In _Plato's_ Timaeus _and the Missing Fourth Guest_, Donna M. Altimari Adler offers an original account of Plato's Timaeus from 35a-36d, yielding a new interpretation of the _Timaeus_ scale and cosmic harmony imbedded in the text.

This book describes various Western musical ecologies of the cosmos developed from the ancient world to the present, ecologies that seek to define the creation and preservation of the universe through musical principles. The author explores centuries of musical treatises, hymns, and Western fiction.

The paper argues that Nikolai Berdyaev’s doctrine of theurgy has remained relevant in today’s cultural-historical context because it highlights a continuing problem in the philosophy of art. The problem is the misunderstanding of the ludic nature of art, its role in the evolution of consciousness and transformation of reality. The author questions the idea that artistic play is deficient compared with religious expression. As a result of this critique, he proposes that the theurgic quest for a radically new form of (...) creativity was misguided and that the true meaning of the aspiration behind it is the need to comprehend culture as a dialectically articulated integral system of the cultural forms that constitute it. (shrink)

The Pythagorean theory of the Harmony of the Spheres has been influential in the history of philosophy and science. While much ink has been spilt over its scientific implications, its mythological formulation has not yet received serious scholarly attention. This groundbreaking book fills that gap by offering a sustained study of the theory s mythological rendition in Plato s Republic and in Iamblichus On the Pythagorean Way of Life. ".

This article revisits the "harmony doctrine" school of economics and its distinctive understanding of how ethics and economics intersect. Harmony doctrine thinkers staked out a “natural” understanding of economic phenomena that in many ways fused the classical political economy of Adam Smith with the earlier French Physiocratic School. Their metaphysically grounded interpretation was largely eclipsed by the developments of utilitarian and marginalist schools by the end of the nineteenth century. Yet harmony doctrine thinking adhered to a distinct (...) understanding of how ethical processes and outcomes play out within the economic sphere that has to date gone under examined by business ethicists. This paper outlines three characteristics of harmony doctrine views: the belief in curative forces empowered to "heal" the economic order, a dichotomous interpretation of the economic realm that distinguishes the “natural” from the “artificial,” and an overarching belief in a harmonious social order actualized by cooperative interdependencies within economic enterprises. Despite falling into obscurity in the economic discipline, all these ideas found new life in intellectual currents of organizational and political thought at the turn of the twentieth century. After surveying these historical developments, this article concludes by demonstrating how harmony doctrine thinking helpfully illuminates persisting metaphysical dimensions of contemporary business ethics. (shrink)

The reception of the heliocentric theory of Nicolaus Copernicus in Jewish thought of the 17th-century period is a good exemplification of the issue concerning the formation of the relationship between natural science and theology, or more broadly: between science and religion. The fundamental question concerning this relationship, which we can ask from today’s perspective of this problem, is: How does it happen that claims of a scientific nature, which are initially considered from a religious point of view to be incompatible (...) with the religious view of the world, are later accepted as possible to agree with this image of reality and are assimilated by a given religion? Based on the reception of the Copernican image of the universe by two representatives of Jewish philosophy in the 17th century—David Gans and Joseph Solomon Delmedigo—it is possible to trace this process and pose the thesis that it takes place according to two strategies. Within the framework of the first one, represented by Gans, in a situation of incompatibility between the scientific and religious images of nature, a scientific theory is sought that explains the observed phenomena and, on the other hand, satisfies the religious claims. Finding such a theory solves the problem of the incompatibility mentioned above of images of the world, gives the theory credibility from the religious point of view and constitutes an argument for its correctness. The second strategy, represented by Delmedigo, consists in refraining from pursuing a direct, immediate, and unequivocal reconciliation of the two images of the world while at the same time recognizing a properly justified scientific theory as correctly describing and explaining the phenomena occurring in nature. Consequently, the apparent incompatibility between the scientific and the religious worldview demands either a reformulation of religious statements in such a way as to remove this incompatibility or the restriction of the meaning of religious statements to the strictly religious and moral sphere, without the ambition to speak about nature. In either case, however, it is already a task for the representatives of the religion concerned who, when confronted with adequately justified scientific claims, to avoid exposing their religion to the accusation that its claims are unreasonable and anachronistic, undertake the task mentioned above of modifying or limiting the scope of their statements. It seems that in the representatives of Jewish thought and Judaism, who are the successors of Gans and Delmedigo, generally speaking, the second strategy has prevailed in this version, in which one abandons the claim of religion to statements about the material world at the price of a significant divergence of the paths of science and religion. Consequently, it treats them as different narratives, describing and explaining two separate spheres of reality. (shrink)

A profound exploration of the simple numerical ratios that underlie our solar system, its musical harmony, and our earliest religious beliefs.

