Plato's Tim. 90b1-c6 describes a pathway to the soul's salvation via the study of the heavens. This paper poses three questions about this theme in Platonism: 1. The epistemological question: How is the paradigmatic function of the visible heavenly bodies to be reconciled with various Platonic misgivings about the faculty of perception? 2. The metaphysical question: How can »assimilation« to the motions of bodies in the realm of Becoming provide for the salvation of souls when souls are »higher«- a mid-point (...) between Being and Becoming? 3. The psychological question: What can it mean for an incorporeal soul to utilise the motions of a body for an ethical and cognitive paradigm? And provides an account of how Proclus and some of his fellow Neoplatonists answered these questions. (shrink)

At the end of the sixteenth century astronomers and others felt compelled to choose among different cosmologies. For Tycho Brahe, who played a central role in these debates, the intersection of the spheres of Mars and the Sun was an outstanding problem that had to be resolved before he made his choice. His ultimate solution was to eliminate celestial spheres in favour of fluid heavens, a crucial step in the abandonment of the Ptolemaic system and the demise of Aristotelian (...) celestial physics. These debates involved issues that had not previously been part of astronomy, and had the effect of undermining the traditional hierarchy of the sciences. While this complicated story involves many scientific personalities of the sixteenth and seventeenth centuries, in the present paper we will concentrate on one figure who has been assigned an unnecessarily minor role in most histories of science: Christoph Rothmann. In the present paper we show that ‘the dissolution of the celestial spheres’ depends on arguments about the substance of the heavens, following a mistaken argument of Gemma Frisius, elaborated by Joannes Pena and appropriated by Rothmann. We next consider the status and origin of the doctrine, as presented by Brahe, that the heavenly spheres are solid, and the impact on Brahe of Rothmann's treatise on the comet of 1585. Rothmann provided several key ideas that enabled Brahe to develop his system, and we suggest in passing that Rothmann may also have precipitated Brahe's re-evaluation of his attempt to detect the parallax of Mars during the opposition of 1582–83. We offer a new account of this central piece of evidence for the Tychonic system. (shrink)

With the introduction of Greco-Islamic science and natural philosophy, medieval natural philosophers were confronted with three distinct astronomical systems: Aristotelian, Ptolemaic, and the system of al-Bitruji. A fundamental problem that each had to confront was how to explain simultaneous contrary motions in the heavens -for example, the sun's motion, which moves east to west with a daily motion while simultaneously moving west to east along the ecliptic- within an Aristotelian physical system that assumed that a simple body could have only (...) one proper motion. How medieval natural philosophers resolved this problem is the focus of the article. (shrink)

Volume 1 (c2015) The heavens and the earth -- Nature, number and substance -- The shape and motion of the heavens -- Harmony and complexity -- Earth at the center of the world -- The world of Ptolemy -- Measuring the tropical Year -- Geometrical tools -- The sun, the moon and the calendar -- From Astronomy to cartography -- Climates and continents -- Heliocentrism: hypothesis or truth? -- Earth as a wandering star -- Re-ordering the heavenly spheres -- (...) class='Hi'>Celestial physics -- Broken spheres -- Kepler's third law -- Kepler's first and second laws -- Mountains on the moon -- The Medician stars -- The luminosity of variable stars -- Galactic spectra -- Measuring astronomical distances -- A new theory of gravity -- Euclid, Gauss and Mercury's orbit -- A finite universe with no boundary -- The structure of the universe -- Measuring the potentially infinite -- The birth of the Big Bang -- The primeval atom. (shrink)

I explore how the nature, scope, and limits of the knowledge obtained in orbital dynamics has changed in recent years. Innovations in the design of spacecraft trajectories, as well as in astronomy, have led to new logics of theory-testing—that is, new research methodologies—in orbital dynamics. These methodologies—which combine resonance overlap theories, numerical experiments, and the implementation of space missions—were developed in response to the discovery of chaotic dynamical systems in our solar system. In the past few decades, they have replaced (...) the methodology that dominated orbital research in the centuries following Newton's Principia. As a result, the kind of knowledge achieved by orbital research has changed: we can know how orbiting bodies in chaotic systems behave, but only over sufficiently short time scales; and we can reliably measure those temporal limitations, using Lyapunov time. (shrink)

The nature of concepts -- Generalizations as hierarchical -- Perceiving first-level causal connections -- Conceptualizing first-level causal connections -- The structure of inductive reasoning -- Galileo's kinematics -- Newton's optics -- The methods of difference and agreement -- Induction as inherent in conceptualization -- The birth of celestial physics -- Mathematics and causality -- The power of mathematics -- Proof of Kepler's theory -- The development of dynamics -- The discovery of universal gravitation -- Discovery is proof -- (...) Chemical elements and atoms -- The kinetic theory of gases -- The unification of chemistry -- The method of proof -- Misapplying the inductive method -- Abandoning the inductive method -- Physics as inherently mathematical -- The science of philosophy -- An end-and a new beginning. (shrink)

The ArgumentOne of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.Galileo argued: only nonviolent motions can be (...) caused by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics. (shrink)

Examining in detail Aristotle's treatment of physical, cosmological, chemical, and meteorological questions, this learned study compares his arguments and conclusions with those of his precursors in order to assess his debt to them and at the same time to show clearly the nature of his own new contributions to the body of scientific thought. It also examines the interrelations of the major topics included in Aristotle's scientific work and the relations between his theology and his science. Describing his work as (...) "a study in continuity and transformation," Friedrich Solmsen writes, "The scientific endeavors of the Presocratics have a sequel.... Aristotle did not discover the subjects with which he deals in his physical treatises. In the questions which he takes up he is neither as free nor as arbitrary as some students of his thought appear to believe, and in the answers which he provides he is not as invariably original as he himself in the course of his arguments may lead us to think." With constant reference to its historical antecedents, Aristotle's system of movement is analyzed and studied, as are his doctrines regarding time, place, matter, and the infinite. In connection with his concept of cosmic order, special consideration is given to the relation between the lower (sublunary) and the upper (celestial) Cosmos in his scheme. Solmsen's mastery of the relevant texts (not only Aristotelian, but also Platonic, Presocratic, and Epicurean) is evident on every page. (shrink)

