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of that of which the differentia itself is predicated.

For instance, if the characteristic ‘terrestrial’ is predicated

of the species ‘man’, the definition also of that characteristic

may be used to form the predicate of the species ‘man’: for ‘man’

is terrestrial.

 

The fact that the parts of substances appear to be present in the

whole, as in a subject, should not make us apprehensive lest we

should have to admit that such parts are not substances: for in

explaining the phrase ‘being present in a subject’, we stated’

that we meant ‘otherwise than as parts in a whole’.

 

It is the mark of substances and of differentiae that, in all

propositions of which they form the predicate, they are

predicated univocally. For all such propositions have for their

subject either the individual or the species. It is true that,

inasmuch as primary substance is not predicable of anything, it

can never form the predicate of any proposition. But of secondary

substances, the species is predicated of the individual, the

genus both of the species and of the individual. Similarly the

differentiae are predicated of the species and of the

individuals. Moreover, the definition of the species and that of

the genus are applicable to the primary substance, and that of

the genus to the species. For all that is predicated of the

predicate will be predicated also of the subject. Similarly, the

definition of the differentiae will be applicable to the species

and to the individuals. But it was stated above that the word

‘univocal’ was applied to those things which had both name and

definition in common. It is, therefore, established that in every

proposition, of which either substance or a differentia forms the

predicate, these are predicated univocally.

 

All substance appears to signify that which is individual. In the

case of primary substance this is indisputably true, for the

thing is a unit. In the case of secondary substances, when we

speak, for instance, of ‘man’ or ‘animal’, our form of speech

gives the impression that we are here also indicating that which

is individual, but the impression is not strictly true; for a

secondary substance is not an individual, but a class with a

certain qualification; for it is not one and single as a primary

substance is; the words ‘man’, ‘animal’, are predicable of more

than one subject.

 

Yet species and genus do not merely indicate quality, like the

term ‘white’; ‘white’ indicates quality and nothing further, but

species and genus determine the quality with reference to a

substance: they signify substance qualitatively differentiated.

The determinate qualification covers a larger field in the case

of the genus that in that of the species: he who uses the word

‘animal’ is herein using a word of wider extension than he who

uses the word ‘man’.

 

Another mark of substance is that it has no contrary. What could

be the contrary of any primary substance, such as the individual

man or animal? It has none. Nor can the species or the genus have

a contrary. Yet this characteristic is not peculiar to substance,

but is true of many other things, such as quantity. There is

nothing that forms the contrary of ‘two cubits long’ or of ‘three

cubits long’, or of ‘ten’, or of any such term. A man may contend

that ‘much’ is the contrary of ‘little’, or ‘great’ of ‘small’,

but of definite quantitative terms no contrary exists.

 

Substance, again, does not appear to admit of variation of

degree. I do not mean by this that one substance cannot be more

or less truly substance than another, for it has already been

stated’ that this is the case; but that no single substance

admits of varying degrees within itself. For instance, one

particular substance, ‘man’, cannot be more or less man either

than himself at some other time or than some other man. One man

cannot be more man than another, as that which is white may be

more or less white than some other white object, or as that which

is beautiful may be more or less beautiful than some other

beautiful object. The same quality, moreover, is said to subsist

in a thing in varying degrees at different times. A body, being

white, is said to be whiter at one time than it was before, or,

being warm, is said to be warmer or less warm than at some other

time. But substance is not said to be more or less that which it

is: a man is not more truly a man at one time than he was before,

nor is anything, if it is substance, more or less what it is.

Substance, then, does not admit of variation of degree.

 

The most distinctive mark of substance appears to be that, while

remaining numerically one and the same, it is capable of

admitting contrary qualities. From among things other than

substance, we should find ourselves unable to bring forward any

which possessed this mark. Thus, one and the same colour cannot

be white and black. Nor can the same one action be good and bad:

this law holds good with everything that is not substance. But

one and the selfsame substance, while retaining its identity, is

yet capable of admitting contrary qualities. The same individual

person is at one time white, at another black, at one time warm,

at another cold, at one time good, at another bad. This capacity

is found nowhere else, though it might be maintained that a

statement or opinion was an exception to the rule. The same

statement, it is agreed, can be both true and false. For if the

statement ‘he is sitting’ is true, yet, when the person in

question has risen, the same statement will be false. The same

applies to opinions. For if any one thinks truly that a person is

sitting, yet, when that person has risen, this same opinion, if

still held, will be false. Yet although this exception may be

allowed, there is, nevertheless, a difference in the manner in

which the thing takes place. It is by themselves changing that

substances admit contrary qualities. It is thus that that which

was hot becomes cold, for it has entered into a different state.