Soon after December 1989, the Romanian political power and the Romanian Orthodox Church have established that they had common interests regarding the preservation of several elements of the old leadership structures. A radical severance with the past has never been accomplished, for, a certain fear for a complete unbalance and of an uncontrollable evolution of the State’s institutions and of the Church’s hierarchy became manifest at that time. Thus, the Orthodox Church and the leading political post-communist party have made a (...) series of mutual good turns, with a view to maintaining the status-quo. At the same time, the political leadership manifested occult trends in order to control the Orthodox Church and to monopolize its huge sphere of influence for political purposes, since the State had no interest in the existence of a very strong and independent Church. This article shortly analyzes some of these cases. (shrink)

The article develops the idea of forming postcapitalist social relations as a social revolution of an individual, which consists in the fact that popularity becomes a key advantage, the “possession” of which is a desired goal and a significant resource of political influence. At the same time, it is shown that this process leads to forming a new dominant stratum — personalities (“people with personality”): celebrities, popular bloggers, social media influencers, micro- and nanosignature. It is substantiated that the personaliat domination (...) is a consequence of contradictory social relations between the new aristocracy represented by the representatives of the personaliat and many people who do not “possess” a popular personality - the impersonaliat (“extra people”, “lower” precariat, those who turn out to be outsiders in the world of social platforms). This contradiction is associated with the rooting of a celebrity’s culture, which encourages a lot of people to fight for popularity and focus on finding advantageous differences from others in the process of self-realization. However, this struggle in the end for the overwhelming majority turns into an increase in creative competition and subtraction. Various new forms of subtraction that appear in situations of widespread self-realization are revealed. Accordingly, arguments are given in favor of the fact that in the context of the “personality revolution”, the truly left will be rather an alternative that will call into question the ways of solving social problems formulated by popular personalities. In other words, it will be possible to oppose the total pursuit of popularity with the projects of society, in which the person is relied not as someone who rises above the others, but as an involved person who values life in harmony with others higher than his own “I”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Martin Heidegger and OntologyEmmanuel Levinas (bio)The prestige of Martin Heidegger 1 and the influence of his thought on German philosophy marks both a new phase and one of the high points of the phenomenological movement. Caught unawares, the traditional establishment is obliged to clarify its position on this new teaching which casts a spell over youth and which, overstepping the bounds of permissibility, is already in vogue. For once, (...) Fame has picked one who deserves it and, for that matter, one who is still living. Anyone who has studied philosophy cannot, when confronted by Heidegger’s work, fail to recognize how the originality and force of his achievements, stemming from genius, are combined with an attentive, painstaking, and close working-out of the argument—with that craftsmanship of the patient artisan in which phenomenologists take such pride. In this study, it is important for us to understand, above all, the true intentions of our author, to illuminate what he thinks really needs to be said, and to surmise what is most critical for him.To get to the heart of Heidegger’s system, it seems fitting to begin with a problem that is generally familiar. We choose the problem of knowledge, a deeper understanding of which takes us to the very threshold of Heidegger’s thought. For this problem, central to modern philosophy, is one of the main obstacles of modern philosophy that Heidegger wishes to surmount. Neo-Kantianism, which takes knowledge as the philosophical problem of the first rank, is the movement against which Heidegger rebels with all his strength. We have, thus, every chance of gaining access to his thought by the main door, so to speak. Once inside the system we will try to trace its outlines, 2 reserving, for a second part of our work, the determination of Heidegger’s place in the history of ideas, especially in the phenomenological movement, as well as of his relations with the philosopher to whom he owes so much—Edmund Husserl. 31In its most general form, the problem of the theory of knowledge has a critical significance. It consists in delineating a domain where knowledge can be certain and in determining the criteria for the legitimate scope of knowledge. But this problem, as normal and as simple as it may appear, has deeper roots. That knowledge should need a criterion at all presupposes that truth is not identical to all that is known and that the course [End Page 11] of things can fail to correspond with the course of thought. “How does knowledge correspond to being?” is a more profound formulation of the problem of knowledge.But we are not going to touch anymore on the primordial phenomenon that generates the problem. The problem of correspondence between thing and thought presupposes a free activity of thought and its isolation in relation to the object. It is precisely this presupposition which renders their harmony and even their contact problematic. “How does the subject take leave of itself to attain the object?” is what the problem of knowledge, in the last analysis, boils down to. Its true source is thus the concept of “subject” as elaborated by modern philosophy. The cogito presided over the subject’s birth. The cogito was the affirmation of the privileged nature of the subject’s immanent sphere, of its unique place in existence; hence, the cogito was the specificity of the subject’s connection to the rest of reality, the sui generis nature which opens up the passage from immanence to transcendence, the passage from ideas contained in the thinking substance to 4 their “formal existence.”The concept of the subject, understood as a substance having a specific position in the entire domain of being, presents us with difficulties of two kinds. First, how do we understand this leave-taking from the self which the thinking substance brings about and which displays an entirely original aspect? Indeed, we could say that thought, in reaching out toward objects, does not actually take leave of itself, since its objects—considered as ideas and contents of thought—are, in a certain sense, already within it. In order to make sense of this paradox, Descartes... (shrink)