Between the appearance of Copernicus’ De Revolutionibus in 1543 and the works of Kepler and Galileo that appeared in 1609–10, there were probably no more than a dozen converts to physical heliocentrism. Following Westman we take this list to include Rheticus, Maestlin, Rothmann, Kepler, Bruno, Galileo, Digges, Harriot, de Zúńiga, and Stevin, but we include Gemma Frisius and William Gilbert, and omit Thomas Harriot. In this paper we discuss the reasons this tiny group of true Copernicans give for believing that (...) Copernicus, not Ptolemy or Tycho Brahe, was correct. We conclude that the early followers of Copernicus can be divided into two main groups, designated mathematicians and physicists. Two main arguments appear in the works of the former: first, the relationship between the velocity of a planet and its distance from the center of the world; second, the explanation of retrogradations. Early Copernicans differed on the reality of celestial spheres, and several attempted to reconcile heliocentrism with scripture. The mathematicians continued to accept a traditional definition of the scope of astronomy and the methods of science, both issues challenged by Kepler and Galileo. Hence the work of Copernicus set in motion a train of events that led to a decisive epistemological shift, but did not itself represent such a shift. The real revolution is the replacement of the methods and goals of Ptolemaic astronomy and Aristotelian physics with Copernicanism in its modern form, which incorporates the conceptual structure of Kepler and the astronomical evidence of Galileo. (shrink)

The paper first discusses the metaphysical framework that allows the soul's integration into the physical world. A close examination of B36, supported by the comparative evidence of some other early theories of the soul, suggests that the word psuchê could function as both a mass term and a count noun for Heraclitus. There is a stuff in the world, alongside other physical elements, that manifests mental functions. Humans, and possibly other beings, show mental functions in so far as they have (...) a portion of that stuff. Turning to the physical characterization of the soul, the paper argues that B36 is entirely consistent with the ancient testimonies that say that psuchê for Heraclitus is exhalation. But exhalations cover all states of matter from the lowest moist part of atmospheric air to the fire of celestial bodies. If so, psuchê for Heraclitus is both air and fire. The fact that psuchê can manifest the whole range of physical properties along the dry-wet axis guarantees that souls can show different intellectual and ethical properties as well. Moreover, Sextus Empiricus, supported by some other sources, provides us with an answer how portions of soul stuff are individuated into individual souls. The paper closes with a brief discussion of the question whether, and if so with what qualifications, we can apply the term 'physicalism' to Presocratic theories of the soul. (shrink)

Catherine Keller's Cloud of the Impossible knits together process theology and relational ontology with quantum mechanics. In quantum physics, she finds a new resource for undoing the architecture of classical metaphysics and its location of autonomous human subjects as the primary gears of ethical agency. Keller swarms theology with the quantum perspective, focusing in particular on the phenomenon of quantum entanglement, by which quantum particles are found to remain influential over each other long after they have been physically separated—what (...) Albert Einstein and his collaborators recklessly dismissed as “spooky action at a distance.” This spooky action, Keller suggests, reroutes process thought—classically concerned with flux—to a new concern with intransigence—particularly the intransigence of the ethical relationship. Attending to the ethical urgency of the Other, she leaves process theology in a position of susceptibility to the moral imperative posed by the marginalized, the victimized, and the oppressed. This essay argues that although the ontological work of Keller's book productively integrates quantum physics into process theology, the ethical dimension of relationality is left cold in the quantum field. This is because, contra the ethical framework of contemporary deconstruction, which, following Emmanuel Levinas, sees ethical relationships as emerging out of a dynamic of infinite distance, moral connection has nothing to do with the remote reaches of the quantum scale or the macro-scale limits of space—nothing to do with “infinity” at all. Ethics emerges out of a much messier landscape—the evolved dynamic of fleshy, finite, material bodies. Rather than seeing ethical labor as a matter of physics, my contention is that interdisciplinary undertakings like Cloud of the Impossible are ethical disciplinary practices, re-acquainting us with the non-sovereignty of the self in order to open up new habits of relating rather than spotlighting ethical imperatives. (shrink)

Il saggio è dedicato ad illustrare la figura di Riccardo Rufo di Cornovaglia del quale si conosce assai poco, soprattutto dal punto di vista biografico. Nella prima parte dello studio l'A., dopo aver tracciato brevemente un profilo della vita e delle opere dell'autore, passa a confutare tre posizioni storiografiche in base alle quali si afferma che 1) Rufo non era ancora maestro quando entrò nell'Ordine dei Minori 2) non avrebbe composto alcun commento alla Metafisica o ad alcuno dei libri naturales (...) di Aristotele 3) le sue lezioni su Aristotele non sarebbero state presentate a Parigi. È al secondo punto che l'A. ha dedicato più attenzione: Rufo infatti non solo sarebbe autore di un commento alla Metafisica che esercitò una notevole influenza su alcuni autori tra cui Ruggero Bacone, Roberto Grossatesta e Bonaventura da Bagnoregio. All'interno del dibattito de aeternitate Rufo fu fortemente influenzato dal Filopono: egli infatti fu il primo ad utilizzare gli argomenti contra basati sulla nozione di infinito, notoriamente ascritti a Bonaventura. Il suo intervento fu molto importante anche per quanto riguarda la dottrina dell'impetus e la discussione sui corpi celesti. (shrink)

