Originally published in 1987.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Originally published in 1987.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


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Overview
Originally published in 1987.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Product Details
ISBN-13: | 9780691606378 |
---|---|
Publisher: | Princeton University Press |
Publication date: | 07/14/2014 |
Series: | Princeton Legacy Library , #825 |
Pages: | 202 |
Product dimensions: | 6.00(w) x 9.10(h) x 0.40(d) |
Read an Excerpt
The Physical World of Late Antiquity
By Samuel Sambursky
PRINCETON UNIVERSITY PRESS
Copyright © 1962 S SamburskyAll rights reserved.
ISBN: 978-0-691-08476-3
CHAPTER 1
SPACE AND TIME
* * *
1. Absolute and relative space
In all periods, philosophers, physicists and psychologists have shared in the analysis of space and time. Some of the greatest minds of Greek antiquity occupied themselves with these central concepts; indeed one of Aristotle's major achievements was his raising of the level of the discussion of these concepts to considerable heights by his own contribution which is such a prominent part of his Physica. Aristotle's idea of space — or rather place, as he termed it — stemmed from his concept of continuity. The whole cosmos, finite in extension and bounded by the uppermost sphere of the fixed stars, was a single continuum in which each body at every instant occupied a certain place whose extent Aristotle defined by 'the inner surface of the container', i.e. of the surrounding body. This surface was thus the total sum of all points of contact with the surrounding body which could be either air, water, or earth, or aether, that fifth element of which the celestial bodies were supposed to be composed. Aristotle's conception therefore was that of a coherent entity inseparable from the matter contained in it. The motions of matter are exchanges of place and, in the case of natural motions, are governed by the teleological principle whereby every body strives to reach perfection. This is attained at the 'natural place' — below for the heavy bodies, above for the light ones, and in circular motion for the divine celestial bodies.
There were no explicit definitions of space before Aristotle, but he rejected the notion implied in the doctrines of the atomists and of Plato. For Democritus space was identical with the infinite vacuum which provided the possibility of free motion for the atoms, whereas for Plato, who denied the vacuum, space was the receptacle, the seat of all material happenings.
Simplicius informs us of the conceptual developments of the idea of space from Aristotle until his time in the Corollary on Space contained in his commentary on Aristotle's Physica which is the source of most of the passages that will be quoted below. Immediately after Aristotle, two basically different definitions of space were given which formed the prototypes of and were used as patterns for the subsequent theories. They are both surprisingly similar to the two fundamental conceptions of space in modern physics. The first, by Theophrastus, is as follows: 'Perhaps space is not a reality by itself but is defined by position and order of the bodies according to their natures and faculties, as is the case with animals and plants and all non-homogeneous bodies which either have souls or are without souls but have the nature of a structure. For these bodies, too, have a certain order and position of their parts with respect to their whole substance. Thus each, being in its proper place, is said to have its specific order, especially as every part of a body desires and strives to occupy its own place and position' [152].
This is a clear statement of the purely relational character of space, and is, in essence, the same as that of Leibniz who says, for instance in his third letter to Clarke, 'that I hold space to be something merely relative, as is time; that I hold it to be an order of coexistences, as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together, without inquiring into their manner of existing. When many things are seen together, one perceives that order of things among themselves.' Theophrastus, even more outspoken than Leibniz, declares order and relative position of bodies to be the essence of space and thus brings out still more clearly the geometrical aspect of the relation between space and matter which has found its physical elaboration in the general theory of relativity.
A second statement on the nature of space, quite different from that of Theophrastus, was made by a man who was almost contemporary with him and one of Aristotle's eminent disciples, Strato of Lampsacus (c. 300 B.c.): 'Some make space equal in extension to the cosmical body and declare it, though being void by its own nature, to be always filled with bodies and only theoretically to be considered as existing by itself. This is the opinion of many of the Platonic philosophers and, I believe, Strato of Lampsacus was of the same opinion' [149]. This view of space as an absolute entity is consistent with what we know of Strato's general approach to physical problems. His fragments show him as being influenced to some extent by the atomists in that he postulated the possibility of a vacuum — not a permanent one, as Democritus thought, but a temporary, artificial one, created for instance by man. Strato himself probably proved this by some experiments in pneumatics on which, at a much later date, Hero based his work in this field.
From a historical point of view, we have to regard Strato as the first proponent of a concept of absolute space, in spite of his qualification that this space is always filled with matter. It is essentially equivalent to Newton's definition in his Principia that 'absolute space, in its own nature, without relation to anything external, remains always similar and immovable'. That many members of the early Academy, according to Simplicius' authority, were also adherents of the doctrine of an absolute space, is of importance for the understanding of the views of some of the Neo-Platonists. On the whole, the speculations of later antiquity on the nature of space were variations of either Theophrastus' or Strato's ideas, but they were all tinged by the basic conception of Stoic physics and cosmology, the notion of the pneuma permeating the cosmos and making it one dynamically interacting organism.