In Avicenna's allegorical treatises humans are envoys of two worlds; on one hand, as products of natural evolution they are representatives of the earthly, physical world; on the other, as products of divine emanation they represent the cosmic principle. But in the process of spiritual contemplation they overcome theduality and split nature of their being and restore the fractured harmony between themselves and the cosmic world. Thus, having attained the highest form of cognition and moral beauty, the individual 'self (...) becomes the universal essence identified in the language of Sufism as 'the perfect human'. Avicenna tries in hisallegorical treatises to makes his of becoming a perfect individual is not a sudden act of illumination, but a pyramid-like development, arranged, like the heavenly spheres, hierarchically, and calling for an incredible exertion of followers recognize that each person is able to rise to the level of the 'perfect individual', the road to which lies through moral purification and mastery of learning and the sciences, primarily philosophy. But the process strength, self-limitation and effort of will to pass through the stages of perfection and achieve the aim. (shrink)

De l'Antiquité à la Renaissance, la notion d'harmonie a lié les mathématiques, l'astronomie et la musique. Renouant avec cette tradition millénaire, Jean-Philippe Uzan vous invite à écouter le chant des étoiles, les vibrations du cosmos et le cri du big bang. Une balade cosmique entre sciences et musique, vertigineuse et inspirante. Jean-Philippe Uzan est physicien théoricien, spécialiste de la théorie du big bang. Il est directeur de recherche au CNRS/Institut d'astrophysique de Paris et directeur adjoint de l'Institut Henri Poincaré.

