In Miletus, about 550 B.C., together with our world-picture cosmology was born. This book tells the story. In Part One the reader is introduced in the archaic world-picture of a flat earth with the cupola of the celestial vault onto which the celestial bodies are attached. One of the subjects treated in that context is the riddle of the tilted celestial axis. This part also contains an extensive chapter on archaic astronomical instruments. Part Two shows how Anaximander (610-547 B.C.) blew (...) up this archaic world-picture and replaced it by a new one that is essentially still ours. He taught that the celestial bodies orbit at different distances and that the earth floats unsupported in space. This makes him the founding father of cosmology. Part Three discusses topics that completed the new picture described by Anaximander. Special attention is paid to the confrontation between Anaxagoras and Aristotle on the question whether the earth is flat or spherical, and on the battle between Aristotle and Heraclides Ponticus on the question whether the universe is finite or infinite. (shrink)

Places the development of Anaximander's thought within social, political, cosmological, astronomical, and technological contexts.

This book is a sequel to Heaven and Earth in Ancient Greek Cosmology. With the help of many pictures, the reader is introduced into the way of thinking of ancient believers in a flat earth. The first part offers new interpretations of several Presocratic cosmologists and a critical discussion of Aristotle’s proofs that the earth is spherical. The second part explains and discusses the ancient Chinese system called gai tian. The last chapter shows that, inadvertently, ancient arguments and ideas return (...) in the curious modern flat earth cosmologies. (shrink)

The idea of the spherical world, poised in space, and encircled at different distances by the celestial bodies, was introduced by the early Greek cosmologists. With some modifications, it is still our Western world-picture. It differs fundamentally from that of other cultures, which all accept, in one version or another, the idea of a flat earth with the dome of the celestial vault above it. The Greek conception, however, entails the problem of falling. How to account for the earth's stability? (...) Why is it that the earth does not fall? This anxious question has already bothered the Presocratics. Aristotle provided the solution that was satisfying for many hundred of years. Falling, according to Aristotle, is not the problem, but the answer, as the earth, consisting of the heaviest of the elements, finds its natural place in the centre of the spherical universe. For the same reason the earth itself, according to Aristotle, has to be spherical. Thus, his main line of argumentation was what we now would call 'metaphysical'. Recently, some scholars have argued that the early Greek idea of a spherical earth was developed as a protoscientifie hypothesis, based on empirical reasoning and observation. In this article, we show this to be an example of the 'anachronistic fallacy' that seriously obscures our understanding of the ancient Greek philosophers. Aristotle's conception held for two millennia, until the work of Copernicus, Kepler, and Thomas Digges overthrew it. Consequently, Newton had to cope with the fear of falling again — a fear that still haunts our modern world-picture and that was brilliantly articulated by Blaise Pascal, in his Pensées. (shrink)

In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of the (...) day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean. (shrink)

In the doxography on Anaximander it is reported that he has made a celestial globe or another kind of model, map or sketch of his astronomical conceptions. Several scholars have tried to reconstruct this model, but without success. In fact the history of the reconstruction of Anaximander's model of the heavens is a concatenation of mistakes and misunderstandings. The various and sometimes ingenious attempts will be discussed hereafter. Mostly the efforts fail through the difficulty of putting oneself into the position (...) of a more primitive astronomy which considers the earth as a flat disk and as the centre of the universe. Yet it is possible to draw a model which is both in agreement with the doxographical tradition on Anaximander's astronomy, without making special assumptions, and explains the movements of the celestial bodies as seen from a flat earth, as will be shown in the present article. (shrink)