It was the doctrine of the pneuma that had transformed the static continuum of Aristotle into a dynamic one. The pneuma was in many respects a precursor of the modern field concept; although it was supposed to be corporeal, a very tenuous matter filling the whole universe and interpenetrating all bodies, it fulfilled the functions of a physical field by its tensional qualities and by its capacity to give bodies a coherent structure with well-defined physical properties. The radical view of the Stoics with regard to the interaction of pneuma and ponderable matter and, as a consequence of this, the interaction between distant bodies, gave enhanced significance to the relational concept of space. Theophrastus' definition that space 'is defined by the position and order of bodies, according to their natures and faculties', introducing geometrical and group-theoretical characteristics, now merged with the Stoic ideas of an all pervading force that created that well-ordered continuum called space. The Stoic ideas had an enormous impact on the minds of scientists and philosophers during the last three centuries B.C. They were intensified and modified during the first centuries A.D. by the spread of the fundamental beliefs of the monotheistic religions. Pneuma was identified with the divine spirit, and its omnipresence became identical with the omnipresence of God. In conjunction with the relational concept of space this led to the identification of space with God in the doctrines of Hellenistic philosophers such as Philo of Alexandria: 'Place has a threefold notion, first as space filled with a body, secondly, as divine order by which God has totally permeated everything with incorporeal faculties, ... and its third significance is God Himself who is called place because He embraces the Whole but is not embraced by anything' [105].
A notable example of the combined influence of Stoic and Judaeo-Christian conceptions on the Neo-Platonists is Iamblichus' exposition on the nature of space. Iamblichus lived about A.D. 300 and his writings reveal a very strange mixture of the most abstruse mystical ideas and some very clear and well-formulated scientific remarks that however remained aphoristic in character in the midst of an obscurantist galimatias. We shall return to Iamblichus at a later stage, but here some passages on space should be quoted: 'Every body, qua body, is in a certain place. Place coexists thus in a natural union with bodies and is never separated from them. ... Therefore, all those who do not make space akin to cause and drag it down to the concept of boundaries of surfaces or of empty extensions or extensions of whatever kind, are making use of foreign notions and miss the whole purpose of the Timaeus which always links nature with creation. One has thus to regard space as depending upon cause, in the same way as bodies were primarily introduced as akin to cause, in the sense in which the Timaeus has guided us' [153]. Iamblichus does not mention the Stoics, but that space is akin to cause is an eminently Stoic idea, even if he tries to link it with Platonic notions. He then attempts to give a definition of space and here his phraseology has a strong biblical flavour: 'Which doctrine will define space completely and in accordance with its essence? That which attributes to space a corporeal force that holds the bodies together and supports them, that raises the falling bodies and gathers together those that are scattered, fills them up and protects them from all sides' [154]. The last phrases are indeed not only strongly reminiscent of, but are literally borrowed from biblical expressions that are used in connection with God. The special Greek verb for 'scatter' used by Iamblichus appears in the New Testament mainly in contexts such as St. John's Gospel 11.52 ('he should gather together in one the children of God that are scattered abroad'). The Neo-Platonists, through their polemics against Christianity, were well versed in the Scriptures and, as this passage proves, consciously or unconsciously adapted some religious associations to their own particular ends.
Two other Neo-Platonists, Syrianus (c. A.D. 400) and Damascius (c. A.D. 525), elaborated on the concept of space as a relational entity, but with special emphasis on the positional aspect. The bodies, so to say, are forced to take up certain relative positions and to arrange themselves in a certain order, and the same applies to the different parts of one body. It was easy to connect this view with Plato's doctrine of the world soul and its creative and harmonizing activities. Simplicius reports on Syrianus' view in the following passage: 'Of those who assumed that space also has form and a power stronger than the bodies, I may mention the great Syrianus, the teacher of Proclus the Lycian. In his tenth treatise on Plato's Laws he has written concerning space as follows: 'It is an interval with its own specific distinctions derived from the various orders of the soul and the illumination of the creative forms. It appropriates the various bodies and, with respect to one element, makes itself the proper place of fire ... and, with respect to another, the proper place of earth ...' [150]. Thus according to Syrianus natural places derive their existence from the relative arrangement of material objects, this itself being the origin of space. Natural motion and rest in the natural place are caused by the relative positions of all the bodies in the cosmos; they do not have absolute significance, nor are they originated by something inherent in the bodies themselves. The quotation from Syrianus closes with the words: 'Thus neither motion nor rest within the extension are subject to the nature of the bodies nor are they caused by this nature.'
