Quantity

‘Quantum’ means that which is divisible into two or more constituent parts of which each is by nature a ‘one’ and a ‘this’. A quantum is a plurality if it is numerable, a magnitude if it is a measurable. ‘Plurality’ means that which is divisible potentially into non-continuous parts, ‘magnitude’ that which is divisible into continuous parts; of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid.

Now it is evident that the whole nature of a substance is under every part of the dimensions under which it is contained; just as the entire nature of air is under every part of air, and the entire nature of bread under every part of bread; and this indifferently, whether the dimensions be actually divided (as when the air is divided or the bread cut), or whether they be actually undivided, but potentially divisible.

For quantity differs from extended substance, and number from what is numbered, not in reality but merely in our thought; so that, for example, we may consider the whole nature of a corporeal substance which is comprised in a space of ten feet, although we do not attend to this measure of ten feet, for the obvious reason that the thing conceived is of the same nature in any part of that space as in the whole; and, on the other hand, we can conceive the number ten, as also a continuous quantity of ten feet, without thinking of this determinate substance, because the concept of the number ten is manifestly the same whether we consider a number of ten feet or ten of anything else; and we can conceive a continuous quantity of ten feet without thinking of this or that determinate substance, although we cannot conceive it without some extended substance of which it is the quantity. It is in reality, however, impossible that any, even the least part, of such quantity or extension, can be taken away, without the retrenchment at the same time of as much of the substance, nor on the other hand can we lessen the substance without at the same time taking as much from the quantity or extension.

If we would know why the same Body seems greater (without adding to it) one time, than another; they say, when it seems lesse, it is Condensed; when greater, Rarefied. What is that Condensed, and Rarefied? Condensed, is when there is in the very same Matter, lesse Quantity than before; and Rarefied, when more. As if there could be Matter, that had not some determined Quantity; when Quantity is nothing else but the Determination of Matter; that is to say of Body, by which we say one Body is greater, or lesser than another, by thus, or thus much. Or as if a Body were made without any Quantity at all, and that afterwards more, or lesse were put into it, according as it is intended the Body should be more, or lesse Dense.

I answer, that quantity is conceived by us in two ways; in the abstract and superficially, as we imagine it; or as substance, as we conceive it solely by the intellect. If, then, we regard quantity as it is represented in our imagination, which we often and more easily do, we shall find that it is finite, divisible, and compounded of parts; but if we regard it as it is represented in our intellect, and conceive it as substance, which it is very difficult to do, we shall then, as I have sufficiently proved, find that it is infinite, one, and indivisible. This will be plain enough to all who make a distinction between the intellect and the imagination, especially if it be remembered, that matter is everywhere the same, that its parts are not distinguishable, except in so far as we conceive matter as diversely modified, whence its parts are distinguished, not really, but modally. For instance, water, in so far as it is water, we conceive to be divided, and its parts to be separated one from the other; but not in so far as it is extended substance; from this point of view it is neither separated nor divisible. Further, water, in so far as it is water, is produced and corrupted; but, in so far as it is substance, it is neither produced nor corrupted.