Thus the fundamental fact everywhere present in Nature is "change," "process," "motion." Since motion in the literal sense of change of position is involved as a condition of every such process, and such motion requires space through which to move and time to move in, the doctrine of space and time will also form part of Physics. Hence a great part of Aristotle's special lectures on Physics is occupied with discussion of the nature of space and time, and of the continuity which we must ascribe to them if the "continuous motion" on which the unbroken life of the universe depends is to be real Aristotle knows nothing of the modern questions whether space and time are "real" or only "phenomenal," whether they are "objective" or "subjective." Just as he simply assumes that bodies are things that really exist, whether we happen to perceive them or not, so he assumes that the space and time in which they move are real features of a world that does not depend for its existence on our perceiving it.
His treatment of space is singularly naïf. He conceives it as a sort of vessel, into which you can pour different liquids. Just as the same pot may hold first wine and then water, so, if you can say, "there was water here, but now there is air here," this implies the existence of a receptacle which once held the water, but now holds the air. Hence a jug or pot may be called a "place that can be carried about," and space or place may be called "an immovable vessel." Hence the "place" of a thing may be defined as the boundary, or inner surface, of the body which immediately surrounds the thing. It follows from this that there can be no empty space. In the last resort, "absolute space" is the actual surface of the outermost "heaven" which contains everything else in itself but is not contained in any remoter body. Thus all things whatever are "in" this "heaven." But it is not itself "in" anything else. In accord with the standing Greek identification of determinate character with limitation, Aristotle holds that this outermost heaven must be at a limited distance from us. Actual space is thus finite in the sense that the volume of the universe could be expressed as a finite number of cubic miles or yards, though, since it must be "continuous," it is infinitely divisible. However often you subdivide a length, an area, or a volume, you will always be dividing it into lesser lengths, &c., which can once more be divided. You will never by division come to "points," i.e. mere positions without magnitude of divisibility.
The treatment of time is more thoughtful. Time is inseparably connected with movement or change. We only perceive that time has elapsed when we perceive that change has occurred. But time is not the same as change. For change is of different and incommensurate kinds, change of place, change of colour, &c.; but to take up time is common to all these forms of process. And time is not the same as motion. For there are different rates of speed, but the very fact that we can compare these different velocities implies that there are not different velocities of time. Time then is that in terms of which we measure motion, "the number of motion in respect of before and after," i.e. it is that by which we estimate the duration of processes. Thus e.g. when we speak of two minutes, two days, two months as required for a certain process to be completed, we are counting something. This something is time. It does not seem to occur to Aristotle that this definition implies that there are indivisible bits of time, though he quite correctly states the incompatible proposition that time is "made up of successive nows," i.e. moments which have no duration at all, and can no more be counted than the points on a straight line. He recognises of course that the "continuity" of motion implies that of time as well as of space. Since, however, "continuity" in his language means the same thing as indefinite divisibility, it ought not to be possible for him to regard time as "made up of nows"; time, like linear extension, ought for him to be a "length of" something.
The Continuous Motion and the "Spheres."--The continuous world-process depends upon a continuous movement set up in the universe as a whole by the presence of an everlasting and unchangeable "First Mover," God. From the self-sameness of God, it follows that this most universal of movements must be absolutely uniform. Of what precise kind can such a movement be? As the source of the movement is one, and the object moved is also one--viz. the compass of the "heaven," the movement of the primum mobile or "first moved"--the object immediately stimulated to motion by God's presence to it, must be mechanically simple. Now Aristotle, mistakenly, held that there are two forms of movement which are simple and unanalysable, motion of translation along a straight line, and motion of rotation round an axis. He is at pains to argue that rectilinear motion, which we easily discover to be that characteristic of bodies near the earth's surface when left to themselves, cannot be the kind of movement which belongs to the "heaven" as a whole. For continuous rectilinear movement in the same direction could not go on for ever on his assumption that there is no space outside the "heaven," which is itself at a finite distance from us. And motion to and fro would not be unbroken, since Aristotle argues that every time a moving body reached the end of its path, and the sense of its movement was reversed, it would be for two consecutive moments in the same place, and therefore at rest. Reversal of sense would imply a discontinuity. Hence he decides that the primary unbroken movement must be the rotation of the "first moved"--that is, the heaven containing the fixed stars--round its axis. This is the only movement which could go on for ever at a uniform rate and in the same sense. Starting with the conviction that the earth is at rest in the centre of the universe, he inevitably accounts for the alternation of day and night as the effect of such a revolution of the whole universe round an axis passing through the centre of the earth. The universe is thus thought of as bounded by a spherical surface, on the concave side of which are the fixed stars, which are therefore one and all at the same distance from us. This sphere, under the immediate influence of God, revolves on its axis once in twenty-four hours, and this period of revolution is absolutely uniform. Next the apparently irregular paths of the "planets" known to Aristotle (i.e. the moon, Mercury, Venus, the sun, Mars, Jupiter, Saturn) are resolved into combinations of similar uniform rotations, each planet having as many "spheres" assigned to it as are requisite for the analysis of its apparent path into