Still more outspoken on this point is Damascius who regards space in its three-dimensional manifold as a kind of matrix which allows for different positions and defines positions in various directions. Space thus becomes a vectorial concept as against the simple concept of length, and is compared with other 'measures ' as follows: 'These dimensions, in order not to relapse entirely into the indefinite, are supported by measures: time, as a measure of the activity of motion; quantity, such as number, as a measure of discrete matter; length, such as for instance a cubit, as a measure of continuous matter; and space as a measure of the ramification of position '[151]. This topological conception is elucidated by Damascius in another passage in a slightly different way: 'The motion of a point generates an interval with which space is associated as a measure defining the position of all things in the universe. This measure implies that there exists an extension in three dimensions, i.e. in every direction, and that the whole will be properly arranged everywhere with regard to its own position as well as that of its parts, and that all the elements will have their proper positions each in its own proper place within the universe. Thus if the universe is a sphere, it will always have a centre and a periphery and will be situated in its proper place' [155].
Most of the Neo-Platonic views quoted up to now can, in the last instance, be traced back to Theophrastus' relational conception of space, and the quotations are of interest because they give an idea of the style peculiar to that late period and of the cumulative effect of various influences of philosophical and spiritual systems, either contemporary or of earlier times. We shall now quote passages from John Philoponus (sixth century) who also was brought up in the Neo-Platonic range of ideas but who, in his conception of space, was a strict adherent of Strato's absolute space, filled with bodies, but conceived as an entity in itself. 'Space is not the boundary of the containing body, as one can well conclude from the fact that it has a certain extension in three dimensions, different from the bodies placed into it, incorporeal according to its proper nature and nothing but the empty interval of a body — in fact, space and the void are the same by their nature. ... How do we explain that bodies exchange their places? If the moving body does not penetrate into another one, and if, further, it is not the surface that moves but the three-dimensional extension, then, if the air is cut through in its place by the moving body, the volumes of the body and of the air exchanging their places must obviously be equal to each other. If now the measure is equal to the object measured, it follows necessarily that if the air measures ten cubic units of length, the amount of space containing it will be the same. It will also hold the same ten cubic units which it had given up before to the moving body. ... Space is thus cubic, namely of threefold extension, and it is a measure of the objects in space, for it is of the same dimension' [71]. Further on, Philoponus makes the same qualification as Strato with regard to the emptiness of space: 'And I do not maintain that this extension either is or can be empty of every body. This is never the case, for though the void in its proper sense is different from the bodies placed into it, as I said before, space is never devoid of bodies, just as we say that matter differs from form but yet can never be devoid of form' [72].
Finally some excerpts from Simplicius' quotations of Proclus will acquaint us with a unique conception that regards space as a corporeal entity, as a body. Proclus' theory again reflects in a highly interesting way the mental attitude of the later NeoPlatonic thinkers. His surprising conclusion that space must be 'an immovable, indivisible, immaterial body', a definition hardly acceptable to any physicist, is reached by a formal reasoning carried through in strict Aristotelian fashion: 'Space must be either matter or form, or the boundary of the containing body, or the interval between the containing boundaries equal to what is referred to as place' [145]. He rejects the first three alternatives and continues as follows: '... one has to regard the extension between the boundaries of the container as the primary place of every body. But the cosmic extension of the whole universe differs from this particular extension, and thus the latter either exists or does not exist. If it were non-existent, then locomotion would take place from nothing into nothing, for in this case the natural places would not exist, and every motion proceeds according to the nature of something which really exists. ... If it is existent, it is either incorporeal or it is corporeal. It would be absurd to assume that it is incorporeal. For space must be of the same kind as the object in space, but body and incorporeality are certainly not of the same kind. ... Thus extension is a body, for space is extension. If it is a body, it is either immovable, or it is moving. If it were somehow moving, it had to undergo locomotion. Thus space would again be in need of space, and this is impossible, as Theophrastus and Aristotle have shown. ... If space is immovable, it must be either indivisible by the bodies placed in it, as in the doctrine of the interpenetration of bodies, or divisible, as air and water are divided by bodies moving in them. If, however, space is divisible, the whole will be split and its parts will have a motion relative to the splitting body. It could follow that space is movable, for its parts move. ... Therefore space must be indivisible. If so, it must be either immaterial or material. But were it material it would not be indivisible. For if material bodies interpenetrate, the result is a division, as is the case when our body is immersed in water. Only immaterial objects cannot be divided by anything, for an immaterial body is impassive, and divisible things are not impassive' [146].
(Continues...)
Excerpted from The Physical World of Late Antiquity by Samuel Sambursky. Copyright © 1962 S Sambursky. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents
- FrontMatter, pg. i
- CONTENTS, pg. v
- PREFACE, pg. vii
- INTRODUCTION, pg. ix
- I. SPACE AND TIME, pg. 1
- II. MATTER, pg. 21
- III. SUBLUNAR MECHANICS, pg. 62
- IV. MODES OF PHYSICAL ACTION, pg. 99
- V. CELESTIAL PHYSICS, pg. 122
- VI. THE UNITY OF HEAVEN AND EARTH, pg. 154
- NOTES, pg. 176
- SOURCES, pg. 179
- INDEX OF PASSAGES QUOTED, pg. 181
- GENERAL INDEX, pg. 185