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Dirk Couprie

University of West Bohemia, Department of Philosophy, temporary researcher (retired)

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Papers by Dirk Couprie

Heaven and Earth in Ancient Greek Cosmology

Astrophysics and space science library, 2011

The Spiral Movement of the Sun on an Imaginary Cylinder According to Empedocles and Anaximander

Philologia Classica, 2020

This article discusses an intriguing text in Stobaeus' Ecl. 1.25.3i about the sun's movement as a... more This article discusses an intriguing text in Stobaeus' Ecl. 1.25.3i about the sun's movement as a spiral on a cylinder. The author offers an interpretation of this text and argue that it is about Empedocles' conception of the solar trajectory during the year. After a preliminary attempt, an interlude is inserted on some strange theories, ascribed to Empedocles, about the two hemispheres of the heaven and two suns. Two of the more reliable theories attributed to Empedocles that are relevant in the context of this paper, namely the tilting and the eggshape of the heaven, as well as the problems of the size of the sun and the shape of the earth, are discussed in successive sections. This allows the author to illustrate some of his ideas on Presocratic flat earth cosmology. Prior to offering a visualization of the cosmos according to Empedocles, Bollack's earlier attempt is subjected to a critical examination. In two additional sections of the article, the author claims that, according to Empedocles, the moon must move on a cylinder as well and that the image of the cylinder for movements of the sun and moon dates back to Anaximander.

" CREPUSCULAR " LUNAR ECLIPSES DURING ANAXAGORAS' LIFETIME

Aristotle's Proofs of the Sphericity of the Earth

A critical analysis of Aristotle's proofs of the earth's sphericity, including his a critical sur... more A critical analysis of Aristotle's proofs of the earth's sphericity, including his a critical survey of arguments that were available to him and which he did not use. The conclusion is that none of these arguments is conclusive, and that some are based on false presuppositions or even contain a petitio principii.

AN ANCIENT CHINESE FLAT EARTH COSMOLOGY

Disclaimer: in this paper I only present the main features of the gai tian system as an extraordi... more Disclaimer: in this paper I only present the main features of the gai tian system as an extraordinary intellectual effort, leaving out many details, such as numerous calculations, several problems that are inherent to the system, the usual interpretation of the sunlight as a cone, the different number of the radius of the area of sunlight, the flat heavens represented as a Chinese hat, and so on. A fuller account will appear in March 2016 in the second volume of the Tsinghua Journal of Western Philosophy, and an even more extensive one in my forthcoming book When the Earth Was Flat). In all civilizations, people believed that the earth is flat, until in ancient Greece the idea of a spherical earth emerged. In China the belief in a flat earth lasted until the end of the sixteenth century, when catholic monks told them the new world picture, albeit not that of Copernicus, but that of Aristotle. Almost all Presocratic cosmologists, too, conceived of the earth as flat, although perhaps somewhat concave. The usual picture was that of the dome of a hemispherical or spherical heaven over or around the flat earth. Not surprisingly, this conception yielded some difficulties that were hard to cope with. Here I will only mention two of them, as they are the most relevant in the context of this paper. In the first place, on a flat earth it is always everywhere the same time. When the sun rises, it rises over the surface of the entire flat earth, and when the sun sets it gets dark all over the flat earth. Or, in the words of Ptolemy: " if the earth were flat, the stars would rise and set for all people together and at the same time ". 1 That at least some of the Presocratics were aware of this problem is clear from an otherwise enigmatic report on Archelaus, who pleads for a concave earth, because " the sun does not rise and set at the same time for all men, as would inevitably happen if the earth were flat ". 2 The second problem was the tilt of the celestial axis. The heavenly bodies seem to orbit around an apparently arbitrary fixed point in the northern heavens. In Presocratic Greek cosmology, the tilt of the heavens was a recurrent topic. As Furley writes: " they commonly explained this by the ad hoc assumption that the heavens tilted somehow, after the formation of the earth ". 3