The usual interpretation has it that Anaximander made ‘the Boundless’ the source and principle of everything. However, in the works of Aristotle, the nearest witness, no direct connection can be found between Anaximander and ‘the Boundless’. On the contrary, Aristotle says that all the physicists made something else the subject of which ἄπειρος is a predicate. When we take this remark seriously, it must include Anaximander as well. This means that Anaximander did not make τὸ ἄπειρον the source or principle (...) of everything, but rather called something else ἄπειρος. The question is, then, what was the subject that he adorned with this predicate. The hypothesis defended in this article is that it must have been ϕύσις, not in its Aristotelian technical sense, but in the pregnant sense of natura creatrix: the power that brings everything into existence and makes it grow and move. This ‘nature’ is boundless. It rules everything and in this sense it can be called ‘divine’. Being boundless, the mechanisms of nature, in which the opposites play an important role, are multifarious. The things created by boundless nature are not boundless, but finite, as they are destined to the destruction they impose onto each other, as Anaximander’s fragment says. (shrink)

Within the timespan of two years, two books have been published on the Presocratics as scientists. In 2011 appeared Carlo Rovelli’s The First Scientist. Anaximander and His Legacy, (Yardley: Westholme), and in 2013 Daniel Graham’s Science before Socrates. Whereas Rovelli, whose main field of study is quantum gravity, argues that Anaximander was the first scientist, Graham maintains that Anaximander should not count as a scientist. Empirical science started with Anaxagoras, who used his assumption that solar eclipses occur when the moon (...) blocks its light (“antiphraxis”) to measure the size of the sun on the occasion of a solar eclipse, and to a lesser extent with Parmenides, who recognized that the moon receives its .. (shrink)

The first part of this article examines Patricia O'Grady's recent attempt to identify the method by which Thales might have successfully predicted a solar eclipse. According to O'Grady, some 60% of the potentially visible lunar eclipses were followed 23½ months later by potentially visible solar eclipses. It is shown that this ratio is no more than 23%, and that the method fails to predict after which specific lunar eclipse a solar eclipse will appear. In the second half of the article (...) it is argued that on the basis of his own observations of major solar eclipses, Thales could have concluded that solar eclipses come in clusters of three, the second appearing 17 or 18 months, and the third 35 months, after the first one. In the years after the "predicted" eclipse of 28 May 585 BC, this apparent pattern disappeared again, which would explain why Thales managed to "predict" only one eclipse. (shrink)

This book offers an innovative analysis of the Greek philosopher Anaximander’s work. In particular, it presents a completely new interpretation of the key word Apeiron, or boundless, offering readers a deeper understanding of his seminal cosmology and, with it, his unique conception of the origin of the universe. Anaximander traditionally applied Apeiron to designate the origin of everything. The authors’ investigation of the extant sources shows, however, that this common view misses the mark. They argue that instead of reading Apeiron (...) as a noun, it should be considered an adjective, with reference to the term phusis, and that the phrase phusis apeiros may express the boundless power of nature, responsible for all creation and growth. The authors also offer an interpretation of Anaximander's cosmogony from a biological perspective: each further step in the differentiation of the phenomenal world is a continuation of the original separation of a fertile seed. This new reading of the first written account of cosmology stresses the central role of the boundless power of nature. It provides philosophers, researchers, and students with a thought-provoking explanation of this early thinker's conception of generation and destruction in the universe. (shrink)

Diogenes Laërtius and Plinius report that Anaximander made a globe, meaning a celestial globe. These statements must be due to an anachronistic misunderstanding, as a celestial globe presupposes a conception of a spherical universe in which the stars make up the outermost sphere. According to Anaximander, however, the stars are nearest to the earth, as is confi rmed by Aëtius and Hippolytus. Generally speaking, Anaximander’s universe of a column-drum-like earth at the center of the concentric wheels of the celestial bodies (...) can hardly be called spherical. Nevertheless we may assume that Anaximander, who drew a map of the earth, offered some representation of his cosmological ideas as well. Although a three-dimensional representation like a celestial globe is not likely, one may readily imagine that he drew a two-dimensional picture, a kind of ground-plan or map of his conception of the cosmos. The doxographers will erroneously have taken an account about this map as standing for a celestial globe such as they knew from their own experience. In this article I will deal with the problems that arise when we try to draw a map of Anaximander’s universe, and suggest ways to solve them. In discussing several authors who have studied the subject I will point out some bothersome inconsistencies and mistakes in their renditions. One problem, however, which has not been noticed before, will prove to be insolvable within the context of the doxographical evidence. I will argue that the only way to meet this problem is to look upon it as circumstantial evidence for the supposition that Anaximander never made a three-dimensional model whatsoever of his conception of the universe. (shrink)