perfectly circular elementary motions. Altogether Aristotle holds that fifty-four such rotating spheres are required over and above the "first moved" itself, whose rotation is, of course, communicated to all the lesser "spheres" included within it. As in the case of the "first moved," the uniform unceasing rotation of each "sphere" is explained by the influence on it of an unchanging immaterial "form," which is to its own "sphere" what God is to the universe as a whole. In the Aristotelianism of the mediæval church these pure forms or intelligences which originate the movements of the various planetary spheres are naturally identified with angels. It is e.g. to the angelic intelligences which "move" the heaven of Venus, which comes third in order counting outward from the earth, that Dante addresses his famous Canzone, Voi ch' intendendo il terzo del movete. The mediæval astronomy, however, differs in two important respects from that of Aristotle himself. (1) The number of "spheres" is different. Increasing knowledge of the complexity of the paths of the planets showed that if their paths are to be analysed into combinations of circular motions, fifty-four such rotations must be an altogether inadequate number. Aristotle's method of analysis of the heavenly movements was therefore combined with either or both of two others originated by pure astronomers who sat loose to metaphysics. One of these methods was to account for a planet's path by the introduction of epicycles. The planet was thought of not as fixed at a given point on its principal sphere, but as situated on the circumference of a lesser sphere which has its centre at a fixed point of the principal sphere and rotates around an axis passing through this centre. If need were, this type of hypothesis could be further complicated by imagining any number of such epicycles within epicycles. The other method was the employment of "eccentrics," i.e. circular movements which are described not about the common centre of the earth and the universe, but about some point in its neighbourhood. By combinations of epicycles and eccentrics the mediæval astronomers contrived to reduce the number of principal spheres to one for each planet, the arrangement we find in Dante. (2) Also real or supposed astronomical perturbations unknown to Aristotle led some mediæval theorists to follow the scheme devised by Alphonso the Wise of Castille, in which further spheres are inserted between that of Saturn, the outermost planet, and the "first moved." In Dante, we have, excluding the "empyrean" or immovable heaven where God and the blessed are, nine "spheres," one for each of the planets, one for the fixed stars, and one for the "first moved," which is now distinguished from the heaven of the stars. In Milton, who adopts the "Alphonsine" scheme, we have further a sphere called the "second movable" or "crystalline" introduced between the heaven of the fixed stars and the "first moved," to account for the imaginary phenomenon of "trepidation."[#] In reading Dante, Shakespeare, and Milton, we have always to remember that none of these reproduces the Aristotelian doctrine of the "spheres" accurately; their astronomy is an amalgam of Aristotle, Ptolemy, and Hipparchus.
[#] Paradise Lost, iii. 481.
"They pass the planets seven, and pass the fixed,
And that crystalline sphere whose balance weighs
The trepidation talked, and that first moved."
So far, the doctrine of the fifty-five "spheres" might be no more than a legitimate mathematical fiction, a convenient device for analysing the complicated apparent movements of the heavenly bodies into circular components. This was originally the part played by "spheres" in ancient astronomical theory, and it is worth while to be quite clear about the fact, as there is a mistaken impression widely current to-day that Aristotle's astronomy is typical of Greek views in general. The truth is that it is peculiar to himself. The origin of the theory was Academic. Plato proposed to the Academy as a subject of inquiry, to devise such a mathematical analysis of astronomical motions as will best "save the appearances," i.e. will most simply account for the apparent paths of the planets. The analysis of these paths into resultants of several rotations was offered as a solution by the astronomer Eudoxus of Cnidus. So far, the "spheres," then, were a mere mathematical hypothesis. What Aristotle did, and it is perhaps the most retrograde step ever taken in the history of a science, was to convert the mathematical hypothesis into physical fact. The "spheres" become with him real bodies, and as none of the bodies we are familiar with exhibit any tendency to rotate in circles when left to themselves, Aristotle was forced to introduce into Physics the disastrous theory, which it was a great part of Galileo's life-work to destroy, that the stuff of which the spheres are made is a "fifth body," different from the "elements" of which the bodies among which we live are made. Hence he makes an absolute distinction between two kinds of matter, "celestial matter," the "fifth body," and "terrestrial" or "elementary" matter. The fundamental difference is that "terrestrial" or "elementary" matter, left to itself, follows a rectilinear path, "celestial" matter rotates, but it is further inferred from the supposed absolute uniformity of the celestial movements that "celestial matter" is simple, uncompounded, incapable of change, and consequently that no new state of things can ever arise in the heavens. The spheres and planets have always been and will always be exactly as they are at the present moment. Mutability is confined to the region of "terrestrial" or "elementary" matter, which only extends as far as the orbit of the moon, the "lowest of the celestial bodies," because it is only "terrestrial" things which are, as we should say, chemical compounds. This is the doctrine which Galileo has in mind when he dwells on such newly-discovered astronomical facts as the existence of sun-spots and variable stars, and the signs of irregularity presented by the moon's surface. The distinction is peculiar to Aristotle. No one before him had ever thought of supposing the heavenly bodies to be made of any materials other than those of which "bodies terrestrial" are made. In the Academic attack on Aristotle's science of which we have already spoken the two points singled out for reprobation are (1) his rejection of the principle that all moving bodies, left to themselves, follow a rectilinear path, and (2) his denial that the heavenly bodies are made of the same "elements" as everything else. (It may just be mentioned in passing that our word quintessence gets its sense from the supposed special "nobility" of the incorruptible "fifth body.")
