leibniz was the last of the great Christian Platonists, and left the world just as Hume, Rousseau, and Kant were about to transform and “secularize” it.I. If one decomposes caritas sapientis into its parts, charity and wisdom, the provenance of both elements is clear enough... (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal (...) analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

This study of the history and contents of a hitherto unedited work on geometry by Vincenzo Viviani seeks to present a picture of the scientific environment in Italy in the second half of the 17th century, with particular emphasis on Tuscany and the impact the condemnation of Galileo had on ongoing scholarship. Information derived from unedited or less well-known material serves to illuminate a range of prominent and marginal figures who adopted different strategies for the dissemination of Galileo’s thought (...) and the application of its principles. A selection of texts, edited here for the first time, is presented in two appendices, while in a third decidedly unusual methods are used to elucidate the mathematical aspects. (shrink)