The Elements

What bodies are subject to generation, and why?

Since in every case knowledge depends on what is primary, and the elements are the primary constituents of bodies, we must ask which of such bodies are elements, and why.

After that what is their number and character. The answer will be plain if we first explain what kind of substance an element is.

An element, we take it, is a body into which other bodies may be analysed, present in them potentially or in actuality (which of these, is still disputable), and not itself divisible into bodies different in form.

That, or something like it, is what all men in every case mean by element. Now if what we have described is an element, clearly there must be such bodies.

For flesh and wood and all other similar bodies contain potentially fire and earth, since one sees these elements exuded from them; and, on the other hand, neither in potentiality nor in actuality does fire contain flesh or wood, or it would exude them.

Similarly, even if there were only one elementary body, it would not contain them. For though it will be either flesh or bone or something else, that does not at once show that it contained these in potentiality: the further question remains, in what manner it becomes them.

Now Anaxagoras opposes Empedocles’ view of the elements. Empedocles says that fire and earth and the related bodies are elementary bodies of which all things are composed; but this Anaxagoras denies.

His elements are the homoeomerous things, viz. flesh, bone, and the like. Earth and fire are mixtures, composed of them and all the other seeds, each consisting of a collection of all the homoeomerous bodies, separately invisible; and that explains why from these two bodies all others are generated.

(To him fire and aither are the same thing.) But since every natural body has it proper movement, and movements are either simple or mixed, mixed in mixed bodies and simple in simple, there must obviously be simple bodies; for there are simple movements. It is plain, then, that there are elements, and why.

Part 4

Are the elements are finite or infinite in number?

Anaxagoras

Anaxagoras believes that all the homoeomerous bodies are elements.

Any one who adopts this view misapprehends the meaning of element.

Observation shows that even mixed bodies are often divisible into homoeomerous parts. Examples are flesh, bone, wood, and stone.

Thus, the composite cannot be an element. And so not every homoeomerous body can be an element.

Elements are those which are not divisible into bodies different in form.

But even taking ’element’ as they do, they need not assert an infinity of elements, since the hypothesis of a finite number will give identical results.

Even 2 or 3 such bodies serve the purpose as well, as Empedocles’ attempt shows.

Even on their view, it turns out that all things are not composed of homocomerous bodies.

They do not pretend that a face is composed of faces, or that any other natural conformation is composed of parts like itself.

Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved.

This is the common demand of mathematicians, who always assume as principles things finite either in kind or in number.

If body is distinguished from body by the appropriate qualitative difference, and there is a limit to the number of differences (for the difference lies in qualities apprehended by sense, which are in fact finite in number, though this requires proof), then manifestly there is necessarily a limit to the number of elements.

Leucippus and Democritus

I think the view of Leucippus and Democritus of Abdera are also unacceptable.

They say that the primary masses are infinite in number and indivisible in mass.

One cannot turn into many nor many into one; and all things are generated by their combination and involution.

This view in a sense makes things out to be numbers or composed of numbers.

The exposition is not clear, but this is its real meaning. And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies.

But they have never explained in detail the shapes of the various elements, except so far to allot the sphere to fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element.

Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate no other alteration in their theory.

Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity. Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement.

They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their atoms, since then they could not be generated out of one another.

The extrusion of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation of water, air, and earth from one another. Again, even on their own presuppositions it does not seem as if the clements would be infinite in number.

The atoms differ in figure, and all figures are composed of pyramids, rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have their principles, and, whether these are one or two or more, the simple bodies must be the same in number as they.

Again, if every element has its proper movement, and a simple body has a simple movement, and the number of simple movements is not infinite, because the simple motions are only two and the number of places is not infinite, on these grounds also we should have to deny that the number of elements is infinite.