Dirk Couprie

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.

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.

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.

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.

In this article the author gives a systematical exposition and interpretation of the concept of a tautology in Wittgenstein's 'Tractatus'. The following questions are discussed successively : 1. What is, according to Wittgenstein, a tautology ? The answer to this question is given by means of an exposition of the definition of 'tautology' in 4.46. The tautology appears to be that result of the manipulation with truth-tables which cancels itself. Within this scope an interpretation is given of the words 'Tatsache', 'Sachverhalt', 'Sachlage' and others, in which the first two are considered to mean 'piece of reality' and the last 'possible piece of reality'. Some methods of recognizing a tautology are treated, especially that of 6.1203. 2. What is the difference between a tautology and the other propositions of language ? Much attention is paid to the use of the word 'truth' in the 'Tractatus', which has three important meanings : a. (possibility of) agreement of (elementary) propositions with reality ; b. agreement of (molecular) propositions with their thrutharguments ; apriorical truth of the tautology. Wittgenstein's theory of probability is explained by means of some examples. 3. Why the propositions of logic are they tautologies ? After a discussion of the theory of inference, in which an inference appears to be a reversed tautological implication, it is shown how Wittgenstein may gather his theory of the propositions of logic as tautologies from the theses discussed before : a. that a tautology is true for all the truth-possibilities of its elementary propositions ; b. that a tautology is unconditionally true ; c. that a tautology is senseless and says nothing, but shows the scaffolding of language ; d. that a tautology has always the probability 1 ; e. that inference is the reversed operation of making a tautology ; f. that inference and tautology are apriorical truths

Von verschiedenen Seiten her sind Versuche unternommen, Wittgensteins Tractates transzendental philosophisch und im besondern kantisch zu interpretieren. Es wird hier eine Beurteilung dieser Versuchen gegeben, ausgehend von der Gedanke, dass Wittgenstein eine Schlüsselstellung zukommen könnte zwischen die kontinentale und die angelsaksische Tradition in der Philosophie. A. Maslow war der erste der Wittgensteins Frühwerk im kantischen Perspektiv sah. Wittgensteins Sprachformen sind ihm die transzendentale Formen Kants. E. Stenius spricht von Wittgensteins transzentalen Deduktionen, aber er versäumt es, sie in Zusammenhang mit der Theorie der sprachlichen Abbildung zu bringen. K.-O. Apel und W. Schulz benachdrücken die Reflexionslosigkeit von Wittgensteins Sprachauffassung, aber der erste charakterisiert Wittgenstein als undialektischer Transzendentalphilosoph, während Schulz dem Tractatus jeden Transzendentalismus abspricht. Im vorliegenden Aufsatze wird erstens behauptet, dass Wittgensteins transzendentale Deduktion in seiner Abbildungstheorie enthalten ist, und zweitens, dass er mit seiner Selbstdestruktion dialektischer als die Dialektiker vorgeht. Die Herausforderung Wittgensteins an das transzendentalphilosophische Denken ist, dass er als Resultat seines eigenen Versuches, transzendentalphilosophisch zu arbeiten, die notwendige Metaphorik, die Quasi-Empirik und die Inadequatheit der transzendentalphilosophischen Sprache von innen her klar vor Augen stellt

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.

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

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.

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

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 ..

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.