Most concepts, as we saw, are empirical. We take certain likenesses and differences we observe as the mark of a real unity in the things. The different natures of different things we do not fully know, but we distinguish them by the different uniformities we observe, and in order to explain our experience we assume the unity underlying these perceived likenesses. Iron, dog, fire, are names for the natures of things which we see manifested in our experience. The concept, then, is got from what we perceive, though it stands for something more than we perceive. How, then, can there be any concepts which are not got from the empirical differences of things we perceive? Let us take such a concept as substance, and see whether we can discover where it comes from. Locke had been puzzled by discovering that he could not, in any object, find anything which was its substantiality. Calling anything a substance is not like saying that it is hard, or green, or heavy; we are not concerned with specific differences in things, but we are not therefore saying what is meaningless. There is something, namely substance, which we can distinguish from the hardness, or colour, or weight that we perceive. That something we do not perceive; we assume it whenever we talk of a thing being hard, and green, and heavy. A thing’s substantiality is just the unity of its perceivable qualities. But such a unity is implied in the concept of any object. Substance, then, is a name for one of the general principles implied in our assuming that what we perceive are real objects. Kant generalises the result of this inquiry into particular concepts of this kind. He holds that a priori concepts or categories (_i.e._ the concepts which we do not get from empirical differences of things) stand for principles implied in thinking of things as objects or in judging. If we want, therefore, to find out the number of the categories, we must ask how many different kinds of unity are implied in judgment, or what are the conditions of judging any object. Kant does not here help, but rather misleads us in this inquiry. For he unfortunately thought that the different kinds of judgment could be discovered without further ado by taking the list given in formal logic. He therefore first makes a list of categories, based on the logical forms of judgment, and then tries to show the connection between these categories and the principles which were, as he had discovered, assumed in the mathematical sciences. The actual movement of his thought is, I think, different. He asks if there are any general conditions implied in all judgment. His answer is that all judgments, all statements, that is, which claim to be true, imply determination of time and space. From that determination certain principles can be deduced. If time and space are implied in all judging, then these principles will equally be implied, and will hold of all things which can be objects for us.