THE ART OF DEFINITION -- SECOND PART ABOUT DEFINITION AND DIVISION

Definition and division are two ways our reason goes from a confused to a distinct knowledge in every form of reasoned out knowledge. We must think out definitions and divisions before we reason out conclusions.

THE TWO KINDS OF DEFINITION

A definition is always a speech composed of names. One name by itself can never be a definition. There are two kinds of definition: the definition of a thing and the definition of a name.

The definition of a thing is speech signifying what a thing is or speech making known distinctly what a thing is. Although one name can signify what a thing is, it cannot do so distinctly as does a definition by its many names. The word triangle signifies what a triangle is, but not distinctly, as does the definition a plane figure contained by three straight lines.

The definition of a name is speech making clear the meaning of a name. Such a definition helps us to use the name correctly because the use of a name is based on its meaning. It also helps people to understand each other by using a name with the same meaning in both their minds.

THE ORDER OF THE TWO KINDS OF DEFINITION

The definition of a name often comes before the definition of a thing in our knowledge because we use the name of the thing to be defined in the question which seeks the definition of that thing. Hence, what we are looking for is not clear if the meaning of the name is not clear. It is especially important to define in what sense we are using the name when, as often happens, the same name can refer to more than one thing.

Further, we must know that a thing exists before we can ask what that thing is. But it is not always clear that some thing exists. Hence, we must in this case ask first whether it exists; and in so doing, we use a name whose meaning must be known to us. It is possible to know the meanings of names even when there are no existing things corresponding to them (except perhaps in fiction). We can know, for example, the meanings of the words mermaid, centaur and unicorn even if there are no things corresponding to them in the real world. But even if there are things corresponding to the names, their existence may not be obvious to us. We must know the meanings of their names when asking about their existence. How can we, for example, begin to answer the question whether atoms exist unless we first understand what is meant by the word atom?

Moreover, since even the definition of a thing is composed of names, it may be necessary to define one or more of the names used in the definition before one can understand the definition of the thing.

From the above, it can be seen how the definition of a name may come before the definition of a thing or be necessary for understanding some definition of a thing.

Although the definition of a name is important, logic is chiefly concerned with defining things whose existence is known to us. For it is things we want to know in the end, not their names. Hence, the rest of our consideration of definition will be about definition of thing in particular.

TWO KINDS OF DEFINITION OF A THING

The definition of a thing can make known inwardly what that thing is by penetrating to its interior and unfolding its nature for reason. Or it may make known only in an outward way what that thing is, by something outside its nature or what it is, but which nevertheless separates that thing from all other things. Only the first of these can be called a definition of the thing in the full sense or simply a definition because only it makes known what the thing is. The second can be called an encircling or drawing a line around.

The above definition of triangle is a definition in the full sense. But if someone defines virtue as a praiseworthy quality, virtue has been encircled, but not defined in the full sense. If one defined triangle as the rectilinear figure with the least sides, this would separate triangle from all other things, but it would not tell us what makes the triangle to be a triangle. Likewise, if one defined a straight line as the shortest distance between two points.

Both the definition of a thing in the full sense and the encircling of a thing should be convertible with that thing. (A and B are said to be convertible if every A is a B and every B is an A.) If animal with reason is the definition of man, every man should be an animal with reason, and every animal with reason should be a man.

THE NAMES USED IN THE TWO DEFINITIONS OF A THING

Every definition of a thing begins with the name called genus, but other names are used to complete the definition.

A definition (in the full sense) adds to the genus the species-making differences that separate inwardly, or in its very nature, the species to be defined from all other species that comes under the same genus. It brings out what makes the species to be what it is.

The encircling or drawing a line around does not use these species-making differences, but rather some property following upon the nature of the thing or some common name that in combination with the genus suffices to separate the thing to be defined from other things, without making it known inwardly or in its nature. If one defines wisdom as the best knowledge, one separates wisdom from everything else. Knowledge, the genus, separates wisdom from everything that is not knowledge; and best separates it from all other kinds of knowledge since best means better than all the rest. Yet this encircling does not make known wisdom inwardly because it does not even tell us what it is knowledge of. If one defined the triangle as the rectilinear figure with the least sides, one would separate triangle from everything else. But one would not bring out what makes the triangle to be a triangle; that it has three straight lines containing it.

DEFINITION BY CAUSE AND BY EFFECT

One can also distinguish between definition of a thing by cause and by effect. When Socrates asks Euthyphro (who has defined the pious as what the gods approve of) whether something is pious because the gods approve of it or whether they approve of it because it is pious, he is asking whether Euthyphro’s definition is by cause or by effect.