In lieu of an abstract, here is a brief excerpt of the content:The Enchantment of Art: Abstraction and Empathy from German Romanticism to ExpressionismDavid MorganA familiar tradition since the eighteenth century has invested art with the power to heal a decadent human condition. Inheriting this ability from religion—the romantic enthusiast Wilhelm Wackenroder considered artistic inspiration to originate in “divine inspiration” in the case of his hero, Raphael 1 —art eventually replaced institutionalized belief in an evolutionary schedule of cultural development determined (...) by German idealism. Hegel, for instance, theorized the evolution of spirit from religion to art as a qualitative advancement over time. Rejecting the metaphysics of German idealism, Friedrich Nietzsche nevertheless contended that “Art raises its head where religions decline.” By assuming the “feelings and moods” of religion which had been dismantled by enlightenment, Nietzsche claimed that art gave new form to the life of feeling and imbued human endeavors with a “loftier, darker coloration.” 2 In the early twentieth century Wassily Kandinsky believed that the “spiritual in art” was the historical manifestation of an “inner necessity” that was in itself timeless and universal. Kandinsky portrayed the “life of the spirit” as “a large acute-angled triangle divided horizontally into unequal parts.” In a kind of “trickle down” aesthetic, the compartments of the triangle move slowly upward toward the apex, which is inhabited by the solitary genius of an age whose vision gradually elevates all those who occupy the lower stages. 3 [End Page 317]The point for proponents of the spiritual in art from romanticism to expressionism (and beyond) was to find in works of art what can best be described as an enchantment. 4 As the negotiation of the gaps or disjunctures separating human beings from complete power over their lives, enchantment conjoins the plane of immediate human experience to a desirable state of affairs through the mediation of such symbolic devices as rituals, incantations, or charms. Thus, evil can be warded off by the use of an apotropaic amulet, and fertility can be enhanced by the recitation of a suitable prayer or the performance of a certain ritual. In a modern analogy a sense of impotence is often alleviated by a trip to the mall where the bored therapeutically lose themselves in symbolic acts of self-renewing consumption. In the traditions of philosophy and science, systems of representation such as astrology, the microcosm, the harmony of the spheres, the great chain of being, the celestial hierarchies, or the mechanisms of theurgy and divination situate humanity within a cosmos that follows a particular order accessible to and in some degree manipulable by human beings. Enchantment consists of an apparatus of belief whose form of representation or enactment is thought to exert influence over the realities it configures.But enchantment is not limited to the spells and magic of premodern metaphysics (or modern consumerism). By means of religion, morality, and aesthetics, Nietzsche once averred, “man likes to believe that... he is touching the heart of the world.” 5 This study will focus on the manner in which art as constructed within the idealist tradition of German art theory functioned as an enchantment. Specifically, it will explore what the history of ideas about abstraction and empathy has to tell us about the spiritualization or enchantment of art. After identifying the philosophical and aesthetic wherewithal of enchantment in nineteenth-century Germany, attention focusses on Franz Marc’s early twentieth-century theorization of abstraction. It is certainly more customary to study Kandinsky, whose writings and early efforts at abstraction are much better known, but Marc’s ideas offer more immediate connections to German intellectual history and clarify the aims of his abstract art as a strategy of enchantment. Moreover, Marc was unusually articulate and wrote often, exploring ideas and artistic efforts with great insight. Focusing on Marc therefore offers a corrective to the historiography that has favored Kandinsky’s writings. Finally, Marc differed from his Russian friend over the cause of the war. Manifesting a difference that is portentous for this study, Kandinsky left Germany for Russia in 1914, while Marc enthusiastically took up arms for the fatherland. Given these circumstances and the unfortunate tendency of art historians to valorize expressionist art rather than situate it in the ideological context of... (shrink)

This paper explores Husserl's phenomenological description of the constitution of the alter ego within the sphere of transcendental subjectivity. It is important at the start to point out that the Other plays a crucial role in securing the intersubjective nature of the experienced world. Although Husserl goes on in the "Fifth Cartesian Meditation" to consider the constitution of an objective world common to all subjects and the establishment of a community of monads, my primary focus in this paper will be (...) the examination of the initial steps whereby the sense, "other ego," is constituted by the transcendental ego. My main task, then, will be to examine the reduction to the sphere of ownness, the appresentative transfer of sense from ego to alter ego, and the criterion of harmonious behavior. My primary criticisms will center around certain difficulties inherent in the attempt to uncover a primordial sphere of ownness and problems that arise from a shift in concern from the life-world (everyday) attitude to the attitude following the performance of the epoché. Part I of the paper will consist of a general discussion of Husserl's phenomenological project, Part II will be a detailed study of the alter ego, and Part III a general statement of problems and objections. (shrink)

In nature scent is important for man primarily as a marker of food and sexual attractiveness, it polarizes as objects of life and decay, death. Scent, just like touch and taste exists till subject and object get opposed to each other, it is the sphere where body is included into material world, and flesh of the world is incrusted into the body. Aesthetics in its anthropologic meaning is limited by a body- perceptible dimension. Development of such categories as the sublime, (...) tragic, comic are not possible here. Creation of compound aromas, including those which do not exist in nature, can not overstep the limits of the beautiful- -ugly opposition. There is no contradiction, nourishing the comic, the tragic or the sublime, in blending of body with the world by means of scent. The spectrum of the aesthetic in the sphere of aromas is expanded in the plane from the beautiful to the ugly: fragrant, heady, amber, garlic, carpic, putrid, hideous, stinking. (shrink)

