Aristotle, On the Heavens

LCL 338: 2-3

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Chapter I


The subject of physical science is material substance, or body, and the living creatures which are made out of it. It is also necessary to get first of all a grasp of the general principles on which material substances are constructed (matter, form, etc.), the laws of change and so forth. These have been dealt with in the Physics, and we now approach the subject of body itself.

Body is defined as a species of the continuous. This in its turn means “a magnitude which is divisible to infinity,” and consists of three species—the line, the surface and the solid body. Since there are only three dimensions, body may be called, on this argument, the complete magnitude. Pythagorean notions of the perfection of the triad, as well as popular custom and language, give further colour to this view, whose proof lies simply in the appeal to experience.

Body, then, is that which has extension in three, i.e. in all, directions, and hence is divisible in all directions. For that reason we speak, on this geometrical argument, of all bodies as “complete magnitudes,” but it is of course only in this


On the Heavens, I. i.

Aristotle on the Heavens

Book I

Chapter I

Argument (continued)

limited sense that they are complete. We also speak of the whole Universe as complete, and we must not be thought to be confusing that sense of the word with this in which we apply it to any body whatsoever. All bodies are complete in the geometrical sense (i.e. it is impossible to add another dimension to them), but only the Universe as a whole can be said to be complete in all respects, i.e. to be the whole of which the separate bodies are parts, and which itself is not the part of any larger whole.

[The arguments of this and some of the following chapters naturally laid themselves open to the charge of using mathematical language in describing concepts that were intended to be physical. To this Simplicius replies (p. 25 Heiberg): “If we spoke of lines in a mathematical sense, we should indeed be wide of the mark. But if, taking into consideration that all motion takes place within linear dimensions (simple motion following a simple line and composite motion a complex) we introduce the different dimensions in illustration of the different varieties of motion, how can we be said to be explaining physical matters by mathematical arguments? The physicist

DOI: 10.4159/DLCL.aristotle-heavens.1939