experienced. Hence the importance of experiment to science. A scientific proposition is, of course, grounded on observation of perceived fact and understanding of universal connection, but it is an assertion of something beyond that.

If, then, all scientific judgments are synthetic, and if both rationalism and empiricism failed to account for the manner in which such judgments go beyond what is immediately given to the mind, ought we not to say that the real problem for Kant is to show not merely how synthetic a priori judgments are possible, but how any synthetic judgments are possible? This seems at first sight plausible, but the suggestion must be rejected; for, when Kant asks how a judgment is possible, he is not asking how we come to make it, but how we know that it is valid. Now, if we consider any empirical judgment about the facts of nature, we must recognise that Locke and Hume were right in denying certainty to such judgments. In all general statements about concrete facts we to a certain extent go beyond our evidence. Empirical scientific statements are not theoretically certain. They may, of course, be certain enough for all practical purposes. They are reasonable expectations of what will happen, but reasonable expectation is a very different thing from the certainty of mathematical insight.

Now Kant maintained that, while such empirical judgments are not certain, they all imply the certainty of a number of general principles on which they depend. These general principles are the synthetic a priori judgments with which he is especially concerned. When we apply the principles of trigonometry to an engineering problem, we know that our measurements are only approximate, and that the result also will only be approximate; but the possibility of arriving at such approximate results depends on the absolute truth of the trigonometrical principles, and on the assumption that they express not simply the agreement or disagreement of ideas, but hold of the real. When we apply the rules of arithmetic to counting objects, there may be a certain arbitrariness in deciding on our unit. There is no such arbitrariness in the rule. All scientific judgments of causation are only approximately certain, but they all imply the certainty of the principle of causation, and are based on the assumption that such a principle is of universal application. This and the other principles assumed in our empirical judgments are, then, the synthetic judgments with which Kant is concerned. Now, it is of the nature of our empirical knowledge that it is fragmentary and not uniform, that we are concerned with an indefinite number of things whose connections we do not wholly understand, and which we cannot therefore anticipate. Yet we assume that all these objects will obey the rules of arithmetic and geometry, and will all be subject in their changes to the principle of causation. On such assumptions all the sciences of applied mathematics depend. How are they justifiable? That is Kant's question.

Kant, when he considers mathematics, is concerned with the assumptions of applied mathematics, of those sciences which, though mathematical, make statements about existing objects, and in which the old distinction between understanding and perception which was based on the difference in the objects of these two faculties breaks down. The sciences which Kant is investigating imply that principles which are clearly not derived from mere observation are yet the basis on which we order and arrange what we observe. Now, if we held that the objects of mathematics were independent entities quite separate from the things we perceive, it would be impossible to explain how we might assume that the things we perceive would be subject to the rules of mathematics. If, on the other hand, we held that in mathematics we were simply concerned with the various objects of the senses, it would be impossible to explain how mathematics can have a generality and necessity which no statements can have which rest on observation of the various things we see. The existence of applied mathematics implies firstly that understanding and perception are distinct, and that neither of them can be reduced to the other, for that would mean that we should have to give up either the element of observation and experiment or the element of necessity and a priority, and secondly, that understanding and perception are combined, and must be combined for any advance in science.

Now, Kant finds his answer to the problem he has raised by concentrating his attention on the fact that, while understanding and perception are distinct, they are both present in all knowledge. His argument is that we are necessarily in a difficulty if we think of understanding and perception as having each its separate objects, and then try to explain their combination. If we begin with their combination, we may see that the reference of principles of thought to objects of sense is not an accident, but that these principles of thought or of understanding, as Kant calls them, are only concerned with objects of sense, and have no other meaning. If we object, But how can principles of thought be universal if they are concerned with the many and varying objects of sense? Kant's answer is that they are not concerned directly with these objects, but with the conditions under which these objects can be understood. They are therefore not statements about objects, but statements of the conditions of possible experience. If we find out that all perceiving and thinking imply certain conditions, then we can affirm the validity of principles based upon these conditions, so long as we do not try to apply the principles beyond our perceiving.

We may put the point in another way by asking by what right the mind can prescribe to or anticipate experience. Kant's answer is just in so far as we can determine the conditions under which alone objects can be known. If that can be done, we can say, These principles will hold of objects in so far as they are known. In the preface to the second edition of the Critique of Pure Reason Kant reverts to the discoveries of Galileo and Torricelli, and points out that their success was due to their asking of nature the right question, and the right question was that which reason could understand. "When Galileo let balls of a particular weight, which he had determined himself, roll down an inclined plane, or Torricelli made the air carry a weight, which he had previously determined to be equal to that of a definite volume of water, a new light flashed on all students of nature. They comprehended that reason has insight into that only which she herself produces on her own plan, and that she must move forward with the principles of her judgments, according to fixed law, and compel nature to answer her questions, but not let herself be led by nature, as it were in leading-strings. Otherwise accidental observations, made on no previously fixed plan, will never converge towards a necessary law, which is the only thing that reason seeks or requires. Reason, holding in one hand its principles, according to which alone concordant phenomena can be admitted as laws of nature, and in the other the experiment which it has devised according to those principles, must approach nature in order to be taught by it, but not in the character of a pupil who agrees to everything the master likes, but as an appointed judge, who compels the witnesses to answer the questions which he himself proposes."

Kant, here, is concerned with reason in its application to experience, and he makes it clear that there is much in all such inquiries which cannot be anticipated a priori. "Reason must approach nature in order to be taught by it." The answer to the questions and experiments cannot be known beforehand. The empirical element in science cannot be explained away. Reason dictates not