When I began working on my dissertation on Kant’s aesthetic theory in 1971, I was able to read virtually all of the extant literature on the Critique of Judgment in English, German, andFrench going back to Hermann Cohen’s Kants Begr¨undung der A¨ sthetik of 1889, while also reading most of what I wanted to read of eighteenth-century British and German aesthetics before Kant—not because I had paid my dues to Evelyn Wood, but just because there was not all that much (...) to read.1 I pity the graduate student who sets out to write a dissertation on the third Critique now: since Donald Crawford, Francis Coleman, Jens Kulenkampff, Eva Schaper, and I published books on Kant’s aesthetics between 1974 and 1979 there has been a continuing flood of articles (this journal receives more submissions on Kant’s aesthetics annually than on any other historical topic) and books, a flood that has only accelerated since 2000. Confining myself only to monographs and anthologies on Kant’s aesthetics or the third Critique as a whole (but not those devoted exclusively to teleology) in English, German, and French on my shelves, and no doubt missing some, at least in German and French, I find twenty-eight monographs and anthologies published in the period between 1980 and 1999 and another twenty-seven just since 2000. (Indeed, two more have arrived on my desk since this article was written.)3 Someone setting out to work on the third Critique now has at least as many books from the last decade alone to read as I had in 1971 from the eight preceding decades. The present review will make only a small dent in this pile: I will discuss just five monographs and one introduction to the third Critique, all published in English in 2006 and 2007. (shrink)

This thesis is directed towards a philosophy of music by attention to conceptions and perceptions of space. I focus on melody and harmony, and do not emphasise rhythm, which, as far as I can tell, concerns time rather than space. I seek a metaphysical account of Western Classical music in the diatonic tradition. More specifically, my interest is in wordless, untitled music, often called 'absolute' music. My aim is to elucidate a spatial approach to the world combined with a (...) curiosity about the nature of the Pythagorean intervals. Thus one question I seek to answer is: What do the Pythagorean intervals import to music? In their original formulation by Pythagoras, and further, by Plato, their import seemed mystical and analogous to a 'harmony of the spheres.' In this spatial approach, the Pythagorean intervals are indicative of infinite depth. The faculty of hearing alone does not ordinarily spatially locate sources. Hearing is ordinarily combined with sight in order to spatially locate a sound. Yet we talk about music as if it were spatially located, that is, as if it were a visible object with a surface and themes or 'objects'. I explore the faculty of vision and consider in what ways the processes of vision might be similar to and distinct from audition. My source for this approach is David Marr's book 'Vision' and his theory of the 2 1/2-dimensional sketch. In a medium in which there is no spatial location, it is important to situate the listener. Newton solved the problem of location by demonstrating the effects of gravity. P. F. Strawson claims that an analogy of distance is required in hearing to situate the listener, that is, a sense of nearer to and further from a source or object that permits a perception of distance. I claim that in music, the key signature and the scalar relations of musical themes provide this analogy of distance. The works of Plato, Aristotle, Descartes, Leibniz, and Newton are studied for their accounts of motion, bodies, and space. From these metaphysicians can be gleaned elements of music that include form, motion, timbre, dynamics, and attraction. By incorporating motion, I aim to show that although we may not know the true nature of space, we can learn from hearing music that space is perceptible in other than three dimensions. (shrink)

La Voix divine, nous disent les mythes et traditions, a créé le monde. Le chant des voix humaines lui répond. Orphée, l'initié des Mystères grecs, personnifie les pouvoirs de la musique. De nos jours, le matérialisme scientiste qui nie l'harmonie cosmique est démenti par la science ± holistique? qui rejoint la sagesse ancestrale. Au confluent de la physique contemporaine et de la métaphysique traditionnelle, de la cosmologie et de l'anthropologie, de la musicologie et de l'ethnomusicologie, cet ouvrage contribue à ce (...) nouveau paradigme en élucidant les arcanes de l'harmonie musicale. Il lui restitue sa dimension symbolique et spirituelle et éclaire l'évolution confuse de la musique occidentale depuis le début du xxe siècle. (shrink)

A central thesis of the book is that we can assume "the worst" about what science tells us about the human animal without having to sacrifice any of the things that are of most importance to ethics: virtue and the good life, harmony of the ...

