ART OF DEFINITION -- THE FIRST PART ABOUT NAMES

WHY NAME SHOULD BE CONSIDERED BEFORE DEFINITION

We should consider name before definition. For we name things before we define them. The reason for this is that we know things in a confused or indistinct way before we know them distinctly; and a confused knowledge of a thing is sufficient to name it while a distinct knowledge of a thing is necessary to define it.

Further, we use the name of the thing to be defined in the question which seeks its definition, as when Socrates asks, “What is virtue?”. But one must understand the question before one tries to answer it.

And most of all, it is necessary to understand name before definition because every definition is composed of names. And a whole that is composed of parts cannot be understood without knowing its parts.

WHAT SHOULD BE CONSIDERED ABOUT NAME

We should first consider what a name is and define it. And since the name of the thing to be defined should not be used in its definition, we must also distinguish between the name of the thing to be defined and the names used in its definition. And since there are many names in the definition, we must also see what is the difference among these names and their order.

THE DEFINITION OF NAME IN LOGIC

A name is a vocal sound signifying by custom, no part of which signifies by itself.

A name is originally a sound. The written name is a sign of the spoken name. We speak before we learn to write and some people do not have a written language. We still use the word call even when talking about the written name. It is not necessary for the logician to explain the nature of sound. That is the concern of the natural scientist.

The word vocal brings out the source or cause of this sound called a name. Only animals have a voice, and not all animals. It does not belong to the logician to consider fully how this sound is produced, but to the natural scientist and the grammarian.

The word signifying separates name from those vocal sounds whose purpose is not to signify something, such as a cough or clearing of the throat. A sign is something that strikes the senses and brings to mind something other than itself.

The words by custom separate a name from those vocal sounds which signify by nature, as a scream or a groan.

The fifth part of the definition, no part of which signifies by itself, separates name from speech. The definition of speech in logic is the same as that of name, except for the fifth part. Speech has parts (at least two) that signify something by themselves. In the speech white animal, animal signifies something by itself and so does white. Likewise in the speech animals sense, both animals and sense signify something by themselves.

The meaning of a speech depends upon the meaning of its parts, but no part of a name signifies something by itself. In the name animal, for example, the parts an, i, and mal do not signify something by themselves. It is only the whole name that signifies something.

Although the grammarian and the poet must take apart speech down to its syllables and letters, the logician’s analysis stops with the name. For the logician is interested in speech or vocal sounds signifying by custom only insofar as they signify something in the mind or reason.

As can be seen from the definition of name given above, the word name is used in a wider sense in logic than sometimes in daily life. There we tend to call only nouns names. But the above definition of name covers adjectives, verbs, etc. Thus in logic, we can call not only man a name, but also colored and walks.

CALLING A THING BY ITS OWN NAME OR THE NAME OF ANOTHER THING

When we know a thing and want to talk about it, we give that thing its own name. This name then belongs to that thing. Other names are given to other things and belong to them. Thus we have called the four-footed animal that meows a cat and the four-footed animal that barks a dog.

It might seem that we should always call a thing by its own name. If we called a cat a dog, we would be speaking falsely or confusing others as to our meaning. But sometimes we call a thing by the name of another thing, speaking not falsely, but figuratively. When Romeo calls Juliet sweet or honey, she understands him even though he is calling her by the name of another thing. Likewise, if we call a man who is eating too much a pig rather than a glutton, he understands our meaning even though pig is the name of a four-footed animal with a tail and a snout.

When someone speaks figuratively, the meaning of the speaker is not the meaning of his word (or words). But there is some way of knowing the speaker’s meaning from the meaning of his word (or words). It may be by likeness as in the figure of speech called metaphor. The above examples of sweet and honey and pig are common examples of metaphors. But there are many other ways of speaking figuratively. For example, when someone is mean to us and we say “gee, you’re nice," everyone knows we mean the opposite of what our word means. This figure of speech is called irony. There are many other possible connections between what the speaker actually says and what he means that give rise to other figures of speech.

We can summarize the above in a division with one member sub-divided: we can call a thing by its own name or by the name of another thing. And when we call a thing by the name of another thing, we are either speaking falsely (incorrectly) or we are speaking figuratively.

WHAT SHOULD WE CALL A THING WHEN SEEKING ITS DEFINITION

When we ask for the definition of a thing, we should call that thing by its own name.