Distortion of Scientific Terms by Supposed Modernizing Translations: The Example ‘orbis’ (sphere)/‘orbita’ (orbit). The use of modern terminology and thinking hinders to understand historic astronomical and physical texts and often misleads the reader, because between celestial physics from Aristotle and Ptolemy to Copernic on the one side and since Kepler and Newton on the other side a fundamental change of paradigm had taken place. The former started from the assumption that planets are indirectly moved by large equally rotating (...) etherical spheres combined with each other to form every kind of unequally apparent planetary motion as a resultant, whereas the later started from Kepler's idea that every motion of a planet is directly caused by two forces moulding his (naturally unequal) ‘orbit’. ‘orbita’ was Kepler's new specific term for the way of the planet coined in late 1604; in contrast, the Latin term of the elder paradigm has been ‘orbis’ (‘sphere’), on the one hand as concentric ‘orbis totalis’ of a planet (or the fixed stars), on the other hand as non‐concentric ‘orbes particulares’ (of the eccenters and epicycles) within the space of an ‘orbis totalis’. These terms were interpreted and translated in accordance with modern dynamic (as the supposed ‘true’) thinking as if they were ‘orbits’ (German: ‘Bahn’). But you cannot bring the two paradigms into line. As a result, the texts of seemingly ‘modern’ translations become incomprehensible, absurd and wrong. The study shows this on thinking (1st) about Aristotelian physics of former times using terms and ideas of modern dynamics, and on thinking (2nd) about the former explanation of apparent motions of heavenly bodies using these dynamics and ignoring the different special Aristotelian and Ptolemaic physics of ‘orbes’ (spheres). (shrink)

ABSTRACT As well as the mathematically-supported celestial mechanics that Newton developed in his Principia, Newton also proposed a more speculative natural philosophy of interparticulate forces of attraction and repulsion. Although this speculative philosophy was not made public before the ‘Queries’ which Newton appended to the Opticks, it originated far earlier in Newton’s career. This article makes the case that Newton’s short, unfinished manuscript, entitled ‘De Aere et Aethere’, should be seen as an important landmark in Newton’s intellectual development, being (...) the first work in which Newton assumed there are repulsive forces operating at a distance between the particles of bodies. The article offers an account of how Newton came to write ‘De Aere et Aethere’ and why. It also outlines its relationship to the ‘Conclusio’, with which Newton briefly intended to finish the Principia, and to the ‘Queries’ in the Opticks. The date of the manuscript is disputed, and the article also aims to settle this dispute. Claims that the ‘De Aere et Aethere’ must have been written before the ‘Hypothesis... of Light’ of 1675 are dismissed, and it is suggested, following R. S. Westfall, that it was written after a well-known letter Newton wrote to Boyle early in 1679. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.1 (2001) 139-141 [Access article in PDF] Helen S. Lang. The Order of Nature in Aristotle's Physics: Place and the Elements. Cambridge: Cambridge University Press, 1998. Pp. xii + 324. £40. This is an unsuccessful book. Some of the reasons for its failure are complex, others are more simple. I cannot address all, but shall simply discuss the fundamental claims about four (...) large topical units—about nature, place, void and elemental motion—indicating why they are untenable.Discussing the celebrated definition of nature in Physics II.1, Lang contends that in it the verb kineisthai should be taken in the passive voice, that nature should be understood as a principle or cause of being moved and of being at rest, and not just blandly as a principle of motion and rest. Since Aristotle asserts in Book VIII of the Physics that the elements contain a passive principle of motion (255b30f), Lang's contention would mean that the elements in this respect do not differ from other natural entities. This is highly unlikely, given the systematic contrast of self-moving composite natural entities and simple, unarticulated elemental natures at 255a5-18. Lang goes so far as to assert [End Page 139] that "kineisthai is always passive, not middle (or reflexive), in both Plato and Aristotle" (42). Fortunately, we need not accept this on her word: although kineisthai can be both passive and middle, in some instances (notably in aorist and future), passive and middle forms are different. Accordingly, Lang's claim must be rejected on the basis of the very first passage she helpfully quotes as an "additional example" in n.24 on p.42: Physics VII.1 242a37f employs the middle voice future, kinesétai, and not the passive form, kinethésetai. The passage, teeming with different forms of the verb kineisthai, describes an entity which contains the principle of motion in itself, which moves naturally. This indisputably shows that Lang's contention is wrong.Lang, contrary to the well-entrenched scholarly consensus, claims that place is not the first (=innermost) extremity or first unmoved boundary of the containing body, but the extremity of the first body, i.e., of the celestial sphere. (The transposition of the qualification "first" happens in several, non-conclusive installments, see e.g. 99f, or 106f.) This transposition, however, runs counter to several of Aristotle's stipulations about place. Lang's all-encompassing extremity can only be the common (koinos) place of everything there is, whereas Aristotle is keen on finding the proper or particular (idios) place, a location which contains nothing but the entity itself (209a32-b1). The entirety of the discussion in Physics IV.4-5 attests that it is this latter place which Aristotle defines here: the first place is neither smaller, nor bigger than the thing in place (211a1f, a23-29, a31-33, etc.). Aristotle repeatedly stresses that the extremities of the contained body and its container are "in the same" (211a33f, b11f). This remark surely would be out of place about the remote extremity of the first containing body. It is also repeatedly set out that the direction of explanation is bottom-up, and not top-down, as Lang's all-encompassing universal place would require: it is by being in a particular locus that we can be said to be in (the sphere of) air, and by this in the heaven (209a33-b1, 211a23-26).Lang's proposal is not just theoretically unappealing. The traditional should not be rejected recklessly, without an attentive discussion. After all, it "apparently beg[a]n immediately with Theophrastus," as Lang rather uncannily admits (105), and it was Theophrastus, and not Lang, who studied and worked for decades with Aristotle.A key assertion of the chapter on void also rests on a grave philological blunder. Lang argues that interpreters switched from Aristotle's expression "that through which" (to di' hou) to "medium," thereby surrendering the original net of notions, in which the natural activity of the element impeded the progression of the... (shrink)

