Daily Aristotle Day two Categories Part two Yesterday he taught you Usia, this man and this horse, each standing on its own. Titus has come for you. Today you will see things that need a partner, as double needs half.

Quantity comes in two kinds. One kind is discrete, cut into separate pieces. The other is continuous, all of a piece, and there is a second way to divide them. Some are made of parts that have a position toward one another. Some are made of parts with no position at all. Number and speech are discrete. A line is continuous, and so is a surface, and so is a thing. And besides these, so are time and place. Take a number. Its parts join at no shared boundary. Say five is a part of ten. The one five and the other five meet at no common line. They stay apart. Take three and seven inside the same ten. Again, no shared boundary where they join. In fact, you could never find a shared boundary between the parts of any number. They are always held apart. So number is one of the discrete kinds. Speech works the same way. It too is one of the discrete kinds. That speech as a quantity is plain enough, because we measure it by the short syllable and the long one. I mean the speech that comes out of the voice. Its parts join at no shared boundary. There is no common line where the syllables meet. Each one stands apart, itself by itself. Now the continuous kinds. Take a line. You can find a shared boundary where its parts join, and that boundary is a point. Take a surface. Here the shared boundary is a line, for the parts of a flat surface join along some common edge. It works the same for a thing. You could find a shared boundary where its parts join, either a line or a surface. Time and place belong here too. The present moment joins the past on one side and what is coming on the other. And place is continuous as well. The parts of a thing take up a certain place, and those places join at a shared boundary. So the parts of place join at the very same boundary where the parts of the thing join. That makes place continuous, since its parts meet at one shared boundary. There is that other division too. Some quantities are made of parts that have a position toward one another. The parts of a line are like this, because each part lies somewhere. You could point out where each one sits on the flat surface and say which of the other parts it joins. It works the same for a surface. You could tell where each part lies and which parts join together, and the parts of a solid are like this and the parts of place too.

What does it mean that the parts of time have an order but no position? Think of a boundary stone. You can point at it, walk around it, say the vine sits to its left and the ditch to its right. Its parts hold a place. Time is not like that. Yesterday is gone. You cannot point at it and say tomorrow joins it here. You can only say yesterday came first. That is order without position. The same is true of counting. One comes before two, but nowhere.

But a number is different. No one could show you that its parts have any position toward one another, or that they lie somewhere, or which parts join to which. Time is the same. No part of time stays put, and a thing that will not stay put can have no position. What you can say is that time has an order. One part comes earlier, another later. Number has an order too. You count the one before the two and the two before the three. So number has a certain order, but you would hardly find a position in it. Speech is the same again. None of its parts stays put. A word is said and then it is gone, and you can no longer catch hold of it. So its parts can have no position, since not one of them stays put. And so it stands. Some quantities are made of parts that have a position and some of parts that have none. Only the things we named are quantities in the strict sense. Everything else is called a quantity by accident, what merely happens to it, not what it is in its own right. We call the rest quantities only by looking to these. Take the white on a surface. We call it much because the surface is much. We call an action long because its time is much, and its change much. But none of these is a quantity in its own right. Ask how much an action is and you bound it by the time. You say it lasted a year or something like that. Ask how much the white is and you bound it by the surface. However much the surface, that much the white. So only the things we named are quantities strictly and in their own right. None of the rest is, except by accident, if at all. Here is something more. Nothing is contrary to a quantity, no paired opposite, the way hot stands against cold. With the bounded quantities, this is plain. Nothing is contrary to two qubits long, or three, or a surface, or anything like these, unless someone says that much is contrary to little or the great to the small. But none of these is a quantity. They belong instead to what is said in relation to something else. Nothing is called great or small in its own right. It is called so by being set against something else. A mountain is called small and a millet seed large. The mountain is larger than others of its kind, and the seed smaller than others of its kind. So the reference is to something else. If a thing were great or small in its own right, the mountain would never be called small, nor the seed large. Think of it another way. We say there are many people in the village and few in Athens, though Athens holds many times more. We say there are many in the house and few in the theater, though the theater holds far more.

If a mountain can be called small, isn't small still a real size? Small is not a size. A cloth two cubits long stays two cubits beside a cloak. Small is only small next to something else. The word Usia means the thing itself, the man you point at. He is sick, then healthy, never both at once. Small never stands on its own. The next lines ask if one thing can be great and small at once.