If we called that thing by the name of another thing, we would either be misdirecting the mind as to what was to be defined if we were speaking incorrectly (for example, calling a cat a dog or a triangle); or, at least, it would not be clear if speaking figuratively (if in ethics, for example, we asked what is a pig instead of what is a glutton).

There are, of course, good reasons for speaking figuratively at times. The lover, the poet and the public speaker often speak figuratively. If one intends to express emotion or to arouse it, or to speak in a colorful way that appeals to the imagination, it is often best to speak figuratively. This can be seen especially in the metaphor which is the most important figure of speech. The lover expresses his emotion and awakes tenderness in his beloved by calling her honey or sweet. Calling a man who eats too much a pig helps to express our disgust with him and to arouse shame in him. When Pericles spoke of the many young men of the city killed in the war, he expressed so well the feeling of the citizens listening to him by saying, metaphorically, that it was as if spring had been taken out of the year. Moreover, because the metaphor is based on likeness, it appeals to the imagination which delights in the likeness of things. But when we seek a definition, it is not the emotions which we are trying to express or arouse, or the imagination which we are trying to appeal to. Rather, we seek to find a definition by reason.

A PROBLEM: SHOULD WE DEFINE A THING BY ITS OWN NAME OR BY THE NAME OF ANOTHER THING?

Everyone has heard (even in grade school and high-school) the rule of logic that we should not define a thing by its own name. If we were to define a thing by its own name, we would not make anything more known. If we say that a dog is a dog, or a rose is a rose, what have we made known or more known?

On the other hand, can we define a thing by the name of another thing? Either we would be speaking falsely or figuratively. If we were speaking falsely, we would not be saying what the thing is, but rather something that it is not. We cannot define a dog as a cat or a triangle. But can we define a thing by figures of speech, by metaphors for example? Does the word pig tell us what a glutton is? The glutton is a not a four-footed animal with a snout and a tail. Although a husband has a reason for calling his wife honey, that word does not tell us what a wife is. A wife is not the yellow, sticky substance produced by the bees.

If we cannot define a thing by its own name and we cannot define it by the name of another thing, it seems that there are no names that can be used to define things.

SOLUTION OF THE PROBLEM

It should not remain hidden to us that the phrase its own (or any like this with other pronouns, such as his own, her own, my own) has two meanings.

In one sense, the strict and perhaps the first, it means what belongs to it alone. My own head belongs to me alone. My head is no one else’s head. One’s own in this sense is opposed to the common; it is private and not shared by others.

In another and broader sense whatever is opposed to another’s is one’s own even if it is shared with others. It is in this second sense that I can speak of my own mother even though I have brothers or sisters, or my own country, even though I share it with my fellow citizens.

The above distinction is very important in thinking about the goods in human life. My good is not only my private good, but also my common good. Indeed, my greatest goods are common goods. As a parent, my greatest good is my child. As a citizen my greatest good is the common good of the city. As a creature, my greatest good is God. When I act for these goods, I am acting for my greatest goods. I am not acting for the good of another as if it was not also my good (and indeed my greatest good).

But this distinction is also the key to the solution of the above problem about the names to be used in the definition of a thing. And that is why we have considered this distinction here.

The rule we all learned in grade-school and high-school about names and definitions was using the phrase its own in the first and strict sense. We should not define the square, for example, by the word square. But we can and indeed must define a thing by its own names in the second and broad sense of its own. Induction shows that define a thing by names that belong to it and other things. When Euclid defines the square as an equilateral and right-angled quadrilateral, he is defining it by names that belong to the square and other figures, by names that are common to the square and other figures. Quadrilateral is a name common to square and oblong and rhombus and rhomboid and the trapezium. Equilateral is a name common to the square and the rhombus. Right-angled is a name common to the square and the oblong. If we define the glutton as a man who eats too much, no part of the definition is private to the glutton. The glutton is not the only man, nor is he the only one who eats, nor is he the only one who does something too much.

Although this second and broad sense of one’s own should not be confused with the first sense, it should not be thought that this is an unreasonable or forced sense of the phrase. Indeed, when we call a dog an animal, we are not calling the dog by the name of another thing as if the dog was not really an animal. But if we were to call the dog a triangle, we would be calling it by the name of another thing. For a dog is in no way a triangle.