By defending the following views – that Aristotle identifies the generator and perhaps the obstacle remover as an essential cause of the natural sublunary elemental motion in Physics VIII 4; that this view is consistent with the view of Physics II 1 that the sublunary simple bodies have a principle of internal motion; and that the sublunary and the celestial elements have a nature in the very same way – I shall offer what has so far eluded (...) Aristotelian commentators: a consistent interpretation of Aristotle's theory of the natural motions of the sublunary and also the celestial elements. (shrink)

The persisting conception of Hegel's criticism of Newton's physics as an irrational or at least hopelessly exaggerated one partly has its roots mainly in Hegel's terminology and in his style. This does not mean that a mere translation of Hegel's arguments into any contemporary philosophical language be sufficient to immediately convince every Newtonian scientist. However, a non-Hegelian way of rephrasing the core of Hegel's anti-Newtonian philosophy of nature can help to understand to which extent the latter does satisfy any (...) scientist's criteria for a rational and self-consistent theory. To demonstrate this is the central aim of my talk, which is structured as follows: In the first part, I'm trying to highlight basic features of Hegel's criticism of Newton's optics and celestial mechanics, eventually focussing on his concept of a "sense of nature". This part has the character of a review. Second -­ and that is supposed to be the "reconsideration" part of my paper -­ I'll try to highlight the fundamental difference between Newton's and Hegel's ideas of natural laws and of the relation between mathematics and physics. Third, the metaphysical background of this difference will be analyzed. It is by the analysis of this metaphysical background that I hope to render Hegel's criticism of Newton's scientific revolution more understandable. (shrink)

When we examine the history of astronomy up to the end of the seventeenth century by considering the relation between mathematical astronomy and natural philosophy, it has been argued that there were two groups of philosophers and astronomers: instrumentalists and realists. However, this classification is deficient when we consider attitudes toward the explanatory power of mathematics in determining astronomical theories. I offer the solution of dividing realists into two subcategories—mathematical realists and physical realists. Mathematical realists include those who thought mathematics (...) could provide the real motions of celestial bodies. The physical realists, who include Ibn Rushd (Averroës), believed mathematics could not provide us with the real structure of the heavens. To avoid contradictions between the physical and mathematical models, the physical realists held that a mathematical model of the heavens should be designed by considering physics. I argue, in this article, that Francis Bacon can be considered a physical realist. (shrink)

One of the distinctive features of George Smith’s work on celestial mechanics is his emphasis on the role of what he calls “second-order phenomena” in the production of high-quality evidence. On Smith’s view, these gaps between theoretical predictions and observations can, under certain circumstances, be a source of evidence far stronger than that achievable through the hypothetico-deductive method. The practice of examining gaps between predictions and observations for the purposes of discovery and testing is commonplace in certain sciences such (...) as seismology, and has played an important role in their development. I use the term reasoning from residuals as a general term for this practice. I think it is worth investigating examples of this set of practices from the history of science, in order to understand the different ways in which reasoning from residuals is done, under what situations it is done, and how it contributes to the growth of knowledge in certain sciences. (shrink)

Commentando Aristotele, Phys. II 4, 6 e 8, Filopono assume costantemente Empedocle come modello di tutta una tradizione filosofica che individua nella materia e nel caso i principi sia dell’universo sia degli enti particolari. Filopono e d’accordo con Aristotele nel ritenere assurda la posizione dei materialisti, che considerano il caso non soltanto come causa degli enti che divengono sempre o per lo piu allo stesso modo, tra i quali talvolta si verificano casi di enti che si generano contro natura, ma (...) anche come causa dei corpi celesti, che si muovono di movimenti sempre identici e tra i quali non si osservano casi di contro natura. Ma se nella Fisica Aristotele ha opposto a questa posizione teorica la sua nozione di natura come causa finale, Filopono oppone al caso dei fisiologi materialisti la provvidenza, che egli chiama anche “provvidenza della natura” e che differenzia come natura universale e natura particolare. Pur utilizzando un concetto non aristotelico, gli argomenti di Filopono sono il frutto di un’eccellente esegesi di Aristotele, e persino l’esclusione del contro natura nell’ambito della natura universale sembra riconducibile a quanto Aristotele insegna nel De generatione animalium. (shrink)

In the field of astronomy, Thomas Hobbes's mechanistic philosophy was influenced by Johannes Kepler. Whereas Galilei still sticks to the circular motion of the planets, Hobbes takes over the Keplerian ellipses. According to Kepler, he defines astronomy as ' celestial physics'. As a consequence, he tries to determine the cause for the planetary motion and the reason why the orbit of the earth is eccentric. Hobbes modifies Kepler's explanation given in the Epitome astronomiae Copernicanae that the earth consists (...) of two parts: one well-disposed, the other hostile towards the sun. Referring to this doctrine, Hobbes developed various astronomical theories throughout a time span of about 35 years in works like "De motu" , De corpore , and the "Decameron physiologicum". (shrink)