Here is more still. Two cubits, three cubits, and each such thing means a quantity. But great and small do not mean a quantity. They mean rather something said in relation to something else. For the great and the small are looked at with reference to something else. So plainly these belong to what is said in relation to something else. And whether you count them as quantities or not, nothing is contrary to them. How could anyone name a contrary to what you cannot grasp on its own, but must refer to something else? Say the great and the small were contraries, paired opposites, hot against cold. Then the same thing takes on those opposites at once, and is contrary to itself, for sometimes the same thing is at once great and small. It is small next to this and great next to that. So the same thing turns out great and small at the same time, taking on both opposites at once, but nothing seems to take on such opposites at the same time. Take Usia, one and the same thing can be first one opposite, then the other, the same man sick, then unhealthy. But nothing is sick and healthy at once, nothing is white and black at once, and no other thing takes on both opposites at the same time either. They also turn out contrary to themselves. Say the great is contrary to the small, and say the same thing is at once great and small, then it would be contrary to itself, but it is impossible for a thing to be contrary to itself in any way, so the great is not contrary to the small, nor the much to the little. So even if someone says these belong not to what is said in relation to something else, but to quantity, they still will have no contrary.

Why is the middle called down? Picture the world as a great ball and the earth resting at its center. Down is not under your feet by accident. Down is the middle of everything, the point farthest from the outer edge on every side. A stone dropped from the theatre seats falls toward that center. It seeks the middle, and the middle is the lowest place there is. So down means toward the center of the whole.

It is in place, most of all, that quantity does seem to have an opposite. People set up the up as opposite to the down. They call the region toward the middle down. They call it so because the middle stands at the greatest distance from the limits of the world order, and they seem to draw the mark of the other opposites from these two. For within one and the same kind, they define as opposites the things that stand farthest apart from one another. A quantity does not seem to take on the more and the less. Take two cubits long. One thing is not more two cubits long than another, nor with number, three is no more three than five is, nor is five more five than three, nor is one time said to be time more than another. In none of the things we named is the more and the less said at all. So a quantity too does not take on the more and the less. What is most of all proper to a quantity is this it is called equal and unequal. Each of the quantities we named is called equal and unequal. A thing is called equal and unequal. Time is called equal and unequal, and each of the others in the same way. But take the rest, all that are not quantities, you would hardly say they are called equal and unequal. A disposition is hardly called equal or unequal, but rather alike. And the white is hardly equal or unequal, but rather alike. So being called equal and unequal would be most of all proper to a quantity. Now to the next kind, something said in relation to something else. These are things that are said to be just what they are, of other things, or in some other way towards something else. The larger is called what it is by pointing to something else, it is larger than something. The double is called what it is by pointing to something else, it is double of something, and so with all such things. There are others of this kind too. A hexus, a disposition, perception, knowledge, position. For each of these is said to be just what it is of something else, and nothing more. A hexus is called the hexus of something, knowledge the knowledge of something, position the position of something, and the rest likewise. So these are things said to be just what they are, of other things, or in some other way towards something else. A mountain is called large in relation to something else, the alike is called alike to something, and the other such things are called relative in the same way.

What is a hexis? It is something you have, you have it of something. A grip is a grip of the javelin. There is no grip without the javelin. Knowledge is knowledge of something in the same way. That is all a hexis is, it always points at what it is of.

Reclining and standing and sitting are certain positions, and position is one of these relatives, but to be reclining or standing or sitting are not themselves positions. Rather, they are named after the positions we just spoke of. Opposites can belong among these things too. Excellence is opposite to badness, and each of the two is said in relation to something else, and knowledge is opposite to ignorance, but not everything said in relation to something else has an opposite. Nothing is opposite to the double, nor to the triple, nor to any such thing. These things also seem to take on the more and the less. The alike and the unalike are called more and less, the equal and the unequal are called more and less, and each of these is said in relation to something else, for the alike is called alike to something, and the unalike unalike to something. But not everything said in relation to something else takes on the more and the less. The double is not called more double and less double, nor is any such thing. Every relative is set towards something that turns back upon it. The slave is called the slave of a master, and the master the master of a slave. The double is the double of a half, and the half the half of a double. The larger is larger than a smaller, and the smaller smaller than a larger, and so with the others, except that sometimes the wording will differ by the shape of the word. Knowledge is called the knowledge of what can be known, and what can be known is called knowable by knowledge. Perception is the perception of what can be sensed, and what can be sensed is called sensible by perception.