THE NEXT PROBLEM

If we define a thing by names common to it and other things, how can our definition do the first thing we expect of a definition? A definition should separate the thing being defined from all other things. Indeed the word definition itself indicates this requirement of a definition. The word definition comes from the Latin word for limit. A farmer was said to define his field when we put a fence or a wall around it, separating it from all the other farmers’ fields. The city limits separate that city from every other city or town around it. How then can the definition of a thing separate that thing from all other things if it is composed of names common to that thing and other things?

SOLUTION

It is the combination of names that enables us to define or limit the thing. Although each name in the definition is common to the thing being defined and something else, the combination of names should belong only to the thing being defined.

We can see this in the above definition of square. Although the square is not the only quadrilateral, nor the only quadrilateral that is equilateral, nor the only quadrilateral that is right-angled, it is the only quadrilateral that is both equilateral and right-angled.

We can compare this to the way we pin-point a target or destination on a map. We give the longitude of the point. But there is an infinity of other points that have this same longitude on the map. We also give the latitude of the point. And likewise, there are an infinity of other points on the map which have the same latitude. How can we pin-point the target giving only what the point has in combination with two infinities of other points? The answer is of course that there in only one point that has both that longitude and that latitude.

We can see from the above that a definition is never one name. It is always a speech composed of many names. Likewise, we can see that a definition is what the logician calls convertible speech, speech convertible with the thing being defined. (A and B are said to be convertible when every A is a B and, vice-versa, every B is an A.)

Why does reason define things by putting together names common to the thing being defined and other things?

Each such name by itself corresponds to a confused or indistinct knowledge of the thing to be defined. By putting together such names into speech convertible with the thing to be defined, reason passes from a confused and imprecise knowledge of the thing to a more precise and distinct knowledge of the thing. It is natural for reason to know things in a confused and indistinct way at first. Definition enables reason to pass from this more confused knowledge of a thing to a more distinct knowledge of the thing.

Since we define things by names they have in common with other things, we must now investigate name common to many things or name said of many things.

By many here is meant more than one (many as opposed to one, not to few).

NAME COMMON TO MANY THINGS OR NAME SAID OF MANY THINGS

A name may have one meaning or more than one meaning. The former is sometimes called a univocal name and the latter an equivocal name.

There are clearly many names which have more than one meaning. There are perhaps few names that have only one meaning or sense.

When a name is said of many things, there may be one or more than one meaning in mind. This is not the same as to say that the word has one or many meanings. Even if a word has more than one meaning, it may be said of many things sometimes with only one meaning in mind and sometimes with more than one meaning in mind. The word bat, for example, has more than one meaning. It can mean a piece of wood used to hit the ball in baseball. It can also mean something that flies out of the belfry at night. But when the word bat is said of three baseball bats, it being said of many things with only one meaning in mind. But when it is said of a baseball bat and a belfry bat, it is said with more than one meaning in mind.

Likewise, the word dry when said of a cloth and a wine has more than one meaning. But when dry is said of two or more wines it means the same.

When a name is said of many things with one meaning in mind, it is said univocally of those things. When a name is said of many things with different meanings in mind, it said equivocally of those things.

Since the purpose of a definition involves pointing out distinctly what a thing is and separating it from all other things, the perfection of definition involves eventually having one meaning in mind when using a word or name to define a thing. Hence, we must study name said with one meaning of many things with a view to definition.

NAME SAID UNIVOCALLY, OR WITH ONE MEANING, OF MANY THINGS

We must now divide name said with one meaning of many things for the purpose of defining things. Since a definition is speech signifying what a thing is, the first division of name said univocally of many things should be in comparison to what a thing is or its nature. (The last sense of the word nature is what it is.)

A name said with one meaning of many things signifies something either within their nature (what they are) or outside their nature. Both quadrilateral and green could be said (with one meaning in mind) of a square and an oblong. But the first name signifies something within what square and oblong are, and the second name signifies something outside their nature or what they are.

We can next subdivide the first part; that is, name said with one meaning of many things signifying something within their nature or what they are.

Since man does not understand distinctly what a thing is at once, there is necessarily a name which signifies only in general what those things are of which it is said. (For the general is to the particular as the confused is to the distinct.) Such a name is called in logic a genus.

Genus is a name said with one meaning of many things other in kind signifying what it is.

Experience shows that we begin with such a name when we are asked to define what a thing is. If we are asked, for example, what a dog is, we begin by saying that it is an animal. The word animal is a genus said of dog, cat, horse and many other kinds of animal.

