Aristotle explains One

‘One’ has several meanings:

1. Something continuous

2. Something whole

Its movement is one and indivisible in place and time.

3. Something indivisible

4. Something universal

These four things all refer to unity.

This is also true of ’element’ or ‘cause’ if “one” both meant:

• the things of which it is predicable and to render the definition of the word.

In one sense, fire is an element.

• In another sense, fire is not an element.

For example, a fire is of the fire element, but is not itself an element.

This is why ’to be one’ means ’to be indivisible.

Being essentially one means it can be isolated physically, or in thought.

But it means especially ’to be the first measure of a kind’, and most strictly of quantity; for it is from this that it has been extended to the other categories.

For measure is that by which quantity is known; and quantity qua quantity is known either by a ‘one’ or by a number, and all number is known by a ‘one’.

Therefore, all quantity qua quantity is known by the one, and that by which quantities are primarily known is the one itself.

And so the one is the starting-point of number qua number.

Hence in the other classes too ‘measure’ means that by which each is first known, and the measure of each is a unit-in length, in breadth, in depth, in weight, in speed.

(The words ‘weight’ and ‘speed’ are common to both contraries; for each of them has two meanings-‘weight’ means both that which has any amount of gravity and that which has an excess of gravity, and ‘speed’ both that which has any amount of movement and that which has an excess of movement; for even the slow has a certain speed and the comparatively light a certain weight.)

In all these, then, the measure and starting-point is something one and indivisible, since even in lines we treat as indivisible the line a foot long.

For everywhere we seek as the measure something one and indivisible; and this is that which is simple either in quality or in quantity. Now where it is thought impossible to take away or to add, there the measure is exact (hence that of number is most exact; for we posit the unit as indivisible in every respect); but in all other cases we imitate this sort of measure.

For in the case of a furlong or a talent or of anything comparatively large any addition or subtraction might more easily escape our notice than in the case of something smaller; so that the first thing from which, as far as our perception goes, nothing can be subtracted, all men make the measure, whether of liquids or of solids, whether of weight or of size; and they think they know the quantity when they know it by means of this measure. And indeed they know movement too by the simple movement and the quickest; for this occupies least time.

And so in astronomy a ‘one’ of this sort is the starting-point and measure (for they assume the movement of the heavens to be uniform and the quickest, and judge the others by reference to it), and in music the quarter-tone (because it is the least interval), and in speech the letter. And all these are ones in this sense–not that ‘one’ is something predicable in the same sense of all of these, but in the sense we have mentioned.

But the measure is not always one in number. Sometimes, there are several.

e.g. the quarter-tones (not to the ear, but as determined by the ratios) are two, and the articulate sounds by which we measure are more than one, and the diagonal of the square and its side are measured by two quantities, and all spatial magnitudes reveal similar varieties of unit.

Thus, then, the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind.

The one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that every ‘one’ is indivisible e.g. a foot and a unit; the latter is indivisible in every respect, while the former must be placed among things which are undivided to perception, as has been said already-only to perception, for doubtless every continuous thing is divisible.

The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude, and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit.

(For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond-it is as if one claimed that the measure of units is units and not a unit; number is a plurality of units.)

“Knowledge, also, and perception, we call the measure of things for the same reason, because we come to know something by them-while as a matter of fact they are measured rather than measure other things.

But it is with us as if some one else measured us and we came to know how big we are by seeing that he applied the cubit-measure to such and such a fraction of us.

But Protagoras says ‘man is the measure of all things’, as if he had said ’the man who knows’ or ’the man who perceives’.

These because they have respectively knowledge and perception, which we say are the measures of objects. Such thinkers are saying nothing, then, while they appear to be saying something remarkable.

Unity in the strictest sense is a measure of first of quantity, and secondly of quality.

Some things will be one if they are indivisible in quantity.

• Others will be one if they are indivisible in quality

And so that which is one is indivisible, either absolutely or qua one.