What are 'heavy' and 'light'?

Our predecessors have asked this and have mostly spoken of light and heavy things based on weight [property of the object].

They consider this a sufficient analysis also of the notions of absolute heaviness, to which their account does not apply.

The Timaeus uses ’lighter’ and ‘heavier’ in the sense that:

• the body which is composed of more identical particles is relatively heavy
• the body which is composed of fewer identical particles is relatively light

A larger quantity of lead or bronze is heavier than a smaller.

This holds good of all homogeneous masses – the superior weight always depends on a numerical superiority of equal particles.

This is precisely the same way, they assert, of how lead is heavier than wood.

All bodies are composed of identical particles and of a single material.

But this analysis says nothing of the absolutely heavy and light.

• Fire is always light and moves upward
• Earth and all earthy things move downwards or towards the centre

They believe that all these bodies are composed of triangles.

I do not think that the fewness of these triangles is the cause which disposes fire to move upward.

If it were the cause, then a larger quantity of fire should move slower due to the increase of weight from the increased number of triangles.

But the fact is that the greater the quantity of fire:

• the lighter the mass is
• the quicker its upward movement

Similarly, in the reverse movement from above downward, the small mass will move quicker and the large slower.

They believe that:

• lighter means having fewer of these homogeneous particles
• heavier means having more
• air, water, and fire are composed of the same triangles

It follows that the only difference is in the number of such particles.

• This must explain any distinction of relatively light and heavy between these bodies.

It follows that there must be a certain quantum of air which is heavier than water.

But the facts are directly opposed to this.

The larger the quantity of air the more readily it moves upward, and any portion of air without exception will rise up out of the water.

Others have a view from an older generation.

They think that there are bodies which are smaller but heavier.

It is therefore obviously insufficient to say that bodies of equal weight are composed of an equal number of primary parts: for that would give equality of bulk.

Those who maintain that the primary or atomic parts, of which bodies endowed with weight are composed, are planes, cannot so speak without absurdity; but those who regard them as solids are in a better position to assert that of such bodies the larger is the heavier.

But since in composite bodies the weight obviously does not correspond in this way to the bulk, the lesser bulk being often superior in weight (as, for instance, if one be wool and the other bronze), there are some who think and say that the cause is to be found elsewhere.

The void, they say, which is imprisoned in bodies, lightens them and sometimes makes the larger body the lighter. The reason is that there is more void.

This would also account for the fact that a body composed of a number of solid parts equal to, or even smaller than, that of another is sometimes larger in bulk than it.

In short, generally and in every case a body is relatively light when it contains a relatively large amount of void. This is the way they put it themselves, but their account requires an addition.

Relative lightness must depend not only on an excess of void, but also an a defect of solid: for if the ratio of solid to void exceeds a certain proportion, the relative lightness will disappear.

Thus fire, they say, is the lightest of things just for this reason that it has the most void. But it would follow that a large mass of gold, as containing more void than a small mass of fire, is lighter than it, unless it also contains many times as much solid. The addition is therefore necessary.

Some deny the existence of a void.

Anaxagoras and Empedocles have not tried to analyse the notions of light and heavy at all; and those who, while still denying the existence of a void, have attempted this, have failed to explain why there are bodies which are absolutely heavy and light, or in other words why some move upward and others downward.

A larger body can be sometimes lighter than smaller ones. They have been silent on this.

Some attribute the lightness of fire to its containing so much void.

• They are necessarily involved in the same difficulties.

Fire has less solid than any other body, and more void.

Yet there will be a certain quantum of fire in which the amount of solid or plenum is in excess of the solids contained in some small quantity of earth.

They reply that there is an excess of void also. But the question is, how will they discriminate the absolutely heavy? Presumably, either by its excess of solid or by its defect of void.

On the former view there could be an amount of earth so small as to contain less solid than a large mass of fire.

Similarly, if the distinction rests on the amount of void, there will be a body, lighter than the absolutely light, which nevertheless moves downward as constantly as the other moves upward.

But that cannot be so, since the absolutely light is always lighter than bodies which have weight and move downward, while, on the other hand, that which is lighter need not be light, because in common speech we distinguish a lighter and a heavier (viz. water and earth) among bodies endowed with weight.

The suggestion of a certain ratio between the void and the solid in a body is no more equal to solving the problem before us. The manner of speaking will issue in a similar impossibility.

For any two portions of fire, small or great, will exhibit the same ratio of solid to void, but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size. This, however, should not be the case if the ratio is the ground of distinction between heavy things and light.

There is also an absurdity in attributing the upward movement of bodies to a void which does not itself move.

If, however, it is the nature of a void to move upward and of a plenum to move downward, and therefore each causes a like movement in other things, there was no need to raise the question why composite bodies are some light and some heavy; they had only to explain why these two things are themselves light and heavy respectively, and to give, further, the reason why the plenum and the void are not eternally separated. It is also unreasonable to imagine a place for the void, as if the void were not itself a kind of place.

But if the void is to move, it must have a place out of which and into which the change carries it. Also what is the cause of its movement? Not, surely, its voidness: for it is not the void only which is moved, but also the solid.

Similar difficulties are involved in all other methods of distinction, whether they account for the relative lightness and heaviness of bodies by distinctions of size, or proceed on any other principle, so long as they attribute to each the same matter, or even if they recognize more than one matter, so long as that means only a pair of contraries.

If there is a single matter, as with those who compose things of triangles, nothing can be absolutely heavy or light: and if there is one matter and its contrary-the void, for instance, and the plenum-no reason can be given for the relative lightness and heaviness of the bodies intermediate between the absolutely light and heavy when compared either with one another or with these themselves.

The view which bases the distinction upon differences of size is more like a mere fiction than those previously mentioned, but, in that it is able to make distinctions between the four elements, it is in a stronger position for meeting the foregoing difficulties.

Since, however, it imagines that these bodies which differ in size are all made of one substance, it implies, equally with the view that there is but one matter, that there is nothing absolutely light and nothing which moves upward (except as being passed by other things or forced up by them); and since a multitude of small atoms are heavier than a few large ones, it will follow that much air or fire is heavier than a little water or earth, which is impossible.