should find, that, although no two of them are exactly alike, they all bear a certain general resemblance to one another. Thus from the multitude of faces which I now perceive it becomes possible for my mind to abstract from them all the essential qualities of a face as a face; and such a mental abstraction of qualities would then constitute what I might call my abstract idea of a face in general, as distinguished from my concrete idea, or memory, of any face in particular.
Thus, then, we have three stages: 1. That of immediate perception; 2. That of ideal representation of particular objects; and, 3. That of a generalized conception, or abstract idea, of a number of qualities which a whole class of objects agree in possessing. It will be convenient to split the latter division into two subdivisions, viz., abstract ideas which are sufficiently simple to be developed without the aid of language, and abstract ideas which are so complex as not to admit of development without the aid of language. As an instance of the former class of abstract ideas we may take the idea of food. This is aroused in our minds by the feeling of hunger; and, while the idea when thus aroused is clearly quite independent of language, it is no less clearly what is called an abstract idea. For it is by no means necessary that the idea of food which is present to the mind should be the idea of some special kind of food; on the contrary, the idea is usually that of food in general, and this idea it is which usually prompts us to seek for any kind of food in particular. Simple abstract ideas, therefore, may be formed without the assistance of language; and for this reason they are comprised within what has been called the Logic of Feelings. But abstract ideas of a more elaborated type can only be formed by the help of words, and are therefore comprised within what has been called the Logic of Signs. The manner in which language thus operates in the formation of highly-abstract ideas is easily explained. Because we see that a great many objects present a certain quality in common, such as redness, we find it convenient to give this quality a name; and having done this we speak of redness in the abstract, or as standing apart from any particular object. Our word "redness" then serves as a sign or symbol of a quality as apart from any particular object of which it may happen to be a quality; and having made this symbolical abstraction in the case of a simple quality, such as redness, we can afterward compound it with other symbolical abstractions, and so on till we arrive at verbal symbols of more and more complex qualities, as well as qualities further and further removed from immediate perception. By the help of these symbols, therefore, we climb into higher and higher regions of abstraction; by thinking in verbal signs, we think, as it were, with the semblance of thoughts, and by combining these signs in various ways, and giving the resulting compounds distinctive names, we are able to condense into single words, or signs, an enormous amount of meaning. So that, just as in mathematics the symbols which are employed contain, in an easily