Why say wing of a bird is wrong? A bird has wings, yes, but so does a bee, and so does a bat. The wing does not belong to the bird as a bird, it belongs to it as a winged thing. Point at the master's rudder on his boat at Ostia. The rudder is not the rudder of a boat, for some boats have none. It is the rudder of the thing a rudder steers. Name it that way, and each name fits the other.

Yet sometimes it will not seem to turn back if you do not give fittingly the thing it is said toward, and the one giving it goes wrong. Say the wing is given as the wing of a bird, then bird does not turn back upon wing, for wing of a bird was not given in the fitting way. It is not as a bird that the wing is called its wing, but as it is winged. There are wings of many other things too, which are not birds, so if it is given fittingly, it does turn back. The wing is the wing of a winged thing, and the winged thing is winged by a wing, and sometimes it is perhaps even necessary to coin a name, if no name has been laid down toward which the thing could be given fittingly. Say the rudder is given as the rudder of a boat, then the giving does not come out fitting. It is not as a boat that the rudder is called its rudder, for there are boats that have no rudders, so it does not turn back, since the boat is not called the boat of a rudder. The giving would perhaps be more fitting this way. The rudder is the rudder of a rudder guided thing, or some other way, since no name has been laid down, and it does turn back, if given fittingly, for the rudder-guided thing is guided by a rudder. Likewise the head would be given more fittingly as the head of a headed thing than as the head of an animal, for it is not as an animal that a thing has a head, since many animals have no head. In this way one would perhaps most easily grasp the things that have no names laid down, by setting down names from the first ones for the things that turn back upon them. So it was in the cases just spoken of, from the wing the winged thing, and from the rudder the rudder guided thing.

Why must you name a winged thing when bird was sitting right there? Because the wing is not a wing by belonging to a bird. Sparrows have wings, so do bees. The bird is only one owner among many. Each name has to fit the other. Point at the very thing that makes a wing a wing, being winged. So you coin the word.

So here is the whole rule for things said in relation to something else. Give them fittingly, and they always turn back upon what they are said toward. But give one toward whatever comes to hand, and not toward the very thing it is said toward, and it does not turn back. Even take a pair everyone agrees turns back, a pair with proper names laid down, give one of them toward some accident, some thing that merely happens to it, and not toward the very thing it is said toward, and it will not turn back. Take the slave, say he is the slave of a man, or of a two-footed thing, or anything else like that, instead of the slave of a master. Then he does not turn back. The giving was not fitting.

Isn't this the same thing you just said with the wing and rudder? It is not. That test asked if each name fits the other. This asks if you named the right other thing. Call him slave of a master. Forget that the master is a man. Keep only that he is a master. You can still call him that. Call him slave of a man. Forget the man is a master. You cannot still call him that man's slave. Man was never the name the pair needed.

Here is another test. Suppose you have given a thing fittingly toward the very thing it is said toward. Now strip away everything else, every accident, everything that merely happens to it, and leave only that one correlate. The thing will still be said toward it, always. Take the slave said toward a master. Strip from the master everything that merely happens to him, being two footed, being able to take on knowledge, being a man, leave only that he is a master. The slave will still be said toward him always. For the slave is called the slave of a master. But suppose you gave it wrongly, then strip away the rest and leave only what you gave, and the thing will not be said toward it. Say the slave is the slave of a man, and the wing the wing of a bird. Now strip from the man that he is a master, the slave will no longer be said toward the man, for if there is no master, there is no slave. In the same way, strip from the bird that it is winged. The wing will no longer be one of these related things. For if there is no winged thing, the wing is the wing of nothing. So you must give a thing said in relation to something else toward whatever it is properly said toward. If a name is already laid down for that other thing, the giving is easy. Take double and half, each already has its name, so you name the one toward the other with no trouble. If there is no such name, then perhaps you must coin one. Give them this way, and one thing is plain. Everything said in relation to something else is said toward a partner that turns back upon it. The greater is greater than the less, and the less is less than the greater. Now, things said in relation to something else seem to exist together by nature, and in most cases this is true. The double and the half are there at the same time. If there is a half, there is a double. If there is a master, there is a slave, and if there is a slave, there is a master. The rest are like these, and they cancel one another too. If there is no double, there is no half, and if there is no half, there is no double. The same holds for all others of this kind.