The aim of the paper is to determine why copernicus made a personal seal of the ancient intaglio with the image of apollo playing a lyre, A representation illustrating the myth of phoebus the sun-God and his music as the source of the harmony of the universe. The reasons seem to be: a remarkable role played by the ancient opinions concerned with the harmony of the world in the creative process of copernicus' cosmological theory (his acceptance of "plato's (...) axiom"), The fact that in his theory the sun became the centre of the universe, And that a harmony of sounds, Supposed to be produced by the spheres moving under the rule of phoebus' music, Became--In his opinion--The real although not acoustical harmony of the simple circular spheres on which planets move in a uniform way around the sun. (shrink)

Once upon a time, the universe was much simpler: before our modern understanding of an infinite formless space scattered with pulsating stars, revolving planets, and mysterious black holes, the universe was seen as a rigid hierarchical system with the earth and the human race at its center. Medieval Views of the Cosmos investigates this worldview shared by medieval societies, revealing how their modes of thought affect us even today. In the medieval world system--inherited by Christians and Muslims from the Greeks (...) and Romans, and modified by their own religious tenets--spheres bearing the planets and stars wheeled around the earth, and at every level there was a moral lesson for humanity and a satisfying metaphor for the nature of God. The authors of this volume explain how the medieval view of the universe was harmonious on theological and practical levels, providing answers to the most puzzling of questions. Medieval Views of the Cosmos is an engaging and beautifully illustrated introduction to a world where every moment was a theater of human drama directed by the hand of God. (shrink)

The music theory of Leibniz was thought to be by most of the scholars a part of the Pythagorean philosophical tradition. This opinion was maintained without a founded knowledge of the Pythagorean sources nor a proper consideration of the contemporary scientific background, upon which Leibniz wrote. The purpose of this article consists of analysing to what extent the Pythagorean tradition in music theory had still an influence in a philosophical age, whose music had already thoroughly abandoned the main statements of (...) the Pythagoreans. Questions belonging to the Pythagorean conception of music, such as the Tetraktys theory, the number proportions regarding musical intervals and the music of the spheres, are discussed here upon the background of the 17th century music theory. After that, Leibniz' considerations of these subjects turn out to be quite different from those of the Pythagorean tradition. Leibniz criticises it or translates it in an utterly modern language. He proposes a contemporary conception of harmony as an anticipation of beauty through the conjunction of the opposites, which emerges in the music theory of his time and will lead to the aesthetics substituting for the mystic. Dissonance, contrast and mistune are the new concepts to be taken into account. (shrink)

According to the Myth of Er we are responsible for our character because we chose it before birth. But any choice is determined by our present character, sothere is an indefinite regress and we cannot be entirely responsible for our character. The Myth of Er can be seen as the first formulation of the problem of free will, which Aristotle demythologizes in Nicomachean Ethics III.5. Plato's solution is that freedom is compatible with causal determinism because it does not mean indeterminism (...) but rationality. The myth links the individual lives to the harmony of the spheres, so our lives are determined not by blind necessity, but by rational necessity that follows from the nature of the universe. Even so, the limitations of determinism prevent rationality from being a sufficient cause of happiness (although the opposite view is usually attributed to Plato), but it remains a necessary one. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 426-427 [Access article in PDF] Timothy Smiley, editor. Mathematics and Necessity: Essays in the History of Philosophy. New York: Oxford University Press, 2000. Pp. ix + 166. Cloth, $35.00.Mathematics and Necessity contains essays by M. F. Burnyeat, Ian Hacking, and Jonathan Bennett based on lectures given to the British Academy in 1998. All concern the history of the philosophical treatment of (...) mathematics, necessity, or both, although there is no single thread running through all three essays.Burnyeat focuses on Plato's understanding of mathematics in the Republic, making use of the Timeaus in particular to defend his interpretation. Plato claimed that in the ideal society mathematics should be studied for a full ten years, which many have thought excessive. To explain it, Burnyeat argues that the role of mathematics is pervasive: ethics and politics are mathematical, because in Plato's view mathematics is a constitutive part of ethical understanding. On Burnyeat's interpretation, goodness is part of the objective world, and mathematics is a science of values. The link between mathematics and goodness in the objective world is forged by the concord, harmony, and unity of proportions, which express the goodness of the Divine Craftsman's beneficent design. Proportions are both intrinsically good and the proper study of mathematics.Burnyeat explains why Plato thinks abstract kinematics (the pure non-sensible counterpart to astronomy) and abstract harmonics lead to knowledge of the good. Abstract kinematics concerns the "harmony of the spheres" described in the Republic. Drawing heavily on the Timeaus, Burnyeat argues that the circular motions of the spheres are motions in the intelligence of the world soul and that there are similar motions in human souls. The world soul and human souls are spatial and have circular motions (invisibility and intangibility make them incorporeal). Souls are the most important subject matter of abstract harmonics—the study of good proportions. A soul that understands the various mathematical disciplines and their relations takes on the harmony and hence goodness of the world soul. Such a soul serves as a model for organizing the social world, a model which properly trained rulers can use to shape a community. Burnyeat's well-argued essay is compelling and exciting. [End Page 427]Ian Hacking's views provide a great contrast to Burnyeat's Plato. Hacking conducts a phenomenological inquiry into why some philosophers have become obsessed by mathematics as a source of philosophical inspiration. He holds that mathematics concerns a relatively minor part of human culture and that the influence of mathematics on philosophy is pernicious; he even describes it as an infection.Hacking examines the views of six philosophers: Plato, Leibniz, Mill, Descartes, Lakatos, and Wittgenstein. Hacking's assessment of the six philosophers is at times disputable, but it is also interesting and stimulating, and serves his phenomenological inquiry.Hacking traces philosophy's infection by mathematics to two factors. A mathematical proof can be perspicuous; that is, a proof can be "grasped," which requires seeing directly why something must be true and being able to recapitulate it. A mathematical proof can also anticipate facts about the world. He thinks that these two factors affect us in two ways: they give us the idea of a priori knowledge, and they dazzle us into unreasoned conviction in proofs. One might respond that, setting aside the feeling proofs give us, we are still justified in being impressed by them. Hacking argues that much of what impresses is based on a misunderstanding of their nature, which he attempts to correct.According to Hacking, a mathematical demonstration involves shifts of meaning that analytically bind the proof and the theorem it establishes. They thereby mutually support each other and provide what he calls self-authentication. The correctness of the proof is supported by the "analytified" truth of the theorem and the theorem is considered true because proven.This bootstrapping feature of mathematical proofs supports Hacking's deflationary account of necessity. Hacking suggests that the "must" of logical necessity rests upon our unwillingness to accept empirical counter-examples to the... (shrink)