THALES AND THE SOLAR ECLIPSE OF 28 MAY 585 BC

Several sources, of which Herodotus is the most famous, report that Thales predicted an eclipse o... more Several sources, of which Herodotus is the most famous, report that Thales predicted an eclipse of the sun. We may ask: 1) did he really predict an eclipse? 2) if so, which one did he predict? 3) if so, how did he do it? The answers to the first two questions will appear to follow from the answer to the third one. If we are able to discover which method Thales could have used, it follows immediately that he predicted an eclipse and also which one it was he foretold. We will answer these three questions: yes, he did predict a solar eclipse; it was the eclipse of 28 May 585 BC, and he did it by making a brilliant mistake. Here is the path of the eclipse of 28 May 585 BC:

Anaximander's Boundless Nature (with Radim Kočandrle)

Anaximander's Boundless Nature, 2013

The usual interpretation maintains that Anaximander made ‘the Boundless’ (τὸ ἄπειρον) the source ... more The usual interpretation maintains that Anaximander made ‘the Boundless’ (τὸ ἄπειρον) 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 (Phys. 203 a 4). When we take this seriously, it includes Anaximander as well. This means that Anaximander did not make τὸ ἄπειρον the source or principle of everything, but called something else ἄπειρος. The question is, then, what was the subject 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 can be called ‘divine’. Being boundless, the mechanisms of nature, in which 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.

The Qumran Roundel and the mrkhyt: A Comparative Approach

The Qumran Roundel and the mrkhyt: A Comparative Approach, 2013

A small saucer-shaped object with engraved concentric rings and radial marks, found at Qumran, is... more A small saucer-shaped object with engraved concentric rings and radial marks, found at Qumran, is usually called a sundial. Several interpretations, some of them very complicated, have been suggested, none of them convincing. The most recent and most extensive interpretation, presented by Paul Tavardon O.C.S.O., receives special attention in this article. The Egyptian mrxyt, consisting of a horizontal piece with at one end an upright block serving as a little gnomon, is also usually called a sundial. In this article the two instruments are examined in comparison with each other, which results in a rather simple interpretation. Current interpretations have studied both instruments as if they were handled in isolation and by one person. In the new interpretation offered here it is argued that, if studied under the assumption that two or more identical copies were used at the same time by different persons, it can be shown that they could have been used as instruments for making appointments when the shadow of the little gnomon had reached an agreed-upon mark.

ANAXAGORAS AND THE SOLAR ECLIPSE OF 17 FEBRUARY 478 BC

Anaxagoras and the Size of the Sun

Plutarch and others report that Anaxagoras compared the sze of the sun wth the Peloponnesus. It s... more Plutarch and others report that Anaxagoras compared the sze of the sun wth the Peloponnesus. It s the am of ths paper to show that ths was a far estmate, from hs pont of vew, whch s that of a flat earth. More precsely, I wll show that, wth the nstruments and the geometrcal knowledge avalable, Anaxagoras must have been able to use the procedures and perform the calculatons needed to reach approxmately hs result. * I am grateful to professor Teje de Jong from the Unversty of Amsterdam, who read an earler verson of ths paper, and to Jan Coupre, who checked the underlyng calculatons.

Archaeology and the Origins of Philosophy

Aestimatio: Critical Reviews in the History of Science, 2015

The Visualization of Anaximander's Astronomy

Apeiron, 1995

Anaxagoras und die Größe der Sonne. Hyperboreus 12 (2006), p. 55-76

Plutarch, Hippolyt und Diogenes Laertius berichten, daß Anaxagoras die Größe der Sonne mit dem Pe... more Plutarch, Hippolyt und Diogenes Laertius berichten, daß Anaxagoras die Größe der Sonne mit dem Peloponnes verglich. Ich will in diesem Aufsatz zeigen, daß Anaxagoras keineswegs von Sinnen war, als er diese Aussage machte, sondern daß dieser Vergleich eine durchaus vernünftige Einschätzung war, und zwar auf Grund seiner Sichtweise, nämlich der einer flachen Erde. Speziell will ich dartun, daß Anaxagoras mittels der seinerzeit verfügbaren Instrumente (Gnomon, Klepsydra, Guckrohr) sowie des damals verfügbaren mathematischen Wissens (die Eigenschaften ähnlicher Dreiecke, einfache Proportionen und der Satz des Pythagoras) in der Lage gewesen sein muß, Verfahren anzuwenden und Berechnungen auszuführen, die erforderlich sind, um das genannte Resultat zu erreichen.

