UNITY AND NUMBER.
PRELIMINARY CONSIDERATIONS ON THE IDEA OF UNITY.
1. Before analyzing the idea of number, let us examine its simplest element, unity. Number is a connection of unities. We cannot know what number is, if we do not know what unity is.[25]
2. What is unity? When is a thing one? We all seem to know what unity is, since upon it we found the fabric of all our arithmetic cognitions. We all know when a thing is one, and we never equivocate on the meaning of the word. In this the learned and the unlearned stand on the same footing. The wordone, in our language, has only one meaning for all who understand it. The same may be said of the word which in other languages expresses the same idea. When we meet the figure 1, which corresponds to this idea, and expresses it in a general manner, abstracting the difference of idioms, all men understand and apply it in the same manner.
3. The idea of unity is the same in all men; it is a common patrimony of the human race. It is not bound to this or that object, nor to this or that act of the mind; it extends to all in the same manner. Even composite and multiple things are called one only, inasmuch as they participate in a general idea. The indivisible point is one. The line composed of many points could not be one were there not a contiguous enchainment of these points, and did they not all unite to formoneobject, which gives usoneimpression, and is submitted tooneact of our understanding.
4. The idea of unity is not a particular sensation, since it applies to all; neither is it sensation in general, since it pertains to what is not sensation. The sensation of color is one; so, also, the consciousness of themeis one, although this is not a sensation. The size of the rectangle which I see is one, and the relation of the equality of its angles is also one, but is not a sensation.
5. The idea of unity is a simple idea, and accompanies our mind from its first steps; we find it everywhere, and understand it well, but cannot explain it as we would, because it is simple, and cannot be decomposed and expressed by various words. We do not mean to say, however, that we must abjure all explanation of it; we only propose to warn the reader of the kind of explanation he may expect, which can be no other than the analysis of the fact, inasmuch as it is an object, and of the phenomenon as presented to our mind.