Such names are found in every matter. In geometry, for example, quadrilateral is a genus said of square, oblong, rhombus and rhomboid. In ethics, habit is a genus said of virtue and vice. In politics, the word government is a genus said of monarchy, oligarchy, and democracy.

The logician also gives a name to the names of those particular kinds of things that come under the genus. Such a name is called a species or a form.

Species or form is the name of one particular kind of thing placed under a genus.

In the above examples, the words dog, cat and horse are species or forms because they are the names of particular kinds of thing placed under the genus animal. Likewise, the names square, oblong, rhombus, and rhomboid are species or forms because they are the names of particular kinds of things placed under the genus quadrilateral. In a similar way, the names virtue and vice are species because they are the names of particular kinds of habit. Monarchy, oligarchy, and democracy also name particular kinds of government so they also are species or forms.

Sometimes the logician uses the names genus and species, not as here for names, but for the general and particular kinds of things signified by these names. (When we speak of dividing a genus into its species, we are thinking of dividing a general kind of thing into the particular kinds or forms it can have.) But we are here defining the names that signify something within the nature of the things of which they are said.

WHY A THIRD NAME IS NECESSARY

Since the genus is said with only one meaning of many things other in kind, it cannot signify distinctly or in particular what each of these is. It cannot bring out what each of these species is in particular as distinct from one another. The genus can only say in general what each is. Hence, there is need of a third kind of name pertaining to the nature of things besides genus and species, a name that will bring out what the species (the particular kind of thing) has in addition to what is signified by the genus which is also that whereby that particular kind of thing differs from other things under the same genus. This name is appropriately called the species-making difference or, in short, the difference.

THREE DEFINITIONS OF DIFFERENCE

Porphyry gives three definitions of difference. The first points to its role in defining a species; the second, to its role in dividing a genus into species; and the third, to its nature as a name said with one meaning of many things.

The first definition of difference is the name of that which the species has in addition to the genus. This definition prepares us for understanding the place of difference in completing the definition of a species. The definition of square, for example, is only begun by giving its genus quadrilateral. A square is not only a quadrilateral, but in addition it is both equilateral and right-angled. These last two names are differences for they signify what the species square has in addition to being a quadrilateral.

The second definition of difference points to its role in dividing a genus into its species and is connected with the etymology of the word difference (which comes from the Latin for carrying-apart). Difference is a name which separates species under the same genus. Using the above examples, we can see that equilateral not only brings out what the square (and also the rhombus) has in addition to being a quadrilateral, but it also separates the square (and the rhombus) from the oblong and the rhomboid and the trapezium which are other species of quadrilateral. Likewise, the difference right-angled also separates square (and oblong) from the other species of quadrilateral. More than one difference is necessary to separate the square from all other species of quadrilateral. This is because of what we shall see in the third definition of difference

Difference can also be defined as a name said with one meaning of many things other in kind signifying how they are what they are.

This definition of difference has the same first four parts as the definition of genus. But the fifth part, signifying how they are what they are, separates difference from genus. For the genus signifies what it is. But the difference signifies how. (This is why we often, grammatically speaking, use a noun for the genus and an adjective for the difference.)

But the (species-making) difference signifies not just how, but how they are what they are. It is necessary to add the latter words for how by itself can refer to something accidental and changing as when we ask someone “How are you today?”.

Difference or species-making difference (to speak more exactly) is an essential difference. It determines how a thing is what it is. Therefore, it signifies what is within the nature of the species (particular kind of thing). Equilateral, for example, is a difference of square for it signifies how the square is what it is; that is how or what kind of quadrilateral it is. But green is not a (species-making) difference of square. Green is not one way of being essentially four-sided.

Since the difference is said of more than one species (although not of as many as the genus), there is need for a combination of differences to define a species. Thus square is defined by Euclid’s combining the differences equilateral and right-angled with the genus quadrilateral. The combination must, as has been said before, make the speech convertible with the species defined.

KNOWING THE ABOVE THREE NAMES FOR DEFINING

The distinction of the above three names is most useful for the art of definition. For species is the name of what is being defined and hence is not a name in the definition. The genus is the name which is the beginning of a definition. Difference is the kind of name used to complete a definition.

There can be only one genus in a definition. Otherwise, one would be talking about two things, not defining one thing. But, as we have seen, more than one difference is used to complete the convertible speech that is a definition.