We propose a characterization of mathematical experiments in terms of a setup, a process with an outcome, and an interpretation. Using a broad notion of process, this allows us to consider arithmetic calculations and geometric constructions as components of mathematical experiments. Moreover, we argue that mathematical experiments should be considered within a broader context of an experimental research project. Finally, we present a particular case study of the genesis of a geometric construction to illustrate the experimental use of hand drawings (...) and computers in mathematical practice. (shrink)

We show that it is impossible in quantum mechanics to describe two separated physical systems. This is due to the mathematical structure of quantum mechanics. It is possible to give a description of two separated systems in a theory which is a generalization of quantum mechanics and of classical mechanics, in the sense that this theory contains both theories as special cases. We identify the axioms of quantum mechanics that make it impossible to describe separated systems. One of these axioms (...) is equivalent to the superposition principle. We show how these findings throw a different light on the paradox of Einstein, Podolsky, and Rosen. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to QFT. By means of the Dirac sea model – exemplified in the electron sector of the standard model neglecting radiation – we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level (...) of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem and explains the appearance of creation and annihilation events. (shrink)

Stoicism was one of the new philosophical movements of the Hellenistic period. The name derives from the porch (stoa poikilê) in the Agora at Athens decorated with mural paintings, where the members of the school congregated, and their lectures were held. Unlike ‘epicurean,’ the sense of the English adjective ‘stoical’ is not utterly misleading with regard to its philosophical origins. The Stoics did, in fact, hold that emotions like fear or envy (or impassioned sexual attachments, or passionate love of anything (...) whatsoever) either were, or arose from, false judgements and that the sage—a person who had attained moral and intellectual perfection—would not undergo them. The later Stoics of Roman Imperial times, Seneca and Epictetus, emphasise the doctrines (already central to the early Stoics' teachings) that the sage is utterly immune to misfortune and that virtue is sufficient for happiness. Our phrase ‘stoic calm’ perhaps encapsulates the general drift of these claims. It does not, however, hint at the even more radical ethical views which the Stoics defended, e.g. that only the sage is free while all others are slaves, or that all those who are morally vicious are equally so. Though it seems clear that some Stoics took a kind of perverse joy in advocating views which seem so at odds with common sense, they did not do so simply to shock. Stoic ethics achieves a certain plausibility within the context of their physical theory and psychology, and within the framework of Greek ethical theory as that was handed down to them from Plato and Aristotle. It seems that they were well aware of the mutually interdependent nature of their philosophical views, likening philosophy itself to a living animal in which logic is bones and sinews; ethics and physics, the flesh and the soul respectively (another version reverses this assignment, making ethics the.. (shrink)

People undergo many idiosyncratic experiences throughout their lives that may contribute to individual differences in the size and structure of their knowledge representations. Ultimately, these can have important implications for individuals' cognitive performance. We review evidence that suggests a relationship between individual experiences, the size and structure of semantic representations, as well as individual and age differences in cognitive performance. We conclude that the extent to which experience-dependent changes in semantic representations contribute to individual differences in cognitive aging remains unclear. (...) To help fill this gap, we outline an empirical agenda that utilizes network analysis and involves the concurrent assessment of large-scale semantic networks and cognitive performance in younger and older adults. We present preliminary data to establish the feasibility and limitations of such empirical, network-analytical approaches. (shrink)

The importance of digital technologies for social and economic developments and a growing focus on data collection and privacy concerns have made the Internet a salient and visible issue in global politics. Recent developments have increased the awareness that the current approach of governments and business to the governance of the Internet and the adjacent technological spaces raises a host of ethical issues. The significance and challenges of the digital age have been further accentuated by a string of highly exposed (...) cases of surveillance and a growing concern about issues of privacy and the power of this new industry. This special issue explores what some have referred to as the “Internet-industrial complex”—the intersections between business, states, and other actors in the shaping, development, and governance of the Internet. (shrink)