The advent of distinctively Modern European philosophy at the turn of the seventeenth century was occasioned by two major developments: the painful recognition after thirty years of religious war that principles of public conduct must be justified independently of sectarian religious dogma; and the growth of natural science, especially discoveries in astronomy that linked terrestrial and celestial physics in a newly mathematicized, explanatory mechanics founded by Galileo and dramatically extended by Newton. The roles of reason and empirical evidence (...) in inquiry, and their superiority to custom and tradition for knowledge of nature were undeniable, though their respective roles and proper epistemological accounting were far from obvious. I review briefly some key points in the advent of natural science in order show that some fundamental philosophical predilections have obscured the proper roles of reason and evidence in the philosophical accounting of scientific knowledge. These predilections are found both among rationalists and among empiricists. Though they may be more readily apparent among seventeenth and eighteenth century philosophers, they are no less prevalent in mainstream analytical philosophy of science. Their diagnosis augurs a fundamental philosophical reorientation, a reorientation inaugurated, indeed, by Hegel. (shrink)

This essay examines the cometary theory of Johannes Kepler and his claim that an “ethereal spirit” could lead a comet to appear at a providential place and time. In his account of the comet of 1607, Kepler suggested that a spirit served as a navigational principle that steered the comet on a particular course. I argue that this principle was an extension of Kepler’s celestial physics and part of his larger conception of causes at work in the heavens. (...) I also explore the critical response Kepler received from the theological faculty at the University of Leipzig, where he planned to publish his account. I explain why Kepler turned to natural philosophy to resolve the opposition of his religious authorities and how this was received as a foreign incursion on Sacred Scripture. In my final analysis, I discuss whether Kepler ultimately abandoned spiritual principles in his cometary theory and arrived at a system of celestial physics that was fully free of animistic ideas. (shrink)

: This paper continues my application of theories of concepts developed in cognitive psychology to clarify issues in Kuhn's mature account of scientific change. I argue that incommensurability is typically neither global nor total, and that the corresponding form of scientific change occurs incrementally. Incommensurability can now be seen as a local phenomenon restricted to particular points in a conceptual framework represented by a set of nodes. The unaffected parts in the framework constitute the basis for continued communication between the (...) communities supporting alternative structures. The importance of a node is a measure of the severity of incommensurability introduced by replacing it. Such replacements occur incrementally so that changes like that from the conceptual structure of Aristotelian celestial physics to the conceptual structure of Newtonian celestial physics occur in small stages over time, and for each change it is in principle possible to identify the arguments and evidence that led historical actors to make the revisions. Thus the process of scientific change is a rational one, even when its beginning and end points are incommensurable conceptual structures. It is also apparent, from a detailed examination of the conceptual structure of astronomy at the time of Copernicus, thatthe kind of conceptual difficulty identified as incommensurability may occur within a single scientific tradition as well as between two rival traditions. (shrink)

This essay deals with Girolamo Fracastoro’s ensouled cosmology. His Homocentrica sive de stellis (1538), an astronomy of concentric spheres, was discussed by the Padua School of Aristotelians. Since the polemics over the immortality of the human soul, which had famously opposed Pomponazzi to Nifo, psychological discussions—including those about heavenly spheres’ souls—raised heated controversies. Fracastoro discussed the foundations of his homocentric planetary theory in a dialogue titled Fracastorius, sive de anima (1555). In a 1531 exchange with Gasparo Contarini, Fracastoro discussed (...) class='Hi'>celestial physics, including problems linked to mathematical analysis of physical causation. Contarini expressed his doubts over Fracastoro’s lack of consideration of Aristotelian viewpoints on heavenly souls and intelligences. Fracastoro offered an account of cosmic animation in his later dialogue “On the Soul,” taking a different path than his Paduan teachers. He picked up the Platonic idea of the “world soul,” freely connecting it with Aristotelian views about the ensouled cosmos of concentric spheres, resulting in an eclectic composition of Platonic, Aristotelian, and Averroistic elements. Fracastoro grounded his renewed mathematical astronomy on an understanding of the cosmos as a living whole. His animated homocentric cosmos represented a development of Aristotelian premises and a step beyond this legacy. (shrink)

‘Poor Borelli!’ exclaimed Alexandre Koyre at the end of his wonderful and by now classic study of Borelli's ‘celestial mechanics’. Koyre frankly admitted that Borelli lacked Newton's genius and intellectual audacity. However, in his story Borelli deserved a place between Kepler and Newton for his ‘imperfect but decisive’ unification of terrestrial and celestial physics. This framework finds a powerful justification in Borelli's extensive usage of Keplerian astronomy and in Newton's references to Borelli's work on the Medicean planets, (...) Theoricae mediceorum planetarum , both in his correspondence with Edmond Halley, with regard to a controversy with Robert Hooke, and in Philosophiae naturalis principia mathematica . Newton's own copy of Borelli's work with signs of his reading – the famous dog-earings – is preserved in the library of Trinity College, Cambridge. The magnitude of Newton's achievement has haunted Borelli's work ever since Principia mathematica appeared in print. For example, although Christiaan Huygens was sent a copy of Borelli's book by Prince Leopold in 1666, his marginal annotations in his own copy of the book were written after he had read Newton's masterpiece, as if Huygens had felt the need to read the book again after 1687. From then onwards Borelli's work has almost inevitably appeared in a new light that has coloured its subsequent readings.My ambition in this paper is to provide a fresh reading of Borelli's work by reconstructing its circumstances of composition, establishing a comparison with a relevant strictly contemporary source, and attending to the immediate reception of Theoricae. Borelli's work was written with an eye to a composite audience including Roman Jesuits, Sicilian intellectual circles and Leopold de' Medici's correspondents across the Alps, such as the Copernican astronomer Ismael Boulliau in Paris. Borelli was aware that his Sicilian readers were likely to have different concerns from those of Roman Jesuits or the Medici. Thus the task of charting the reception of his work is a formidable one. For a variety of reasons, including availability of sources, limitations of space, taste and competence, my analysis of Borelli's work on the Medicean planets is limited to a few themes and is not only no less partial than Koyre's, but in many respects it relies on it. If readers feel stimulated to re-read Koyre's text, one of the aims of this paper will have been fulfilled. (shrink)