This distinction is almost the same as the above. For the species-making differences are what make the species to be what it is and hence are as causes of the species. But definition by property, which follows upon the nature of the thing, is like defining by effect. The property would seem to be an effect of the species’ nature.

Sometimes it is more convenient to ask what kind of definition of the thing has been made using this distinction between cause and effect. Thus after the good is defined as what all desire, we can imitate Socrates’ question and ask whether something is good because we desire it or do we desire it because it is good. Is desire the cause or the effect of the good?

THE ORDER OF THE DEFINITIONS OF A THING

If the property of a thing or its effect is more known to us than its species-making differences or its causes, we define first by the property or the effect. Usually properties and effects are more known to us, as can easily be seen in both natural and human things. In mathematics, however, we do not have to encircle before defining (in the full sense). In this science, defining (in the full sense) does not come after encircling. There is no need to encircle at all since reason easily sees what these things are. But almost everywhere else, we both encircle and define in the full sense (or try to do so), and the encircling of the thing comes before its definition in the full sense. Some of the reasons for this should now be considered.

We must separate a thing from other things before we can grasp what it is (just as the hand cannot grasp the center of the desk before it has been separated from the rest of the desk). We can separate it from all other things without understanding or grasping what it is, but the reverse is impossible. The encircling of a thing allows us to separate it from other things. But we grasp or understand (fully) what it is after it has been defined (in the full sense).

Again, we think about a thing before we understand what it is. But encircling is to thinking about a thing as definition is to understanding what it is. Hence, also, encircling comes before defining (fully). And we must encircle the thing in order to think about it rather than anything else. But we understand fully what the thing is only after its definition has been thought out.

Moreover, since the encircling of a thing involves only a vague or indistinct knowledge of that thing while the definition of the thing involves a precise and distinct knowledge of it, we naturally encircle before we define. For we naturally know things in a confused or indistinct way before we know them in a precise and distinct way.

Further, we think about a thing before we have insight into what it is. This is because our knowledge begins with the senses which know things in an outward way. But the encircling of a thing only requires us to know that thing in an outward way while the definition in the full sense penetrates within to the nature of the thing or what it is. Hence, the encircling of the thing, as an outward knowledge of that thing (and hence closer to the senses), naturally comes before the definition which gives us an inward knowledge of the thing.

Moreover, we have seen that the definition of a name comes before the definition of a thing. But the encircling is closer to the definition of the name than is the definition of the thing. A sign of this is that the elements of the definition of the name can also serve (after the existence of the thing is known) as the elements of an encircling of that thing. Since we name things, the definition of a name often has some reference to the thing named by it. Hence, from the definition of a name, we can often get to an encircling once it is clear that the thing exists.

Not only does the encircling come before the definition in the full sense, but it is also a beginning for reasoning to the definition in the full sense.

DEFINITION OF SUBSTANCE AND OF ACCIDENT

There is another distinction among definitions of things which is quite different from the above two similar distinctions. Its basis is also different. Instead of distinguishing definitions by how they define the same thing, this distinction is based first on the difference of the things being defined which require diverse ways of being defined.

We have seen before the distinction between things that are substances and things that are accidents. Substances are things that exist not in another as in a subject, such as this man or that dog. Accidents are things that exist only in another as in a subject apart from which they are incapable of being, such as the shape or health or knowledge of a man or a dog. Accidents are really something of another thing (their subject), as health is something of the body.

A substance then can be defined by itself, but an accident cannot be defined by itself. We cannot say what an accident is without saying what it is of another thing (its subject). Health, for example, must be defined as something of another thing, its subject, the body. One would define health as the good condition of the body or something like that. Likewise, one cannot define poetic meter without bringing syllables (its subject) into our definition. Although syllables can be without meter (as in prose), poetic meter can exist only in syllables as in a subject. Hence, poetic meter would have to be defined as something of syllables, as an order or alternation of accented and unaccented syllables or something of this sort.

Some things then can be defined by themselves while others (like accidents) must be defined as something of another thing. We call the first definition definition of substance and the second, definition of accident. But this distinction is broader than substance and accident. There are things which must be defined as something of another even though they are not accidents. (The soul is one important example of this.) Hence, the phrase definition of accident is short for definition of a thing as something of another. Likewise, something may be defined like substances, by themselves, even though they are not substances. This happens perhaps most in pure mathematics because of its abstract character.

This distinction points to a difference in the kind of definition and not just to a difference in the things being defined. Or rather it points to a distinction in things which requires diverse kinds of definition. Indeed, to define a thing as something of another would seem contrary to definition as first understood since one is bringing within the limits of the definition something other than the things being defined.