In his writings on the foundations of logic, Gottlob Frege, the father of modern logic, sketched a conception of truth that focuses on the following questions: What is the sense of the word “true”? Is truth a definable concept or a primitive one? What are the kinds of things of which truth is predicated? What is the role of the concept of truth in judgment, assertion and recognition? What is the logical category of truth? What is the significance of the (...) concept of truth for science in general and for logic in particular? The present volume is dedicated to the interpretation, reconstruction and critical assessment of Frege’s conception of truth. It is of interest to all those working on Frege, the history of logic and semantics, or theories of truth. The volume brings together nine original papers whose authors are all widely known to Frege scholars. The main topics are: the role of the concept of truth in Frege’s system, the nature of the truth-values, the logical category of truth, the relationship between truth and judgment, and the conception of the truth-bearers. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave (...) functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2The Dirac Sea Model3Equilibrium States and the Vacuum4Excitations of the Vacuum and the Fock Space Formalism5The Appearance of Particle Creations and Annihilations6The Merits of the Bohmian Approach. (shrink)

Surveys the ideals of friendship in ancient Greco-Roman philosophy. The notion of the best friendship inevitably reflects the various conceptions of a good life.

Dirk Paul Bogner widmet sich der Frage, welche Relevanz Kurt Lewins Feldtheorie im Bereich der pädagogischen Diagnostik haben könnte. Er untermauert die These, dass die Lewin’sche Feldtheorie eine völlig neue Sicht auf Lern-, Entwicklungs- und Erziehungsprozesse eröffnen würde, und legt dar, inwiefern die Einbeziehung der Dimension des Raumes die Analyse dieser erziehungswissenschaftlich relevanten Topoi verfeinern könnte. Er erörtert mittels hermeneutischer Textauslegung und vergleichender Dokumentenanalyse, warum Lewin keine erziehungswissenschaftliche Resonanz erzeugen konnte, obwohl in der Erziehungswissenschaft auch heute noch intensiv Begriffe, (...) die entweder direkt aus der Feldtheorie stammen oder aber von dieser konsequent definiert wurden, verwendet werden. (shrink)

Unter dem Eindruck einer "Renaissance des Religiösen" einerseits und der zunehmenden Politisierung von Religionen andererseits rückt die Verhältnisbestimmung von Politik und Religion im staatlichen wie im internationalen Kontext verstärkt in den Fokus des politischen und gesellschaftlichen Interesses. In den letzten Jahren trägt auch die politische Philosophie dieser Situation vermehrt Rechnung, was sich in einer steigenden Zahl von Veröffentlichungen zu diesem Thema niederschlägt. Dabei kann sie auf eine reiche Tradition philosophischer Modelle zum Neben-, Mit- oder Gegeneinander von Politik und Religion zurückblicken. (...) Was in dieser Diskussion bisher jedoch fehlt, ist eine differenzierte Darstellung der für die Verhältnisbestimmung von Philosophie, Politik und Religion klassischen Modelle, angefangen von der griechischen Antike bis in die Liberalismus-Kommunitarismus-Debatte des ausgehenden letzten Jahrhunderts. Diese Lücke schließt der vorliegende Band: In 15 Beiträgen namhafter Experten werden klassische Modelle der Verhältnisbestimmung von Philosophie, Politik und Religion, beginnend mit Platon bis hin zu Charles Taylor, eingehend behandelt. (shrink)

Der Aufsatz verfolgt die Frage, welchem Wissenschaftstypus die Psychologie zuzuordnen ist, ob sie als eine Verlaufsgesetze aufstellende oder aber besser als eine hermeneutisch vorgehende Disziplin verstanden und betrieben werden soll. Dazu wird eine Systematik der Wissenschaften vorgeschlagen und die Psychologie darin eingeordnet. Davon ausgehend wird dafür argumentiert, dass die Psychologie als eine Realwissenschaft mit einem naturwissenschaftlichen und einem kulturwissenschaftlichen Zweig verstanden werden sollte, da sie sowohl technische als auch soziopolitische Praxen stützt.