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On The Heavens   

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. Again, 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.

There is, further, another view-that of Leucippus and Democritus

of Abdera-the implications of which are also unacceptable. The primary

masses, according to them, 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. Now 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

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