The Aristotelian Universe and Space

In order to understand the significance of the modern science, you have to see the historical and intellectual background against which Copernicus, Galileo, Kepler, and many others propounded their own views (伊東1985、75). This applies, in particular, to the theories of space and time, theories of motion, etc. Galileo, for instance, continually refers to Aristotelians in his dialogues; but what did they believe? Here is a diagramatical representation of the Aristotelian view, against which the founders of modern science worked.

If you think the three dimensional, homogeneous and infinite Euclidean space is a "common sense", you may fail to see the real novelties of Galileo and Newton, for instance! But such "Newtonian common sense" may be another "prejudice" imposed by culture and education, against which Einstein, for instance, had to fight!

Maybe it is instructive to quote some of Aristotle's words on physics and the heavens:

... the natural motion of the earth as a whole, like that of its parts, is towards the center of the Universe: that is the reason why it is now lying at the center. ...

From these consideations it is clear that the earth does not move, neither does it lie anywhere but at the center. In addition the reason for its immobility is clear from our discussions. If it is inherent in the nature of earth to move from all sides to the center (as observation shows), and of fire to move away from the center towards the extremity, it is impossible for any portion of earth to move from the center except under constraint. ... If then any particular portion is incapable of moving from the center, it is clear that the earth itself as a whole is still more incapable, since it is natural for the whole to be in the place towards which the part has a natural motion. ... (Aristotle, On the Heavens (W.K.C. Guthrie's translation), Loeb Classical Library, 243-7 [296b8-297a1])

Thus you can see the distinction between natural and constrained motion is crucial for Aristotle. Incidentally, he argues in this part of his book that (1) the earth is at rest in the center of the universe, (2) it is spherical, and (3) it is small in comparison with the other stars.

Now it is important to see that this naturalness has a close connection with the geometry of space (universe); or more carefully, so it may be regarded. On this point, let me quote Kuhn's clear statement:

These natural positions and the lines by which bodies move to them are determined entirely by the intrinsic geometry of an absolute space, a space in which each position and direction is permanently labaled whether or not the position is occupied. Therefore, as Aristotle says elsewhere in On the Heavens, "If the earth were removed to where the moon is now, separate parts of it would not move towards the whole, but towards the place [the center] where the whole is now." The natural motion of a stone is governed by space alone, not by the stone's relation to other bodies. Therefore, a stone thrown vertically upward moves away and returns along a straight line fixed once and for all in space, and if the earth moves while the stone is in the air, the stone will not rejoin the earth at the point from which it departed. (Kuhn 1957, 87)

The passage quoted by Kuhn comes from Book IV, Chapter iii where Aristotle presents his own view of "weight and lightness"; since this is the Aristotelian view of "gravity" so to speak, let me add more quotations.

The motion of a thing towards its proper place must be regarded as analogous to other forms of generation and change. There are three forms of motion, change of size, change of form, and change of place, and in each one the change may be observed to proceed from opposites to opposites (or intermediate states). A thing does not change at random into anything else whatsoever. Similarly, any and every mover cannot affect any and every object, but just as what is capable of alteration is different from what is capable of growth, so is the cause of alternation different from the cause of growth. In the same way with locomotion we must suppose that there is no mere chance relationship between mover and moved. We may say, then, that the cause of motion upwards and downwards is equivelent to that which makes heavy or light, and the object of such motion is the potentially heavy or light, and motion towards its proper place is for each thing motion towards its proper form. ... It follows therefore that to ask the reason why fire moves upwards and earth downwards is the same as asking why the curable, when moved and changed qua curable, progresses towards health and not towards whiteness. ... Now whenever air is generated from water, a light thing from a heavy, it progresses to the upper region. Once arrived, it is light---no longer "becomes", but "is". Clearly then it is moving from potentiality to actuality, and that means attaining the place, quantity and quality proper to its actual state. It is for the same reason that what already is and exists as earth or fire moves towards its own place unless something prevents it. (On the Heavens, 345-351; 310a21-311a8)

Here are clear statements of "proper place", and of change as "becoming" from potentiality to actuality. The sentence quoted by Kuhn appears in the first omitted part (...), and you can confirm that it is not out of context.

As many historians point out, "Aristotle was fired by the ambition to unify all the separate branches of natural philosophy" (Toulmin and Goodfield 1961, 92), and came to this view. You may see that Aristotle's view sketched above resembles, in some respects, more to the Einsteinian view than to the Newtonian view, but in other respects, quite the reverse!

The notion of "natural motion" survived, in some sense, even in general relativity. For what is a geodesic, if not the path of a "natural motion"? In the Newtonian mechanics, inertial motions were a substitute for "natural motion"; in general relativity, Einstein's field equations (together with boundary conditions etc.) generate metric, which in turn determines geodesics. Local inertial system (its other names are local Lorentzian system, free-float system, etc.) still plays an essential role in general relativity.



Kuhn, Thomas (1957) The Copernican Revolution, Harvard University Press.

Toulmin, S. and Goodfield, June (1961) The Fabric of the Heavens, Harper.


Last modified Sept. 20, 2007. (c) Soshichi Uchii