The theory of beauty has always rested on the representation of the infinite, understood in its finite expression and perceptible through the senses. The relationship of beauty to truth, of art to science, is inevitably modified with the new way of treating the infinite in the modern conception of the world. Non-classical science works with the notions of “infinitely large” and “infinitely small,” modifying their meanings in terms of experimental observations. We put these words in quotation marks because the Whole (...) may be considered as finite or infinite according to the angle from which it is viewed: the “infinitely small” only becomes so in determined circumstances, for example, when we consider the extended and discrete elements of space and time in a macroscopic approximation, as infinitely small elements of perpetual motion. Modern science studies these two poles of being—the Whole and its parts—in their interaction, admitting the dependence of macroscopic and even cosmic processes with regard to the processes being created in infinitely small spheres (or, according to another interpretation, finite but extremely small). However, as characteristic of our time as these concepts are—most often hypothetical—they nonetheless express a very old historical tradition that contemporary retrospection, turned toward classical science and the past of science in general, allows us to discern very clearly. All the culture of the past was dominated by the principle of the authority of the Whole over its parts. In peripatetic cosmology and physics, individual processes depended on the cosmic harmony of the center and frontiers of the universe, on the spheres and places toward which bodies tend. This authority of the general law, of universal harmony, of the system hinging on individual processes, is confirmed in Aristotle's Physics, but not only there: we find it in almost all the thinkers of antiquity. On the plane of general logic, it received expression in the Hegelian concept of the true infinite, a concept constituting to a high degree the philosophical equivalent of classical science. In Hegel's time, this last was already drawing away somewhat from the idea of an absolute and strict subordination of elementary processes to integrating systems and general laws, laws being realized through the probability of microprocesses, thus statistical laws, and whose exact application ignored individual acts, for example, the mechanism of molecules in thermodynamics. The statistical theory of heat has rendered continual a discrete microcosm—for the movement of individual molecules it substituted the average speed of the molecules—and continual laws became supreme points determining macroscopic processes. These laws had a differential nature. In other words, they prescribed the defined relationships between the infinitely small increases in size. Also, the schema of the classic law consisted in defining infinitely small processes by an infinitely large integral legality because of the number of processes. The infinitely true of Hegel is the actual infinite being realized in each of its finite elements; it is the subjection of the finite element to the infinite. (shrink)