One of the paradoxes of the physical sciences is that as our knowledge has progressed, more and more diverse physical phenomena can be explained in terms of fewer underlying laws, or principles. In Hidden Unity, eminent physicist John Taylor puts many of these findings into historical perspective and documents how progress is made when unexpected, hidden unities are uncovered between apparently unrelated physical phenomena. Taylor cites examples from the ancient Greeks to the present day, such as the unity of (...) class='Hi'>celestial and terrestrial dynamics (17th century), the unity of heat within the rest of dynamics (18th century), the unity of electricity, magnetism, and light (19th century), the unity of space and time and the unification of nuclear forces with electromagnetism (20th century). Without relying on mathematical detail, Taylor's emphasis is on fundamental physics, like particle physics and cosmology. Balancing what is understood with the unestablished theories and still unanswered questions, Taylor takes readers on a fascinating ongoing journey. John C. Taylor is Professor Emeritus of Mathematical Physics at the University of Cambridge. A student of Nobel laureate Abdus Salam, Taylor's research career has spanned the era of developments in elementary particle physics since the 1950s. He taught theoretical physics at Imperial College, London, and at the Universities of Oxford and Cambridge, and he has lectured worldwide. He is a Fellow of the Royal Society and a Fellow of the Institute of Physics. (shrink)

Este texto pretende analizar tres argumentos esgrimidos por Johannes Kepler en su polémica contra la cosmología de Giordano Bruno. Se ha considerado que existe una diferencia fundamental entre Bruno, quien hizo de la idea de un universo infinito la base de su filosofía natural, y Kepler, quien optó por un universo finito y concéntrico para su sistema astronómico. A pesar de que existen diferencias entre los dos autores mencionados, yo sostengo que también se dio un progresivo acercamiento de Kepler a (...) algunas tesis de Bruno. (shrink)

How coherent is Descartes' conception of vacuum in the Principles? Descartes' arguments attacking the possibility of vacuum are difficult to read and to understand because they reply to several distinct threads of discussion. I separate two strands that have received little careful attention: the scholastic topic of annihilation of space, particularly represented in Albert of Saxony, and the physical arguments concerning vacuum in Galileo that are also continued after the publication of the Principles in Pascal. The distinctness of the two (...) sorts of opponent accounts for Descartes' odd habit of summarily declaring vacuum "contradictory" in some contexts, while providing extended conceptual and physical arguments meant to establish its "impossibility" in others. In several passages late in the Principles, Descartes also considers the physical ramifications of "empty space," including a discussion of the appearance of a star, were an empty space situated at the center of the celestial vortex. I argue that the discussion allows for a sensible conception of space with extension, but without matter, quite adequate to the physical discussions of vacuum among Descartes' contemporaries. (shrink)

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's (...) work from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in (...) 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics. (shrink)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. (...) Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

In ancient times was known two kinds of physics. On one side there was the astronomy , which is characterized by the use of exact mathematical principles, on the other hand, there was the physics in the true sense of the word, a science, which coincides often with what we now call `metaphysics' . While astronomy has to do with the region of celestials and the imperishable, the physics is about the range of the sublunary, terrestrial things (...) that come and go, and from their movements. The physicist is familiar with the nature of things, of which he speaks, and so he also understands the causes of their movements. It was not until Copernicus dared to equate the Earth to other planets that all physical events explain the same system to be dynamic postulates. This is still regarded as a commonplace of both philosophy and science of the natural world. I want to show in what follows that we now return from rather unexpected reasons the old dualistic view and we should no longer be guided by the sole prerogative of nachgalileischen physics. (shrink)

In early modern science, the struggle between feminine and masculine allegories of science was played out within fixed parameters. Whether science itself was to be considered masculine or feminine, there never was serious debate about the gender of nature, one the one hand, or of the scientist, on the other. From ancient to modern times, nature—the object of scientific study—has been conceived as unquestionably female.5 At the same time, it is abundantly clear that the practitioners of science, scientists, themselves, overwhelmingly (...) have been men.But what about science? What gender was it—as an activity and set of ideals—to have? In one tradition the answer was clear: science was a woman. This tradition, stretching back at least to Boethius’ sixth-century portrayal of Philosophy as a woman, was codified and explained in Cesare Ripa’s Iconologia, the Renaissance bible of iconography.6 In this work, Ripa portrayed each of the sciences as a woman. “Scientia”—knowledge or skill—was portrayed as a woman of serious demeanor, wearing stately robes . “Physica”—physical science—was a goddess with a terrestrial globe at her feet. Geometry was a woman holding a plumb line and compass. Astrology, too, was a woman, dressed in blue, with a crown of stars and wings signifying the elevation of her thoughts to the distant stars. With a compass in her right hand and the celestial sphere in her left, she studied the movement and symmetry of the skies. 5. See Carolyn Merchant, The Death of Nature: Women, Ecology, and the Scientific Revolution .6. Boethius describes female Philosophy as she appeared to him in a dream in his De consolatione philosophiae. See also Cesare Ripa, Iconologia , first illustrated in 1603. Londa Schiebinger is an assistant professor of history at Pennsylvania State University. Her book, “The Mind has no Sex”: Women in the Origins of Modern Science, will be published next spring. (shrink)

