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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.


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


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

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