The Paths of the Celestial Bodies According to Anaximenes

Anaximenes is said to have maintained that the celestial bodies do not go underneath the earth, b... more Anaximenes is said to have maintained that the celestial bodies do not go underneath the earth, but move laterally around it like a kind of felt cap around our head. In this article the interpretations of McKirahan and Bicknell are discussed and a new interpretation is proposed. McKirahan’s interpretation is shown to suffer from several shortcomings, such as not to account for the stars in the southern part of the heavens. Bicknell’s interpretation presupposes that Anaximenes taught a dip of the earth as is reported of Leucippus and Democritus. In this article it is argued that this interpretation is wrong, mainly because there did not exist such a thing as a Presocratic theory of a dip of the earth: Leucippus and Democritus taught a tilt of the heavens, just like other Presocratics. Following a suggestion of Wöhrle’s, it is argued that what Anaximenes meant to describe was not the actual state of celestial affairs but that before the tilt of the heavens.

Review of J.C. Morrison, Meaning and Truth in Wittgenstein's Tractatus

Review of: J.C. Morrison, Meaning and Truth in Wittgenstein's Tractatus. The Hague/Paris 1968.

Science before Socrates: Parmenides, Anaxagoras, and the New Astronomy by Daniel W. Graham

Journal of the History of Philosophy, 2014

The Tilting of the Heavens in Presocratic Cosmology

Apeiron, 2009

„Hätte die Welt ein Ziel, [ ... ] so wäre es [ ... ] mit allem Werden längst zu Ende“

Nietzsche-Studien, 2000

Some Remarks on the Earth in Plato's Phaedo. Hyperboreus 11 (2005), p. 192-204

Anaxagoras and Aristotle on the Sun at the Horizon. Hyperboreus 14 (2008), p. 39-49

Heaven and Earth in Ancient Greek Cosmology

Astrophysics and space science library, 2011

The Spiral Movement of the Sun on an Imaginary Cylinder According to Empedocles and Anaximander

Philologia Classica, 2020

This article discusses an intriguing text in Stobaeus' Ecl. 1.25.3i about the sun's movement as a... more This article discusses an intriguing text in Stobaeus' Ecl. 1.25.3i about the sun's movement as a spiral on a cylinder. The author offers an interpretation of this text and argue that it is about Empedocles' conception of the solar trajectory during the year. After a preliminary attempt, an interlude is inserted on some strange theories, ascribed to Empedocles, about the two hemispheres of the heaven and two suns. Two of the more reliable theories attributed to Empedocles that are relevant in the context of this paper, namely the tilting and the eggshape of the heaven, as well as the problems of the size of the sun and the shape of the earth, are discussed in successive sections. This allows the author to illustrate some of his ideas on Presocratic flat earth cosmology. Prior to offering a visualization of the cosmos according to Empedocles, Bollack's earlier attempt is subjected to a critical examination. In two additional sections of the article, the author claims that, according to Empedocles, the moon must move on a cylinder as well and that the image of the cylinder for movements of the sun and moon dates back to Anaximander.

" CREPUSCULAR " LUNAR ECLIPSES DURING ANAXAGORAS' LIFETIME

Aristotle's Proofs of the Sphericity of the Earth

A critical analysis of Aristotle's proofs of the earth's sphericity, including his a critical sur... more A critical analysis of Aristotle's proofs of the earth's sphericity, including his a critical survey of arguments that were available to him and which he did not use. The conclusion is that none of these arguments is conclusive, and that some are based on false presuppositions or even contain a petitio principii.