Leibniz's dispute with Newton over the physico-mathematical theories expounded in the Principia Mathematica have long been identified as a crucial episode in the history of science. Dr. Bertoloni Meli examines several hitherto unpublished manuscripts in Leibniz's own hand illustrating his first reading of and reaction to Newton's Principia. Six of the most important manuscripts are here edited for the first time. Contrary to Leibniz's own claims, this new evidence shows that he had studied Newton's masterpiece before publishing An Essay on (...) the Causes of Celestial Motions. This article, representing his response to Newton, is included here in English translation. Dr. Bertoloni Meli analyses the important implications of this episode on a variety of themes ranging from priority claims to the mathematization of nature in the seventeenth century. Besides providing a careful study of Leibniz's style and strategy, the author examines how our perception of Newton's achievement is affected and the reception of the rival theories by the mathematical community around 1700. "Bertoloni's book provides a very detailed and deep analysis of Leibniz's calculus and dynamics by focusing on a consistent and important set of previously unknown manuscripts..." Niccolo Guicciardini, Universita de Bologna "...Equivalence and Priority is a major contribution to our understanding of the development of mathematical physics in the late seventeenth and early eighteenth century." Daniel Garber, University of Chigago. (shrink)

Descartes and his early followers were widely seen to be enemies of superstition and the occult. This was particularly visible in the Cartesian movement’s antagonism to astrology. However, why Descartes and his early followers were so pitted against astrology is less than clear given the flexibility afforded to them through their system of philosophy and various mechanical explanations. Claude Gadroys (1642-1678), for example, produced a short treatise that provided a mechanical explanation consistent with Cartesian physics to allow for (...) class='Hi'>celestial influence on Earth. In doing so, he exposed a contradiction in Cartesian vortex theory that seemed to disallow any such influence. In this way, Gadroys brought against himself and then dispelled one of the strongest objections to a Cartesian astrology. Oddly, no other Cartesian relied on principles specific to Cartesianism to argue against astrology as a legitimate science. This paper’s goal is to give a survey of some of the most prominent anti-astrological influences on Descartes, as well as some of the most prominent anti-astrological Cartesians in the second half of the 17th century. In doing this, I hope to show two things. First, in mainstream Cartesianism of the period, the anti-astrological sentiment was in no way part of the debate surrounding Descartes’ philosophy. Instead, ‘Cartesian’ anti-astrological arguments were based on well-worn arguments with an emphasis on experimental difficulties in establishing an astrological science. Second, the explanation for the curious lack of distinctly Cartesian anti-astrological arguments reflects an inherent flaw in Cartesianism; namely, it lacked the theoretical tools to completely rule out ‘occult’ sciences such as astrology. (shrink)

Originally published in English in 1973. This volume traces the development of the revolution which so drastically altered manâes view of the universe in the sixteenth and seventeenth centuries. The "astronomical revolution" was accomplished in three stages, each linked with the work of one man. With Copernicus, the sun became the centre of the universe. With Kepler, celestial dynamics replaced the kinematics of circles and spheres used by Copernicus. With Borelli the unification of celestial and terrestrial physics (...) was completed by abandonment of the circle in favour the straight line to infinity. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space (...) vehicles. This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The illuminating Guide to Newton's _Principia_ by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students. (shrink)

It is tempting to see in the life of Archimedes an event that could serve as a foundational moment to the myth of the Archimedean point, where the promised firm point from which to move the earth is itself given a basis and physical context for exposition. As earthbound as Archimedes himself, this foundation is not celestial – not a point in the far reaches of space – but rather terrestrial in nature, located in proximity to the border of (...) land and sea. It is the moment when Archimedes the mathematician launches a half-built ship with the aid of one of his inventions. Further details and further interpretations are open to debate. The ship in question, the Syracusan, seems to have been no ordinary one. The .. (shrink)

This is the first volume compiling English translations of Leibniz's journal articles on natural philosophy, presenting a selection of 26 articles, only three of which have appeared before in English translation. It also includes in full Leibniz's public controversies with De Catelan, Papin, and Hartsoeker. The articles include work in optics, on the fracture strength of materials, and on motion in a resisting medium, and Leibniz's pioneering applications of his calculus to these issues by construing them as mini-max and inverse (...) tangent problems. Other topics covered by the articles include: criticisms of the Cartesian estimate of motive force and Leibniz's proposal of a different way of estimating force to replace it; a proposed theory of celestial motions and gravitation, and derivation of the inverse square law; challenge problems concerning the isochronous curve and the catenary; a sample of work on gaming theory; and Leibniz's critique of atomism. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute (...) to society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

This paper seeks to demonstrate that propositions 23–27 of the Euclidian Optics originated in the context of geometrical astronomy. These entries, which deal with the geometry of spheres and rays, present material that overlaps considerably with propositions 1–3 of Aristarchus of Samos’ On the Sizes and Distances of the Sun and the Moon. While all these theorems deal with material that could conceivably be native to celestial illumination, the proofs do not work for binocular vision. It therefore seems probable (...) that the proofs were borrowed from Aristarchus or, more likely, some common astronomical predecessor. As an extension of this observation, this paper argues that the Optics displays a far less unified purpose than has typically been assumed. Instead, it reflects a conglomerate of concerns, goals and dependencies, insofar as it presents multiple proofs that emerge from a set of geometrical concerns not directly related to vision as a physical phenomenon. These entries complicate the idea that the Optics is about explaining light, sight or false appearances in any straightforward sense. Instead, the text is oriented toward a somewhat more diffuse goal: simply to articulate the geometry of vision and rays. Optics as a discipline should should therefore be understood not as a purely mathematical explanation of vision, but as a target-field of explanation constituted by features and boundaries derived from extra-visual geometric concerns. (shrink)