The primary task confronting an examination of the claimed connection between Kant's general theory of cognition and his account of aesthetic judgment requires clarifying perhaps the most obscure component of that account, the doctrine of the harmony of the faculties. Kant's presentation of this doctrine makes it notoriously difficult to penetrate. Much of what Kant says about the harmony of the faculties – perhaps the very phrase “the harmony of the faculties” – is rather imprecise and metaphorical. (...) Yet, the importance of a correct understanding of the harmony of the faculties to assessing both the merits of Kant's aesthetic theory and his claims for the epistemological significance of reflection is difficult to overstate, for it is precisely this state of harmony that ultimately grounds the validity of judgments of taste and does so in virtue of being a state in which the most general prerequisites to conceptual judgment are present. (shrink)

Unraveling all the mysteries of the khipu--the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies--will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among Quechua-speaking (...) peoples of the Andes. Based on fieldwork in communities around Sucre, in south-central Bolivia, Urton argues that the origin and meaning of numbers were and are conceived of by Quechua-speaking peoples in ways similar to their ideas about, and formulations of, gender, age, and social relations. He also demonstrates that their practice of arithmetic is based on a well-articulated body of philosophical principles and values that reflects a continuous attempt to maintain balance, harmony, and equilibrium in the material, social, and moral spheres of community life. (shrink)

CHAPTER ONE THE PHILOSOPHER MOSAIC IN NAPLES Ever since the discovery in Torre Annunziata of a duplicate1 of the Villa Albani mosaic showing a group of ...

A most unusual guide to the solar system, A Little Book of Coincidence suggests that there may be fundamental relationships between space, time, and life that have not yet been fully understood. From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet (...) in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons. (shrink)

Epidemiological studies of the last decade have shown a low prevalence of hypomania and bipolar I disorder in Western societies while pointing to a prevalence of unipolar mania in non-Western societies. This work seeks to investigate the explanatory role of the Stimmung concept to understand these differences, as much as the increase in the number of cases of mania in the West in the last two decades. It attempts to explore the relationship between the phenomenology of hypomania and its adaptation (...) to the atmosphere of its environment. Our hypothesis is that the experience of hypomania would be in harmony with the narrative of Western societies and with Stimmung (in the sense of the term used by Spitzer and Heidegger) of these societies. Finally, we will present a clinical case and analyzes of business leadership manuals that will illustrate the phenomenological relationship of Stimmung and mania, as well as its transformation in the sphere of work. (shrink)

We propose a model which argues that aesthetics is based on biosemiotic processes and introduces the non-anthropomorphic aesthetics. In parallel with habit-taking, which is responsible for generating semiotic regularities, there is another process, the semiotic fitting, which is responsible for generating aesthetic relations. Habit by itself is not good or bad, it is good or bad because of semiotic fitting. Defining the beautiful as the perfect semiotic fitting corresponds to the common conceptualisation of the aesthetic as well as extends it (...) over all umwelten. Perfection is not omnipotence, it only means the omnirelational semiotic fitting in the umwelt, or harmony with context. The process that presents something to be perceived as beautiful is of the same kind as the semiotic process that builds something to become beautiful. The argument is based on the observation that learning has a tendency towards perfection, until it is grounded. Semiosis is usually biased towards semiotic fitting, which stepwise leads towards perfection, and thus towards beauty. Such a general semiotic model implies that beauty is species-specific; that it is not limited to the sphere of emotions; that the reduction of the evolution of aesthetic features to sexual selection is false; and that humans should learn the aesthetics of other beings in order to avoid destroying valuable biocoenoses. (shrink)

While every music lover senses the power and truth that reside in music, very few actually approach music as a path to cosmic knowledge. But the idea that the universe is created out of sound is an ancient one. This book brings together three contemporary German thinkers who exemplify this tradition: Marius Schneider, Rudolf Haase, and Hans Erhard Lauer.

The last centuries before the beginning of the Christian era, the first centuries after that, were enveloped in the history of mankind as a period of the total crisis and the decline of the Greco-Roman civilization, a crisis that covered virtually all spheres of the social life of the Roman world and which, as ever before, experienced almost every one, whether he is a slave or a free citizen, a small merchant or a big slave or an aristocrat. As (...) a reaction to the crisis, in various parts of the empire the civil wars and the slavery uprising erupt in different parts of the empire. Under such conditions of life, the world around itself no longer seemed to man to be self-sufficient, harmonious, stable, "good" and warded by a cohort of traditional deities. Yes, and the gods themselves were now turned out to be incapable, unable to change the unceasing flow of fatal doom. (shrink)