You ask whether a slave vanishes the moment there is no master. Not the man, the word. The man stands there, breathing, whatever we call him. What goes is the naming. Take away the master, and no one is a slave any longer, because slave means slave of a master. Name either one, and you have named the pair. Like the double and the half. Kill the half, and the double is no longer double of anything. The person stays, the pairing does not.

But it does not seem true of all of them that they exist together by nature. Take knowledge and the knowable. The knowable would seem to come before knowledge, for as a rule, the things are already there first, and we take up our knowledge of them afterward. In few cases or none would you see the knowledge coming to be at the very moment the knowable does. And here is the deeper difference. Do away with the knowable and you cancel knowledge along with it. But do away with knowledge and the knowable is not cancelled. For if there is no knowable, there is no knowledge, since it would be knowledge of nothing. But if there is no knowledge, nothing stops the knowable from still being there. Think of the squaring of the circle, if indeed it is a knowable. No knowledge of it exists yet, but the thing itself is knowable all the same. Or again, do away with every animal, and there is no knowledge left, yet many of the knowables may still be there. It is the same with perception as with knowledge and the knowable. What can be sensed would seem to come before the sensing of it. Do away with what can be sensed, and you cancel the sensing along with it. But the sensing does not cancel what can be sensed. Here is why. Our sensings are about a thing and are in a thing. Do away with what can be sensed, and the thing is done away with too, for the thing is one of the things that can be sensed, and if there is no thing, there is no sensing either. So what can be sensed cancels the sensing of it, but the sensing does not cancel what can be sensed. Do away with every animal, and the sensing is gone, yet something to be sensed will still be there, a thing and the hot, the sweet, the bitter, and all the rest that can be sensed. And notice the timing. The sensing comes to be at the same moment as the animal that senses, for it comes to be along with the animal. But what can be sensed is there even before there is any animal or any sensing at all. Fire and water and such things, the very stuff the animal is made from, are there before there is any animal at all or any sensing. So what can be sensed would seem to come before the sensing of it.

Why isn't a hand a hand of something? You cannot say master without saying slave. You can say hand without saying whose. Then you name the owner. We do the same with a cloak. The cloak is a cloak, and it is yours. He will ask the same of man and of wood.

Now a hard question. Take Usia. Thing most truly is. Is no Usiya something said in relation to something else? That is how it seems. Or could some of the secondary Usi, the species and kind, be said that way? Take the primary Usii, this man, this ox. The answer is plain. They are not said in relation to something else. Neither the whole thing nor its parts are said in relation to anything. Take this man here. We do not call him a certain man of something, nor a certain ox an ox of something, and the parts work the same way. A certain hand is not called a certain hand of something. We call it the hand of someone. A certain head is not a certain head of something, but the head of someone. It is much the same with the secondary Usi. In most cases, at least. We do not call man the man of someone, nor ox the ox of someone, nor would the wood of someone. We call wood someone's possession.

What's the difference between primary and secondary Usia? That word means what a thing most truly is. Primary is this thing here, that bust of your ancestor on the shelf, the one you sorted for me. You point at it. Secondary is what you say it is, a statue, a made thing. You say that of it. The thing comes first, what it is comes after. You will need both. The next lines ask if either is said in relation to something else.