Early medieval Irish literature presents several types of voyages into the afterworld: echtrai (various adventures into Mag Mell), immrama (sea travels to the enchanted islands of the Ocean), fisi (ecstatic revelations of Christian eschatology), journeys into Saint Patrick’s Purgatory. In this paper, we seek to contrast the fisi and the descents into the cave of Saint Patrick. From a morphological point of view, both have a great deal of topoï in common, which describe the structure of the Christian other world: (...) the waste land of pains, the infernal pit, the ordeal bridge, the land of the blessed, the celestial Kingdom of God, etc. However, between the two genres appear some major differences, such as the order in which these places are visited. The main distinction lies in the fact that the fisi are mainly ecstatic voyages (i.e. psychanodias ), implying a “ raptus animae ”, while the voyages into Saint Patrick’s Purgatory are physical expeditions (i.e. somanodias ), during the actual life of the adventurers. Although many of the common themes of the two genres derive from the medieval Christian tradition (especially the apocryphal apocalypses and visiones ), we argue that the differences may be due to the input of local Irish Celtic heritage. (shrink)

This book continues the classical Newtonian theory in both its initial spirit and the spirit of general relativity. It throws a bridge between classical Newtonian theory of forces and some contemporary concepts of the atomic, nuclear and particle theories. This book takes the Skyrme theory of nuclear matter mainly from the point of view that it allows the initial analogy between the atomic edifice and the solar system in all details. Especially important is the detail that the atomic nucleus works (...) exactly like the Sun, and they can be described in the same way. Based on this unitary description, the authors go further on, in showing that the Skyrme theory is the only theory naturally suited for the explanation of structure of nuclear matter. Thus it should be actually a classical theory, inasmuch as it simply carries over into microcosmos the very Newtonian theory of forces extracted from the planetary Keplerian synthesis of celestial motions. By this the problem of structure of the nucleus becomes actually a problem of classical physics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:There are only three surviving biographical notices regarding Marcus of Orvieto: two as colophons of Vatican manuscripts and a third as an entry in a catalog of the papal library in Avignon where we read: "Item, liber de mortalitatibus septem Martini de Urbevetani Ordinis Minorum." While the spelling of the book title and its author can be attributed to scribal errors or misreadings, the 'seven,' place of origin, and (...) religious order affiliation are accurate. Marcus's Liber de Moralitatibus is indeed divided into seven treatises: On the celestial bodies, On the elements, On the birds, On the fish, On the animals, On trees and plants and On precious gems. The colophons of the two Vatican manuscripts attest to his being a Friar Minor: Ego frater Marcus Urbis Veteris Fratrum Minorum Ordinis pauperculus. The prooemium of the Liber de Moralitatibus attests to the fact that Marcus's patron was Benedict Gaetani cardinal of St. Nicholas in carcere Tulliano,' the future pope Boniface VIII. This would put the time of composition circa 1290. Several allusions in Marcus's work to Paris, viz. the Parisian masters, its patron Ste. Genevieve, indicate that Marcus was at one time a student there and it is conceivable that Benedict commissioned the work while he was a papal legate there. Marcus's opus falls into the category of exempla literature, i.e. a source book for preachers.We offer the English translation of the chapter on pelicans as typical of Marcus's way of proceeding which, generally speaking, is threefold. First a physical description, which was generally copied from Bartholomew of England's 'On the Properties of Things,' secondly its spiritual signification attested to by pertinent passages from Scripture and bolstered by citations from the Fathers and Doctors of the Church, and thirdly examples of persons who exemplify the spiritual lesson either supportively or adversely. The legend of the pelican piercing its breast in order to revivify its dead chicks was familiar in Christian literature and art signifying analogously Christ's salvific blood redeeming the human race from its fallen state. The following is the English translation of Marcus's treatise 3, 'De avibus,' chapter 31.Chapter 31: On the pelicanThe pelican is seen to possess the following conditions or properties according to the doctors.1. First of all, as Isidore says, it is a "bird dwelling in solitude along the banks of the Nile." This signifies preachers and contemplative persons who flee the vanities of the world and occupy themselves with heavenly consolations or delightful and re-creative consolations of Sacred Scripture, Psalm 54, 8-9: Far away I would flee; I would lodge in the wilderness. I would hasten to find shelter from the violent storm and the tempest. Bernard, On the Canticle of Canticles and in his sermons: "Divine consolation is delicate, it is not given to those preoccupied with what is alien to it." Ambrose, On Luke: "Those preoccupied with secular vanities cannot know what is divine."2. Secondly, as Isidore says, whatever it eats, it first dips in water with its foot and having done so, using the foot as a hand as it were, puts it [the morsel] in its mouth. This signifies doctors [i. e. teachers] and preachers who practice what they teach or preach after the example of the Apostle, Romans 15, 18: I will not dare to speak of anything except what Christ has accomplished through me. Jerome, To Nepotian: "Make sure your deeds do not 'confound' your words, lest when you speak in the assembly someone might say to himself: 'Physician, cure yourself'."3. Thirdly, as Isidore says, of all the birds, with the exception of the phylargum, only the pelican uses its foot as a hand. This signifies a devout religious who frequently, motivated by holy desires and affections, prefers holy meditations rather than manual labor. 1Tim. 4: 7-8: Train yourself for devotion, for while physical training is of.. (shrink)

In this fascinating and bold discussion, a renowned neurobiologist serves as guide to the most complex physical object in the living world: the human brain. Taking into account the newest brain research—morphological, physiological, chemical, genetic—and placing these findings in the context of psychology, philosophy, art, and literature, Changeux ventures into the unexplored territories where these diverse disciplines intersect. Changeux's book draws on Plato's notion that the Good, the True, and the Beautiful are celestial essences or ideas, independent but so (...) intertwined as to be inseparable. Placing these essences within the characteristic features of the human brain's neuronal organization, the author addresses unsolved questions in neuroscience today. With imagination and deep insight, Changeux illuminates the evolution of the brain and deciphers what new developments in neuroscience may portend for the future of humanity. (shrink)