WAYS OF INVESTIGATING A DEFINITION IN THE FULL SENSE

Since we seek not just to know what is a definition (in the full sense), but to acquire such definitions in every form of reasoned out knowledge, it remains to consider the ways in which we can investigate a definition in the full sense.

The definition of a thing in the full sense can be investigated starting from what is less universal than the thing to be defined, or from what is more universal than the thing to be defined, or from what is equally universal (or convertible with) the thing to be defined. The way of going forward to the definition from each of these three beginnings is also different.

We investigate the definition of a thing starting from what is less universal than the thing to be defined when we begin from examples of the thing to be defined. The examples will always be singulars or individuals when we are trying to define a lowest species. But when the species one is trying to define is also a genus, the examples may be species of that genus. The only examples of circle are individual circles. But examples of moral virtue are the species courage, moderation and justice.

We go forward from examples of the thing to be defined to its definition by comparing the examples and separating out what they have in common while leaving asides their differences.

When we investigate the definition from what is more universal than the thing to be defined, we begin from its genus. The genus we begin from may be the proximate genus or a remote one.

We go forward from the genus to the definition by dividing the genus through species-making differences, seeing under which difference the species to be defined comes, adding this difference to the genus and checking whether the resulting speech is convertible or not with the thing to be defined. If the speech is not convertible, we go through the same steps again until a convertible speech is achieved.

When we investigate the definition from what is equally universal with the thing to be defined, we begin from an encircling or a strict property or a proper effect of that thing.

We go forward from what is equally universal with the thing to be defined by reasoning.

The definition is often investigated in more than one of these three ways. Knowing these three ways does not make arriving at a definition automatic. Much thinking is necessary. Logic is not, as some have wished, a substitute for thinking. Rather it is a help to thinking. The definition of a basic or great thing is often a major work of reason.

The division of a whole into its parts also contributes much towards understanding what the whole is. However this is not as proximate as the division of a genus by specie-making differences. For neither the name of the whole can be said of any part, properly speaking, nor can the name of any part be said properly (and not figuratively) of the whole. (We are speaking, of course, of whole and part in their original sense.) One cannot say, for example, that a man is a hand or a hand is a man.

DIVISION

Division is speech separating the parts of some whole. There are two kinds of division corresponding to the two main senses of the word whole.

The first meaning of whole is that which is composed of its parts or put together from its parts. A chair is put together from the seat and legs and back. The word cat is put together from three letters. Such a whole is called an integral whole.

The second meaning of the word whole is that which is said of its parts. The most important example of such a whole is a genus or general kind of thing which is said of its species that are particular kinds of the same thing. Number is a universal whole having as parts two particular kinds of number, odd number and even number. Such a whole is called a universal whole. This is not the first meaning of whole. But as the word particular (which is taken from the word part) indicates, the universal which can be said of many particulars is to those many something like a whole to its parts. (Hence, the words whole and part are equivocal by reason and not by chance.) And since only the integral whole comes under the senses which are the beginning of our knowledge, the integral whole must be the first meaning of whole. For we name things as we know them.

We can also divided as a universal whole, a subject by the accidents which can be found in it, or an accident by the subjects in which it can be found, or an accident by the accidents which are found with it is some subject. For example, we can divide men by their color or we can divide white by the subjects in which it is found (such as paper, man, house, etc.) or we can divide white by sweet (both are in sugar) and salty (both are in salt) and so on. But these accidental divisions are not very important for reason as is the division of a genus or general kind of thing into the particular kinds of the same.

We can distinguish clearly between the division of an integral whole into its parts and the division of a universal whole (especially a genus) into its parts by denying as well as by affirming. An integral whole is composed of its parts, but not said of them. A universal whole is said of its parts, but not composed of them. Animal is said of dog and cat and horse, but it is not composed of them. (If it were composed of them, then when we said a dog is an animal, we would be saying that a dog something composed of cat, dog and horse.) Likewise, a speech is composed of names but a name is not a speech.

In every reasoned-out knowledge, we divide an integral whole into its parts and the universal whole called a genus into its particular kinds. Often the same thing must be divided in both ways. This is not to confuse the two kinds of whole and the corresponding two kinds of division for the same thing is not both kinds of whole in comparison to the same parts. The chemist, for example, can divide atom as an integral whole into nucleus and electronic shell. But in the periodic table, he divides atom as a universal whole. The same can be seen inductively in all forms of reasoned-out knowledge.

Both in dividing an integral whole into its parts and in dividing a genus into its particular kinds, reason seeks to be complete, to exhaust the whole and its ability to have parts. It is easy to see that a circle is divided completely into two semi-circles or that there is no possibility for a triangle other than to have all or just two or none of its sides equal. It is more difficult to see whether government can have only three integral parts (legislative, executive and judicial) or whether tragedy and comedy are the only kinds of drama.