Similarly that which was white becomes black, and that which was

bad good, by a process of change; and in the same way in all

other cases it is by changing that substances are capable of

admitting contrary qualities. But statements and opinions

themselves remain unaltered in all respects: it is by the

alteration in the facts of the case that the contrary quality

comes to be theirs. The statement ‘he is sitting’ remains

unaltered, but it is at one time true, at another false,

according to circumstances. What has been said of statements

applies also to opinions. Thus, in respect of the manner in which

the thing takes place, it is the peculiar mark of substance that

it should be capable of admitting contrary qualities; for it is

by itself changing that it does so.

 

If, then, a man should make this exception and contend that

statements and opinions are capable of admitting contrary

qualities, his contention is unsound. For statements and opinions

are said to have this capacity, not because they themselves

undergo modification, but because this modification occurs in the

case of something else. The truth or falsity of a statement

depends on facts, and not on any power on the part of the

statement itself of admitting contrary qualities. In short, there

is nothing which can alter the nature of statements and opinions.

As, then, no change takes place in themselves, these cannot be

said to be capable of admitting contrary qualities.

 

But it is by reason of the modification which takes place within

the substance itself that a substance is said to be capable of

admitting contrary qualities; for a substance admits within

itself either disease or health, whiteness or blackness. It is in

this sense that it is said to be capable of admitting contrary

qualities.

 

To sum up, it is a distinctive mark of substance, that, while

remaining numerically one and the same, it is capable of

admitting contrary qualities, the modification taking place

through a change in the substance itself.

 

Let these remarks suffice on the subject of substance.

Part 6

Quantity is either discrete or continuous. Moreover, some

quantities are such that each part of the whole has a relative

position to the other parts: others have within them no such

relation of part to part.

 

Instances of discrete quantities are number and speech; of

continuous, lines, surfaces, solids, and, besides these, time and

place.

 

In the case of the parts of a number, there is no common boundary

at which they join. For example: two fives make ten, but the two

fives have no common boundary, but are separate; the parts three

and seven also do not join at any boundary. Nor, to generalize,

would it ever be possible in the case of number that there should

be a common boundary among the parts; they are always separate.

Number, therefore, is a discrete quantity.

 

The same is true of speech. That speech is a quantity is evident:

for it is measured in long and short syllables. I mean here that

speech which is vocal. Moreover, it is a discrete quantity for

its parts have no common boundary. There is no common boundary at

which the syllables join, but each is separate and distinct from

the rest.

 

A line, on the other hand, is a continuous quantity, for it is

possible to find a common boundary at which its parts join. In

the case of the line, this common boundary is the point; in the

case of the plane, it is the line: for the parts of the plane

have also a common boundary. Similarly you can find a common

boundary in the case of the parts of a solid, namely either a

line or a plane.

 

Space and time also belong to this class of quantities. Time,

past, present, and future, forms a continuous whole. Space,

likewise, is a continuous quantity; for the parts of a solid

occupy a certain space, and these have a common boundary; it

follows that the parts of space also, which are occupied by the

parts of the solid, have the same common boundary as the parts of

the solid. Thus, not only time, but space also, is a continuous

quantity, for its parts have a common boundary.

 

Quantities consist either of parts which bear a relative position

each to each, or of parts which do not. The parts of a line bear

a relative position to each other, for each lies somewhere, and

it would be possible to distinguish each, and to state the

position of each on the plane and to explain to what sort of part

among the rest each was contiguous. Similarly the parts of a

plane have position, for it could similarly be stated what was

the position of each and what sort of parts were contiguous. The

same is true with regard to the solid and to space. But it would

be impossible to show that the arts of a number had a relative

position each to each, or a particular position, or to state what

parts were contiguous. Nor could this be done in the case of

time, for none of the parts of time has an abiding existence, and

that which does not abide can hardly have position. It would be

better to say that such parts had a relative order, in virtue of

one being prior to another. Similarly with number: in counting,

‘one’ is prior to ‘two’, and ‘two’ to ‘three’, and thus the parts

of number may be said to possess a relative order, though it

would be impossible to discover

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