Terrestrial Bodies.--As we have seen already, Aristotle was out of sympathy with the tendency to regard the sensible differences between bodies as consequences of more ultimate differences in the geometrical structure of their particles. Hence his whole attitude towards the problems of that branch of natural science which we call physics is quite unlike any view to which we are accustomed. He reverts from the mathematical lines of thought current in Plato's Academy to the type of view more natural to the "plain man," and, like the earliest sixth-century men of science, regards the qualitative differences which our senses apprehend as fundamental. Among these, particular stress is laid on the difference in sensible temperature (the hot--the cold), in saturation (the dry--the moist), and in density (the dense--the rare). If we consider the first two of these oppositions, we can make four binary combinations of the elementary "opposite" characters, viz. hot and dry, hot and moist, cold and moist, cold and dry. These combinations are regarded as corresponding respectively to the sensible characteristics of the four bodies which Empedocles, the father of Greek chemistry, had treated as the ultimate components of everything. Fire is hot and dry, air hot and moist, water moist and cold, earth cold and dry. This reflection shows us why Aristotle held that the most rudimentary form in which "matter" ever actually exists is that of one of these "elements." Each of them has one quality in common with another, and it is in virtue of this that a portion of one element can be assimilated by and transmuted into another, a process which seems to the untutored eye to be constantly recurring in Nature. We also observe that the order in which the "elements" appear, when so arranged as to form a series in which each term has one quality in common with each of its neighbours, is also that of their increasing density. This would help to make the conception of their transmutability all the more natural, as it suggests that the process may be effected by steady condensation. We must remember carefully that for Aristotle, who denies the possibility of a vacuum, as for the mediæval alchemists, condensation does not mean a mere diminution of the distances between corpuscles which remain unchanged in character, but is a process of real qualitative change in the body which undergoes it. Incidentally we may remark that all changes of quality are regarded by Aristotle as stages in a continuous "movement" from one extreme of a scale to another. For example, colours, with him as with Goethe, form a series of which the "opposites" white and black are the end-points. Every other colour is a combination of white and black according to a definite proportion.
The Aristotelian doctrine of weight was one of the chief obstacles which seventeenth-century science had to contend with in establishing correct notions in dynamics. It is a curious feature of Greek science before Aristotle that, though the facts connected with gravity were well known, no one introduced the notion of weight to account for them. The difference between heavy bodies and light bodies had been previously treated as secondary for science. Plato's treatment of the matter is typical of the best fourth-century science. We must not try to explain why the heavier bodies tend to move towards the earth's surface by saying that they have a "downward" motion; their motion is not downward but "towards the centre" (the earth, though not fixed at the centre of the universe, being nearer to it than the rest of the solar and sidereal system). Plato then explains the tendency in virtue of which the heavier bodies move towards the "centre" as an attraction of like for like. The universal tendency is for smaller masses of "earth," "water," "air," "fire" to be attracted towards the great aggregations of the same materials. This is far from being a satisfactory theory in the light of facts which were not yet known to Plato, but it is on the right lines. It starts from the conception of the facts of gravity as due to an "attractive force" of some kind, and it has the great merit of bringing the "sinking" of stones and the "rising" of vapours under the same explanation.
Aristotle, though retaining the central idea that a body tends to move towards the region where the great cosmic mass of the same kind is congregated, introduced the entirely incompatible notion of an absolute distinction of "up" and "down." He identified the centre of the universe with that of the earth, and looked on motion to this centre as "downward." This led him to make a distinction between "heavy" bodies, which naturally tend to move "down," and "light" bodies, which tend to move "up" away from the centre. The doctrine works out thus. The heaviest elements tend to be massed together nearest the centre, the lightest to be furthest from it. Each element thus has its "proper place," that of water being immediately above earth, that of air next, and that of fire furthest from the centre, and nearest to the regions occupied by "celestial matter." (Readers of Dante will recollect the ascent from the Earthly Paradise through the "sphere of fire" with which the Paradiso opens.)