WHY WE MUST DIVIDE NAME SIGNIFYING SOMETHING OUTSIDE NATURE

We divided name said with one meaning of many things into name signifying what is within the nature of the things of which it is said and name signifying what is outside the nature of those things. Having distinguished the first part into genus and species and difference, it might seem superfluous to subdivide the second part with a view to definition. Since the definition of a thing signifies what it is, it would seem at first sight that all names of the second kind are useless with regard to definitions.

But this is a serious mistake. There is an important difference among names of this kind which is very important for definition as well as other things in logic. This will become clear when we subdivide such names in comparison to the nature of a thing.

THE DIVISION OF NAME SIGNIFYING SOMETHING OUTSIDE THE NATURE

A name signifying something outside the nature of those things of which it is said can signify something either following upon that nature or not following upon that nature. The former signifies something like an effect of the nature while the latter has no connection with the nature of the thing. The former is called in logic a property and the latter an accident.

Green is an accident of triangle. It has no connection with the nature of triangle. But to have interior angles equal to two right angles is a property of triangle. It is not what a triangle is (this is to be a plane figure contained by three straight lines), but it follows upon that nature as an effect or result of it. Half of four is a property of the number two. It does not pertain to what two is in its nature as do the units in two. Rather it is a relation to another number following upon what two is.

A property in the strictest sense may be defined as the name of that which belongs to only one species, to every member of it, and always. Half of four is a property of the species two in the strictest sense. For only two is half of four, every two is half of four, and two is always half of four.

But we can also speak of a property in a less strict sense when only two or even one of these is true, provided there is a connection with the nature. Thus less than ten is a property of two in that every two is less than ten and always less than ten. But less than ten does not belong only to two. Yet it is obviously connected with what two is and hence can be considered a property of two although not in as strict a sense as half of four. To be a geometer can be considered in some way a property of man since only man is a geometer. But not every man is a geometer and even though who are were not always geometers. Yet this has a connection with what man is (an animal with reason).

An accident here in logic (it has other meanings elsewhere in logic) is the name of that which can be present or absent with the same nature remaining in those things of which it is said. Hence, the origin of this word which means happening in Latin. Red is an accident of triangle. The nature of a triangle can be found with or without the color red. There is no basis in the nature of a triangle for it to be red. But a triangle could happen to be red.

WHY PROPERTY IS IMPORTANT FOR DEFINITION

Property can be useful for the definition of things in two ways. First, it is useful in investigating the unknown nature of a thing because of its connection with the nature. Sometimes we reason to the nature or the difference from the property, just as in general we reason from effects to causes.

Second, when the species-making difference is unknown, we sometimes give the property in place of the difference. This gives, of course, an imperfect definition, but it is better than complete ignorance of the thing in particular. For the property is connected with the nature and is, at least, a sign of a different nature.

Property is also important in the most perfect kind of argument in which we reason from the nature of the thing to its property. Thus the geometer reasons from the nature of the triangle to its property of having its interior angles equal to two right angles.

But accident is useless for definition and argument. An accident is something that happens but has no connection with the nature of the thing. Hence it is known more by sense than by reasoning.

EPILOGUE

Having distinguished and defined genus, species, difference, property and accident, we can now see what is the name of the thing defined, what are the names used in beginning and in completing a definition, the name useful for an imperfect definition or investigating a better one, and the names useless for defining.

CAN THE SAME NAME BE BOTH A GENUS AND A SPECIES?

There are two kinds of distinction found in every matter: absolute or in itself and relative or towards another. In itself, a number is either odd or even; but towards another, a number may be half or double. Likewise, in human beings, the distinction between a man and a woman is absolute while the distinction between a father and a son, or between a mother and a daughter, is relative.

Where the distinction is absolute, one is never the other. An odd number is never an even number. A prime number is never a composite number. A man is never a woman. This is because the distinction is of things considered in themselves or by themselves.

Where the distinction is relative or towards another, the same thing can be both, but not toward the same. The same number can be both double and half, but not toward the same. Four is double of two and half of eight. Henry the Fifth of England was the son of Henry the Fourth and the father of Henry the Sixth.

One should not think that a relative distinction cannot be a real distinction, or that it is a sloppy or an uncertain distinction. Four is really double of two and two is really half of four. And this is very precise and also certain.

Is the distinction between the names called a genus or a species an absolute or a relative distinction?

