[CHAPTER IV].
LOGIC OF CONCEPTS.
The device of applying symbols to stand for ideas, and then using the symbols as ideas, operates to the formation of more highly abstract ideas in a manner that is easily seen. For instance, because we observe 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 so, 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, apart from any particular object of which it may happen to be a quality; and having made this symbolic abstraction in the case of a simple quality, such as redness, we can afterwards compound it with other symbolic abstractions, and so on till we arrive at verbal symbols of more and more abstract or general qualities, as well as qualities further and further removed from immediate perception. Thus, seeing that many other objects agree in being yellow, others blue, and so on, we combine all these abstractions into a still more general concept of Colour, which, quâ more abstract, is further removed from immediate perception—it being impossible that we can ever have a percept answering to the amalgamated concept of colour, although we have many percepts answering to the constituent concepts of colours.
So in the analogous case of objects. The proper names Peter, Paul, John, &c., stand in my mind as marks of my individual concepts: the term Man serves to sum up all the points of agreement between them—and also between all other individuals of their kind—without regard to their points of disagreement: the word Animal takes a still wider range, and so with nearly all words denoting objects. Like words connoting qualities, they may be arranged in rank above rank according to the range of their generality: and it is obvious that the wider this range the further is their meaning withdrawn from anything that can ever have been an object of immediate perception.
We shall afterwards find it is of the highest importance to note that these remarks apply quite as much to actions and states as they do to objects and qualities. Verbs, like nouns and adjectives, may be merely the names of simple recepts, or they may be compounds of other concepts—in either case differing from nouns and adjectives only in that they have to do with actions and states. To sow, to dig, to spin, &c., are names of particular actions; to labour is the name of a more general action; to live is the symbol of a concept yet more general. And it is obvious that here, as previously, the more general concepts are built out of the more special.
Later on I will adduce evidence to show that, whether we look to the growing infant or to the history of mankind as newly unearthed by the researches of the philologist, we alike find that no one of these divisions of simple concepts—namely, nouns, adjectives, and verbs—appears to present priority over the others. Or, if there is any evidence of such priority, it appears to incline in favour of nouns and verbs. But the point on which I desire to fasten attention at present is the enormous leverage which is furnished to the faculty of ideation by thus using words as the mental equivalents of ideas. For by the help of these symbols we climb into higher and higher regions of abstraction: by thinking in verbal signs we think, as it were, with the semblance of ideas: we dispense altogether with the necessity of actual images, whether of precepts or of recepts: we quit the sphere of sense, and rise to that of thought.
Take, for example, another type of abstract ideation, and one which not only serves better than most to show the importance of signs as substitutes for ideas, but also best illustrates the extraordinary results to which such symbolism may lead when carried out persistently. I refer to mathematics. Of course, before the idea of number or of relation can arise at all, the faculty of conception must have made great advances; but let us take this faculty at the point where the artifice of substituting signs for ideas has gone as far as to enable a mind to count by means of simple notation. It would clearly be impossible to conduct the least intricate trains of reasoning which invoke any ideas of number or proportion, were we deprived of the power of attaching particular signs to particular ideas of number. We could not even tell whether a clock had struck eleven or twelve, unless we were able to mark off each successive stroke with some distinctive sign; so that when it is said, as it often is, that an animal cannot count, we must remember that neither could a senior wrangler count if deprived of his symbols. “Man begins by counting things, grouping them visibly [i.e. by the Logic of Recepts]. He then learns to count simply the numbers, in the absence of things, using his fingers and toes for symbols. He then substitutes abstract signs, and Arithmetic begins. From this he passes to Algebra, the signs of which are not merely abstract but general; and now he calculates numerical relations, not numbers. From this he passes to the higher calculus of relations.”
And just as in mathematics the symbols that are employed contain in an easily manipulated form enormous bodies of meaning—possibly, indeed, the entire meaning of a long calculation,—so in all other kinds of abstract ideation, the symbols which we employ—whether in gesture, speech, or writing—contain more or less condensed masses of signification. Or, to take another illustration, which, like the last example, I quote from Lewes, “It is the same with the development of commerce. Men begin by exchanging things. They pass to the exchange of values. First money, then notes or bills, is the symbol of value. Finally men simply debit and credit one another, so that immense transactions are effected by means of this equation of equations. The complicated processes of sowing, reaping, collecting, shipping, and delivering a quantity of wheat, are condensed into the entry of a few words in a ledger.”