name there is “invented,” i.e. made and constructed, the object to be named; so that here idea and object coincide—whether the object is thought of as thing or as event. That which we desire to say of the concept we must apply immediately in the construction of our concept of the abstract concept. We define the abstract concept as a work of art of scientific thought, but scientific thought as an operation with such creations by comparing them, partly with one another, partly with concrete concepts or with particular ideas. The abstract concept is an object to which any characteristics are given, whether presentable to sense or not, whether found connected in reality (“in experience”) or not; it is determined only by the end which the creation is to serve, and this end is knowledge of the relations between objects experienced, and capable of being experienced. There stands therefore at the head of abstract concepts, the concept of the simply thinkable, to which any name, e.g. A, may be attached as representing it. The operations of scientific thought begin by equating this concept to itself, which takes place through “words” in the form of the judgment A = A, the so often misunderstood proposition of identity. The proposition signifies the will of the scientific thinker to treat his concept as equal to itself, i.e. not subjected to change; and this will claims to be a valid will, because it is appropriate to that end within wide limits. For in a certain degree it is true that all objects of experience are not subject to change, i.e., they may be so thought of, and this thought again serves an end, is indeed necessary, because it is only upon this assumption that we can compare such objects with concepts and therefore with each other. For the comparison of objects of experience is completely effected by referring them to the thought-object and expressing them therein. The thought-object is a standard. It may be described as an individual. While the universal idea becomes poor in characteristics in proportion as it is wide and more general, the abstract concept, no matter to how many phenomena it is to be referred, may be as richly furnished with characteristics as the end demands. It represents its own idea, the idea of a universal which is at the same time singular (particular); it is itself a sign, a symbol, and nothing else. It serves its end the better in proportion as its characteristics are clear and determinate, and in proportion as they are conditioned by each other and therefore referable to each other in equations; on the other hand it becomes useless if its characteristics are even in thought mutually exclusive, or—what is the same thing—contradict each other.