AN ANCIENT CHINESE FLAT EARTH COSMOLOGY

Disclaimer: in this paper I only present the main features of the gai tian system as an extraordi... more Disclaimer: in this paper I only present the main features of the gai tian system as an extraordinary intellectual effort, leaving out many details, such as numerous calculations, several problems that are inherent to the system, the usual interpretation of the sunlight as a cone, the different number of the radius of the area of sunlight, the flat heavens represented as a Chinese hat, and so on. A fuller account will appear in March 2016 in the second volume of the Tsinghua Journal of Western Philosophy, and an even more extensive one in my forthcoming book When the Earth Was Flat). In all civilizations, people believed that the earth is flat, until in ancient Greece the idea of a spherical earth emerged. In China the belief in a flat earth lasted until the end of the sixteenth century, when catholic monks told them the new world picture, albeit not that of Copernicus, but that of Aristotle. Almost all Presocratic cosmologists, too, conceived of the earth as flat, although perhaps somewhat concave. The usual picture was that of the dome of a hemispherical or spherical heaven over or around the flat earth. Not surprisingly, this conception yielded some difficulties that were hard to cope with. Here I will only mention two of them, as they are the most relevant in the context of this paper. In the first place, on a flat earth it is always everywhere the same time. When the sun rises, it rises over the surface of the entire flat earth, and when the sun sets it gets dark all over the flat earth. Or, in the words of Ptolemy: " if the earth were flat, the stars would rise and set for all people together and at the same time ". 1 That at least some of the Presocratics were aware of this problem is clear from an otherwise enigmatic report on Archelaus, who pleads for a concave earth, because " the sun does not rise and set at the same time for all men, as would inevitably happen if the earth were flat ". 2 The second problem was the tilt of the celestial axis. The heavenly bodies seem to orbit around an apparently arbitrary fixed point in the northern heavens. In Presocratic Greek cosmology, the tilt of the heavens was a recurrent topic. As Furley writes: " they commonly explained this by the ad hoc assumption that the heavens tilted somehow, after the formation of the earth ". 3

THALES AND THE SOLAR ECLIPSE OF 28 MAY 585 BC

Several sources, of which Herodotus is the most famous, report that Thales predicted an eclipse o... more Several sources, of which Herodotus is the most famous, report that Thales predicted an eclipse of the sun. We may ask: 1) did he really predict an eclipse? 2) if so, which one did he predict? 3) if so, how did he do it? The answers to the first two questions will appear to follow from the answer to the third one. If we are able to discover which method Thales could have used, it follows immediately that he predicted an eclipse and also which one it was he foretold. We will answer these three questions: yes, he did predict a solar eclipse; it was the eclipse of 28 May 585 BC, and he did it by making a brilliant mistake. Here is the path of the eclipse of 28 May 585 BC:

Anaximander's Boundless Nature (with Radim Kočandrle)

Anaximander's Boundless Nature, 2013

The usual interpretation maintains that Anaximander made ‘the Boundless’ (τὸ ἄπειρον) the source ... more The usual interpretation maintains that Anaximander made ‘the Boundless’ (τὸ ἄπειρον) 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 (Phys. 203 a 4). When we take this seriously, it includes Anaximander as well. This means that Anaximander did not make τὸ ἄπειρον the source or principle of everything, but called something else ἄπειρος. The question is, then, what was the subject 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 can be called ‘divine’. Being boundless, the mechanisms of nature, in which 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.

The Qumran Roundel and the mrkhyt: A Comparative Approach

The Qumran Roundel and the mrkhyt: A Comparative Approach, 2013

A small saucer-shaped object with engraved concentric rings and radial marks, found at Qumran, is... more A small saucer-shaped object with engraved concentric rings and radial marks, found at Qumran, is usually called a sundial. Several interpretations, some of them very complicated, have been suggested, none of them convincing. The most recent and most extensive interpretation, presented by Paul Tavardon O.C.S.O., receives special attention in this article. The Egyptian mrxyt, consisting of a horizontal piece with at one end an upright block serving as a little gnomon, is also usually called a sundial. In this article the two instruments are examined in comparison with each other, which results in a rather simple interpretation. Current interpretations have studied both instruments as if they were handled in isolation and by one person. In the new interpretation offered here it is argued that, if studied under the assumption that two or more identical copies were used at the same time by different persons, it can be shown that they could have been used as instruments for making appointments when the shadow of the little gnomon had reached an agreed-upon mark.

