The element of truth in Locke’s position is this. When we are examining concrete things like pieces of gold or any chemical substance, we find in them a number of varying qualities whose connection we cannot understand. We do not know why a metal of a certain specific gravity should also be yellow; we can only note the fact. Hence in chemistry our method must be quite different from the method of mathematics. In mathematics we start from the definition, and we can understand the connection of the properties of a geometrical figure, and see that they all follow necessarily from the definition. But in sciences like chemistry a definition does not take us any further; we can only find out the properties of a substance by observation and experiment. Locke explains this difference by saying that in the former case we are only concerned with agreement among our own ideas, in the second place we are concerned somehow with things outside us. This explanation will not stand. It is not true that mathematics is simply analysis of an arbitrary definition, as Locke seems to suggest. It involves construction, or, as Kant calls it, synthesis. It is a process of discovering new truths. Secondly, our statements about concrete objects are not statements of qualities we see co-existing at the moment. They are statements about all gold or all men; in other words, they are universal, and Locke found it impossible to explain the universality of such propositions--what we mean, _e.g._ when we talk about the nature of gold or of man, not of this gold or this man that I see before me. Lastly, this distinction of mathematics and the empirical sciences by a distinction of spheres does not allow, as we saw, for a science like astronomy, which builds on mathematics and yet applies to the concrete world. These difficulties were seen more clearly by Hume, at once the greatest and the most thorough-going of empiricists. He cut the knot in regard to mathematics by asserting that geometry, just because it has clearly an application to the existing world, had no more certainty than any other empirical inquiry, while arithmetic and algebra, he agreed, were certain, but confined their application to the sphere of our own ideas. Both positions are almost obviously inconsistent with the facts. In considering the nature of our judgments about concrete existences he raised a more profound problem. All such judgments, as he said, imply the principle of causation, or of what is called, in modern times, the principle of the uniformity of nature. That principle we take with us in our investigation of the existing world. Yet, as Hume saw, we do not observe causes; we only observe succession and change. We seem, therefore, to put into the world we see a necessity and uniformity which the observed facts do not warrant. How is this to be explained?