So for cases like those, it is clear they are not said in relation to something else, but some of the secondary oozei are open to dispute. A head is called the head of something, a hand is called the hand of something, and so with each such part, so these would seem to be said in relation to something else. Now, suppose the definition of relatives was given well enough, then it is either very hard or downright impossible to show that no uzii is said in relation to something else. But suppose it was not given well enough, suppose the true things said in relation to something else are the ones for which to be is the same as to be somehow disposed towards something. Then perhaps something can be said about them after all. The earlier definition does hold for all of them, but being said in relation to something else is not the same as this, being said to be just what you are of other things. From all this, one thing is clear. Suppose you know in a fixed and settled way that something is said in relation to something else, then you must also know, just as fixedly, the thing it is related to. You can see this from the things themselves. Say you know that something is said in relation to something else, and to be such a thing is to stand somehow toward something, then you know the thing it stands toward as well. For if you have no idea at all what it stands toward, you cannot know whether it stands toward anything. Look at particular cases. If you know in a marked off way that a thing is double, you know at once, just as marked off, what it is double of. For if you do not know it to be double of some definite thing, you do not know whether it is double at all. It is the same with more beautiful. If you know a thing is more beautiful, you must know at once, in a marked off way, what it is more beautiful than. You will not know in a loose, unfixed way that it is more beautiful than something worse. That kind of knowing turns into a mere belief, not knowledge, for you will no longer know exactly that it is more beautiful than a worse thing, since it may turn out that nothing is worse than it at all.

The double one is easy. You know your javelin is double the length of Titus's, and you know at once what it doubles, his. Drop the his, and you no longer know it is double at all. Double of what? So knowing the one means knowing the other, fixed together. Now the hand. You can know this hand for the very thing it is, and still not know whose it is. There the two come apart, and that, watch closely, is how the master will show you a hand is not said in relation to something else.

So this much is plain. Whatever relative you know in a marked off way, you must also know marked off the thing it is related to. But take the head or the hand or any such part, these are usi. You can know each one determinately, know it as the very thing it is, yet you need not know the thing it is said in relation to. Whose head this is or whose hand, you cannot know for certain. So these would not be things said in relation to something else. And if these are not, then it would be true to say that no Usiya is said in relation to something else. Still, it is perhaps hard to speak firmly about such things without having gone over them many times, yet to have worked through the difficulties point by point is not without its use.

What we learned keep four distinctions from today. First, how a quantity is cut. Second, why small is not a size. Third, how a thrower needs a catcher. Fourth, whether this man here is said towards something else. First, you asked why I count speech as a quantity. Say a word aloud. It runs a short time or a long time. We measure it by the short syllable and the long one. Take ten. Five sits in it, and another five. Those two fives meet at no shared line. Each syllable stands itself by itself. A line is not like that. Its parts meet at a point, so some quantities are discrete, cut into separate pieces. Some are continuous, all of a piece. Second, you asked if a mountain can be called small, and whether small is still a real size. Small is not a size. A cloth two cubits long stays two cubits beside a cloak. The mountain is called small only next to a larger mountain. A millet seed is called large only next to a smaller seed. Nothing is great or small in its own right. Great and small are said in relation to something else. They are not quantities. A quantity has no paired opposite, the way hot stands against cold. What belongs to a quantity most of all is this. It is called equal and unequal. Now the third. Watch Titus at the throw. A thrower is a thrower because a catcher exists. Take away the catcher, and the thrower stops being a thrower without moving his arm. The slave is called the slave of a master, and the master the master of a slave. These are what they are by pointing to a partner. You asked if this was the same as the wing and the rudder. It is not. That test asked if each name fits the other. This asks if you named the right other thing. You asked whether a slave vanishes the instant there is no master. Not the man, the word. The man stands there breathing. What goes is the naming. Last, you asked the difference between primary and secondary oosia. That word means what a thing most truly is. Point at the bust of your ancestor on the shelf. That bust itself is a primary Usia. Man is a secondary Usia, the species. Animal is a secondary Usia too, the kind above it. We do not call this man a certain man of something. You can know a head as the very thing it is, and still not know whose head it is. So no Usia is set in relation to something else. We have finished the lesson. Before you go, remember one moment from the day. You did not notice when the hour ended. You were watching for the ball at the edge of Titus's game. I said the lesson was over an hour and a quarter after it began. On the walk home, you discovered the extra quarter of an hour, and you resented it. You looked for someone to resent, and you found no one at all, and the sourness sat in you the rest of the way home anyway. Tomorrow, what sort of thing stays in a wrestler after the sand is empty? You already watch the one who keeps winning, and that question is about him. The Daily Aristotle. More at dailyaristotle.com.