The same name can be both a genus and a species as defined above, but not towards the same. Quadrilateral is a species in comparison to rectilinear plane figure and a genus in comparison to square, oblong, rhombus, rhomboid and trapezium. Animal is a species of living body and a genus of dog, cat and horse. And virtue is a species of habit (or firm disposition) and a genus of courage and moderation and justice. Hence, the distinction of genus and species is a relative distinction of names and not an absolute one.

It can be seen from the above that the distinction between the name of the thing being defined and the name used in the definition is not an absolute distinction of names, but a relative distinction of names. Since the name of the thing being defined is a species and the first name in a definition is a genus, and the same name can be both in reference to different things, it is clear that the name of what is being defined in one definition, may be the first name in the next definition. For example, quadrilateral is before the name of a species of rectilinear figure being defined and after the first name in the next definition of square.

IS EVERY SPECIES A GENUS?

Once we know that the same name can be both a genus and a species (but not in comparison to the same), two questions arise: “Is every species a genus?” and “Is every genus a species?” These are proportional to the questions we might ask about a father and a son once we know the same man can be both a father and a son (but not of the same man). Is every son a father? Is every father a son?

Another way of asking the question whether every species is a genus is this: does every species have a species below it, or is there a lowest species?

Here it should be understood that not every difference is a species-making difference. Species making differences must determine what is intrinsic to the nature of the genus they are dividing. When the geometer divides triangle into scalene, isosceles, and equilateral, he is determining what is intrinsic to the nature of triangle as can be seen from its definition. A triangle is a plane figure contained by three straight lines. These three lines can be equal or just two of them or none. And the species-making differences (scalene, isosceles and equilateral) determine this possibility intrinsic to the nature of triangle. The triangle must be contained by three straight lines and since a line has length, these lines must be either all equal or just two of them or none of them. But if we divided triangle into red, white and blue, we would not have three species of triangle. For red white and blue are not ways of being three-sided. These differences are sometimes called accidental differences to distinguish them from species-making differences (for brevity, the former are called accidents in logic and the latter, differences).

Moreover, since a genus is said of many things other in kind, a species is not a genus if it is said of many things that are not particular kinds of it. Many individuals of the same kind (as many circles) are not many species.

There are lowest species, species that are not genera. This is most easily seen in mathematics. Circle is a lowest species of plane figure. Although circle is said of many individual circles, these are not different kinds of plane figure. Even if these circles differ in size or color, these differences would not make them different kinds of plane figure. They all have the same shape, whether they are large or small, green or red. But triangle is not a lowest species of rectilinear plane figure. But equilateral triangle would seem to be a lowest species. Odd number is not a lowest species. Odd number is both a species of number and a genus of three, five and so on. But seven is a lowest species of number. Seven cannot be divided into different kinds of number. Seven men and seven horses differ by differences that are extrinsic to the nature of the number by which we number.

Outside of mathematics it is often difficult to tell when one has come to a lowest species. Is man a lowest species? If man is defined as an animal with reason and there is only one kind of reason, then man is a lowest species. Differences among men such as white, black and yellow, do not distinguish different kinds of reason and hence are accidental differences.

Although the logician as logician tells us what a lowest species is, he leaves to the particular thinkers the determination of when a lowest species has been reached in the particular matter considered by that thinker. The particular thinker must of course know both logic and his particular matter or subject to answer this question. The student of drama, for example, must answer from his experience and thought about drama whether comedy is a lowest species or there are different kinds of comedy. This depends upon knowing what comedy is and what the laughable is and it does not belong to the logician to know these particulars. But to know what a genus is and what a species is and what a lowest species is, comes within the logician’s knowledge.

A lowest species is a name said with one meaning of many individuals (not other in kind) signifying what each is.

Genus thus differs from lowest species because it is said of many things other in kind and it differs from difference because it signifies what it is.

IS EVERY GENUS A SPECIES?

We now ask the question going in the other direction. Does every genus have a genus above it (so that every genus is also a species) or is there a highest genus (or highest genera)?

If every genus had a genus above it, we could never define anything. There would be an infinity of definitions before any definition. Euclid, for example, defines triangle before equilateral triangle. And before triangle, he defines rectilinear plane figure. And before this, the genus plane figure. And before this, he defines the genus figure. If this went on forever, there would be an infinity of definitions to go through before one could define anything.

Further, one could not even begin to define anything since one would have to go define that thing�s genus before one could begin the definition with it. Anywhere one attempted to begin would always have to be defined first. Hence, there would be no place to begin.