ANAXAGORAS AND THE SOLAR ECLIPSE OF 17 FEBRUARY 478 BC

Anaxagoras and the Size of the Sun

Plutarch and others report that Anaxagoras compared the sze of the sun wth the Peloponnesus. It s... more Plutarch and others report that Anaxagoras compared the sze of the sun wth the Peloponnesus. It s the am of ths paper to show that ths was a far estmate, from hs pont of vew, whch s that of a flat earth. More precsely, I wll show that, wth the nstruments and the geometrcal knowledge avalable, Anaxagoras must have been able to use the procedures and perform the calculatons needed to reach approxmately hs result. * I am grateful to professor Teje de Jong from the Unversty of Amsterdam, who read an earler verson of ths paper, and to Jan Coupre, who checked the underlyng calculatons.

Archaeology and the Origins of Philosophy

Aestimatio: Critical Reviews in the History of Science, 2015

The Visualization of Anaximander's Astronomy

Apeiron, 1995

Anaxagoras und die Größe der Sonne. Hyperboreus 12 (2006), p. 55-76

Plutarch, Hippolyt und Diogenes Laertius berichten, daß Anaxagoras die Größe der Sonne mit dem Pe... more Plutarch, Hippolyt und Diogenes Laertius berichten, daß Anaxagoras die Größe der Sonne mit dem Peloponnes verglich. Ich will in diesem Aufsatz zeigen, daß Anaxagoras keineswegs von Sinnen war, als er diese Aussage machte, sondern daß dieser Vergleich eine durchaus vernünftige Einschätzung war, und zwar auf Grund seiner Sichtweise, nämlich der einer flachen Erde. Speziell will ich dartun, daß Anaxagoras mittels der seinerzeit verfügbaren Instrumente (Gnomon, Klepsydra, Guckrohr) sowie des damals verfügbaren mathematischen Wissens (die Eigenschaften ähnlicher Dreiecke, einfache Proportionen und der Satz des Pythagoras) in der Lage gewesen sein muß, Verfahren anzuwenden und Berechnungen auszuführen, die erforderlich sind, um das genannte Resultat zu erreichen.

The Paths of the Celestial Bodies According to Anaximenes

Anaximenes is said to have maintained that the celestial bodies do not go underneath the earth, b... more Anaximenes is said to have maintained that the celestial bodies do not go underneath the earth, but move laterally around it like a kind of felt cap around our head. In this article the interpretations of McKirahan and Bicknell are discussed and a new interpretation is proposed. McKirahan’s interpretation is shown to suffer from several shortcomings, such as not to account for the stars in the southern part of the heavens. Bicknell’s interpretation presupposes that Anaximenes taught a dip of the earth as is reported of Leucippus and Democritus. In this article it is argued that this interpretation is wrong, mainly because there did not exist such a thing as a Presocratic theory of a dip of the earth: Leucippus and Democritus taught a tilt of the heavens, just like other Presocratics. Following a suggestion of Wöhrle’s, it is argued that what Anaximenes meant to describe was not the actual state of celestial affairs but that before the tilt of the heavens.

Review of J.C. Morrison, Meaning and Truth in Wittgenstein's Tractatus

Review of: J.C. Morrison, Meaning and Truth in Wittgenstein's Tractatus. The Hague/Paris 1968.

Science before Socrates: Parmenides, Anaxagoras, and the New Astronomy by Daniel W. Graham

Journal of the History of Philosophy, 2014

The Tilting of the Heavens in Presocratic Cosmology

Apeiron, 2009

„Hätte die Welt ein Ziel, [ ... ] so wäre es [ ... ] mit allem Werden längst zu Ende“

Nietzsche-Studien, 2000

Some Remarks on the Earth in Plato's Phaedo. Hyperboreus 11 (2005), p. 192-204

Anaxagoras and Aristotle on the Sun at the Horizon. Hyperboreus 14 (2008), p. 39-49

When the Earth Was Flat: Studies in Ancient Greek and Chinese Cosmology

New York: Springer, 2018

For those who want to get a quick impression of the contents of my new book: The frontmatter (in... more