Part I, Chapter 6: Of Ideas, considered in relation to their Generality, Particularity, and Singularity
ALTHOUGH all things that exist be singular, we are nevertheless, by means of these abstractions which we have just explained, enabled to have many sorts of ideas, some of which only represent to us a single thing; as the idea which any one has of himself;—others being able equally well to represent many; as when any one has conceived a triangle, without considering anything else respecting it, except that it is a figure containing three sides and three angles, the idea which he has formed of it will enable him to conceive all other triangles.
Those ideas which only represent a single thing are called singular or individual, and the things they represent individuals; and those which represent many individuals are called universal, common, or general.
The names which we employ to mark the first are called proper, as Socrates, Rome, Bucephalus; and those which are employed to mark the last, common, and appellative, as man, town, horse; and the universal idea, as well as the common names, may be called general terms.
But it must be remarked that words are general in two ways: One which is called univocal, which is, when they are connected with general ideas, so that the same word answers to many, both according to its sound, and according to the idea itself, with which it is connected; such are the words to which we have referred—man, town, horse. The other, which is called equivocal, is when the same sound has been joined by men to different ideas, so that the same sound applies to many, not according to the same idea, but according to different ideas with which it has become connected through custom. Thus the word canon signifies an engine of war, a decree of council, and an article of dress; but it also signifies these in relation to ideas altogether different.
This equivocal universality is, nevertheless, of two kinds. For the different ideas which are united to the same sound have either no natural relation between themselves, as in the word canon; or they have some connection, as when a word being principally united to an idea, we only join it to some other idea, because it has some relation of cause, or effect, or sign, or resemblance, to the first; and these kinds of equivocal words are then termed analogous, as when the word healthy (sain) is attributed to an animal, to the air, and to food; for the idea united to this word is principally health (sante), which applies only to an animal; but there is united to it another idea related to that, which is being the cause of health, which leads us to say that the air is healthy (sain), that food is healthy, because they contribute to the preservation of health.
When, however, we here speak of general terms, we understand the univocal, which are united to universal and general ideas.
Now, in these universal ideas there are two things, which it is very important accurately to distinguish—COMPREHEN SION and EXTENSION. I call the COMPREHENSION of an idea, those attributes which it involves in itself, and which cannot be taken away from it without destroying it; as the comprehension of the idea triangle includes extension, figure, three lines, three angles, and the equality of these three angles to two right angles, &c.
I call the EXTENSION of an idea those subjects to which that idea applies, which are also called the inferiors of a general term, which, in relation to them, is called superior, as the idea of triangle in general extends to all the different sorts of triangles.
But although the general idea extends indistinctly to all the subjects to which it belongs,—that is to say, to all its inferiors, and the common name expresses them all,—there is, nevertheless, this difference between the attributes which it comprehends and the subjects to which it extends, that none of its attributes can be taken away without destroying it, as we have already said, whereas we may restrict it, as to its extension, by applying it only to some of those subjects to which it agrees, without effecting its destruction by so doing.
Now this restriction or contraction of the general idea, as to its extension, may be effected in two ways.
The first is, by joining to it another idea, distinct and determined; as when, to the general idea of triangle, I add that of having a right angle, this restricts that idea to a single species of triangle, which is the rectangled triangle.
The other is, by joining to it only an indistinct and indeterminate idea of a part, as when I say some triangle.; the common term is then said to become particular, since it extends only to a part of these subjects to which it before extended, while it is, nevertheless, not determined what that part is, to which it is thus restricted.