Further, in any series of genera which are above and below each other, one could not know the middle or the last without knowing the first. But if every genus had a genus above it, there would be no first genus. Every genus would be a middle genus. And since the middle cannot be known without the first being known, no genus could be known. Hence, one would not understand anything which is manifestly absurd.

From the above, it can be seen that not every genus is a species. There must be a highest genus or genera. But is there one highest genus or more than one? Do all genera come under one highest genus or under more than one?

WHETHER THERE IS ONE HIGHEST GENUS?

There is one name said of all things. The word thing is clearly said of all things. Likewise, the word something is said of all things. Further, the word being can be said of everything that is in any way.

But are such names genera? They are said of many things other in kind, but are they said of all things with one meaning in mind.

A man and a dog are two things. But is a man and his health or his shape two things? A man and his health do not seem to be the same thing for a man is sometimes healthy and at other times, sick. Likewise, his shape is not always the same. But are a man and his health two things in the same sense that a man and a dog are two things? Clearly not, for the man and the dog exist apart from each other, but the health or shape of the man exists only in that man as in a subject. Philosophers call a thing that exists by itself, as a man or a dog does, a substance. They call a thing which exists only in another as in a subject (which it cannot exist apart from) an accident. Substance gets its name because it stands under the accidents that happen to it, as a subject of them. When the word thing is said of substance and accident, it is not said of them univocally (with one meaning) but equivocally (with more than one meaning). Substance is the first sense of the word and accident is a second sense. Anyone who saw a man and a dog in the room would say, if asked, that there are two things in the room. But if the man left, we would not say that there are two things left, the dog and its shape; or three things, the dog and its shape and its health. Since the word thing is said with more than one meaning of substance and accident, it cannot be a genus said of all things.

The same could be said of the word being which is as common as the word thing. The word being is formed from the verb to be. If a man dies, we would say that he has ceased to be. But if a man who is sitting stands up, we would not say that he has ceased to be. Or if we did, we would have to qualify it by saying that he has ceased to be sitting. Clearly, the first and full sense of being is substantial being and only in a secondary sense do we speak of being or not being according to accidents.

A genus is said equally of its species and not of one before the other. Animal is said equally of dog and cat, and a dog is not an animal before a cat is or vice-versa. But words like thing and being are said of substance before accident and only fully of substance. Hence, thing or being cannot be one genus said of both substance and accident.

From the above, we can see some of the reasons why the great logicians say there cannot be just one highest genus. But if there is more than one highest genus, how are they to be distinguished and how many are there?

THE CATEGORIES OR HIGHEST GENERA

The logician distinguishes the highest genera by the ways something can be said of individual substances like this man or that dog.

Something can be said of this man or that dog by reason of what they are or by reason of something existing in them which is not what they are or by reason of something outside them.

In the first way, we can say of this man, that he is a man or more generally an animal or above this, a living body and above that a body, and at last, a substance. Substance is the first highest genus.

We can say something of this man by reason of something existing in him (that is not what he is), either absolutely or relatively (towards another). If absolutely, either by reason of how much there is of him -- his size or quantity; or how he is -- his qualities. We might say, for example, by reason of how much there is of him that he is six feet tall. In this way, there arises the highest genus of quantity. As to how he is, we might say, for example, that he is healthy or wise. And this leads to the highest genus of quality. But if we say that he is a father or taller than another, we say something of him by reason of what is in him towards another. This gives rise to the highest genus of relation.

We can also say something of this man by reason of something outside him. In one way that is private to man, as when we say that this man is clothed or armed. This gives rise to the highest genus of outfit which is private to man and is not found in the other animals except when man clothes them for his own use or amusement.

Something can also be said of other substances as well as man by reason of something outside them. This happens in two ways. Sometimes by reason of an outside thing that is a measure of the other. In another way, by reason of an outside thing that is a cause or effect.

There are two outside measures, time and place. Place gives rise to the highest genus of where and also of position (which adds to where the order of parts in place). Thus, we might say of Socrates that he is in Athens and that he is sitting. Time gives rise to the highest genus of when. When was Socrates? Socrates was in the fifth century BC

By reason of an outside cause or effect, something is said of substance either in comparison to the effect or the cause. Thus fire is said to be heating the air because it is acting upon the air. The air can be said to be heated because it is undergoing something from the fire. In this way arise the last two highest genera, acting upon and undergoing.