Can any general rule be given as to the number of parts into which one should divide an integral whole or a genus?

THE RULE OF TWO OR THREE

No universal rule without exceptions can be given for the number of parts into which one should divide an integral whole or the number of species into which one should divide a genus. One must always think of the whole in question and what will exhaust it. The better one understands the genus, for example, the better one can think about the differences that will exhaust it. This is why we define a genus if possible before trying to divide it into its species.

Nevertheless, there is a rule which is true of the majority of divisions and which is very useful both in making divisions and in understanding divisions made by those wiser than us. Most single divisions of integral wholes and of genera are into two or three parts. I say single because often we combine the results of two or more divisions and end up with more than three parts. There are two ways in which we combine divisions. Sometimes we combine a division with the subdivision(s) of one (or more) of the parts. At other times, we criss-cross two divisions (with different bases) of the same thing. But when we take apart such divisions, we find that most single divisions are into two or three. If someone, for example, divided human beings into four parts such as good men, bad men, good women, and bad women, it is easy to see that two divisions have been criss-crossed to get four parts. But each of these single divisions are into two parts only. Likewise, when the political philosopher divides government into six kinds, he criss-crosses a division of government on one basis into three (government by one or by the few or by the many) and another division on another basis into two (government aiming at the good of the whole or at the good of just one part). We divided name said with one meaning of many things into five (genus, difference, species, property and accident) But this was not by one division. We divided into two and subdivided one part into three and the other into two. There is an enormous difference between just enumerating more than three parts and understanding how many divisions were combined to arrive at the parts enumerated. One could divide an English or Shakespearean sonnet into fourteen lines, but such a division would not help one to understand the sonnet�s structure. Such a sonnet should be divided into two parts (the quatrains which develop a thought or feeling and a couplet which answers or completes or contrasts with what is developed in the quatrains).

Socrates in some of the Dialogues consistently divides into two parts. A reason why we divide into two so often can be seen. The parts must be distinct (one cannot be or come under the other) and distinction in kind is based on some kind of opposition and opposites are two. Thus in the reasoned-out knowledge of numbers, we divide number into even and odd and also into prime and composite, both of which are based on opposites. We also divide integral wholes into two parts by opposites. A simple statement is divided into noun and verb. The verb signifies with time and the noun without time, and a plot is divided into the tying of the knot and the untying of the knot. Animals are divided into vertebrates and invertebrates, and this is clearly by opposites. Aristotle however (in his biological works) argues against always dividing into two.

Hegel in his System consistently divides into three. It would be difficult to give a reason why we should divide into three. But a sign that we should divide into three is found in many languages where three is the first number about which we say all. And a long induction could be given in support of the statement that three in enough and contains all. Thus triangle is divided into equilateral, isosceles, and scalene. Rectilinear angle is divided into right, obtuse and acute angles. The Greeks divided government into the rule by one or few or the many. Likewise, integral wholes are divided into three. The Constitution divides government into legislative, executive and judicial parts. A plot can be divided into beginning middle and end. Under the influence of Hegel, the young Karl Marx divided everything into three; but later, he came to see this as not always the natural way to divide.

Sometimes the same whole is divided into two and into three as can be seen in the above example of plot.

It is significant that no one has ever tried to divide consistently or always into any number other than two or three. This adds some probability in addition to the reason and sign above that most single divisions of integral wholes into their parts and genera into species should be into two or three. Some hesitation and caution are in order before dividing into more than three parts by one single division. (It is common, of course, when combining divisions.) And when some thinker divides into more than three, we should first examine whether they are combining two or more divisions.

Nevertheless there are important examples where it seems natural to make a single division into more than three parts. Such divisions are hard to understand and it is more difficult to be sure of such divisions.

DEFINITION, DIVISION AND DISTINCTION

One should note the following order among definition, division and distinction.

Every definition can be seen to involve a division. A definition is an integral whole: and unlike the name which signifies in a confused way, the definition has distinct parts. But every division does not involve a definition.

Likewise, every division involves a distinction, for every division separates or distinguishes the parts of some whole. But every distinction is not a division (in the strict sense). A division in the strict sense is the separation of the parts of some whole. Hence, there are distinctions which are not divisions. (Nevertheless, we sometimes call any distinction a division, speaking loosely.)

Among the distinctions that are not divisions in the strict sense is the very important one that we have already used many times. This is the distinction of the senses or meanings of a word. This should not be confused with the division of a universal whole into its parts. The universal whole is signified by a word having one meaning (or used in only one of its meanings).

We shall meet other distinctions which are not divisions (in the strict sense) later when we consider the most common mistakes in reasoning.