By defining a thing I understand expressing it in the terms of other things already known, of course. By positive definition I understand one in which we assert that which the defined is and not merely what it is not, as happens with infinity. A complete definition I take to be one in which are included all the attributes of the thing defined. Thus to say of a man that he is a thing that moves is well but insufficient; it is a positive definition, yet lacks the character of completeness.

Plato has noticed three kinds of definition: definition by enumeration of parts, definition by (...), and the definition by the difference, the difference, that is, in regard to other things.

The last kind needs to be well considered. Its basis seems correct and true — to define a thing by what is proper to it, by separating it distinctly from other things.

True definition should, by saying what a thing is, at the same time to say what it is not.

Definition is based, of course, on things which are known. Thus if an Englishman were to ask me what was the metre I might answer «39 odd inches» and he would understand me well, for he knows quite well what is an inch.

Obviously in going back in the line of definition I shall reach things which I cannot define (if I reach anything). Now these are either unknown or they are known things, yet which are known by intuition, [...] by definition. After almost endless worry we are brought, for instance, to the notion of colour, or to the notion of weight and we are called to define it.

1. We know a thing only by definition; i.e. definition (positive and complete) is the proof of our knowledge.

2. We go on from definition to definition. Either we have to stop or we have not to stop. If we have to stop we do or either by moving in a circle, or by stopping somewhere in a straight line.

Consider the bearing of these things upon our knowledge. If we move in a circle, obviously we do not know the thing defined, for we make the knowledge thereof rest upon itself. If our motion is towards the infinite, and itself, therefore, indefinite, we do not know any more, and knowledge is impossible.

If we, in defining, passing from definition to definition, have to stop somewhere and can go no further, we have arrived at some primary notion which either marks our complete ignorance or has to be conceived as known by intuition. Thus, if, in defining a triangle, we were ultimately arrested, brought up, at the notions of number (from 3 sides) and of form, what have we to say of human knowledge? Are we to accept the conclusion of the sceptics? Or must we ultimately be dogmatic in our theory of knowledge? We shall endeavour, by close examination of the problem, to arrive at some conclusion with regard to this, the primary question in philosophy.

It is best to begin by an example: «give the definition of a piano». We take it from a dictionary: «a musical instrument, consisting of a series of wires of graduated length, thickness and tension, struck by hammers moved by keys». The first thing to be done is to reduce this to a more logical form through less elegant and of less practical use. «A piano is an instrument (I) for the production of music (2) and which consists of wires struck by hammers which are moved by keys (3).»

This definition consists of (1) (...), the end and at the same time the species (2), the contents or (...)

Let us plunge deeper into this. «An instrument (1) is that by means of which anything is effected.» And what is a mean? «Intermediate agency» is the answer; more logically it is «the material relation between Cause and end». Here are we brought to the ideas of relation, of cause, of end. What is relation, what is cause, what is end? Relation cannot be well defined; it is primary and primitive in the human mind. Yet there is a definition of it, which I have made for the moment: «Relation is that which a (any) number of things being given, is contained to (the) perception, in their plurality.» (Plurality creates relation).