Thus, the sciences of arithmetic, algebra, and geometry may be successfully prosecuted by a man who has reflected little upon the nature of numbers and who has never asked himself seriously what he means by space.  The assumptions which he is justified in making, and the kind of operations which he has the right to perform, do not seem, as a rule, to be in doubt.

So it is also in the sciences of chemistry and physics.  There is nothing to prevent the chemist or the physicist from being a philosopher, but he is not compelled to be one.  He may push forward the investigations proper to his profession regardless of the type of philosophy which it pleases him to adopt.  Whether he be a realist or an idealist, a dualist or a monist, he should, as chemist or physicist, treat the same sort of facts in the same sort of a way.  His path appears to be laid out for him, and he can do work the value of which is undisputed by traveling quietly along it, and without stopping to consider consciously what kind of a path it is.  There are many who work in this way, and they succeed in making important contributions to human knowledge.

Such sciences as these I call the non-philosophical sciences to distinguish them from the group of sciences I have been discussing at length.  What marks them out is, that the facts with which the investigator has to deal are known by him with sufficient clearness to leave him usually in little doubt as to the use which he can make of them.  His knowledge is clear enough for the purpose in hand, and his work is justified by its results.  What is the relation of such sciences as these to philosophy?

79.  THE STUDY OF SCIENTIFIC PRINCIPLES AND METHODS.—­It is one thing to have the instinct of the investigator and to be able to feel one’s way along the road that leads to new knowledge of a given kind, and it is another thing to have the reflective turn of mind that makes one clearly conscious of just what one has been doing and how one has been doing it.  Men reasoned before there was a science of logic, and the sciences made their appearance before what may be called the logic of the sciences had its birth.

“It may be truly asserted,” writes Professor Jevons,[1] “that the rapid progress of the physical sciences during the last three centuries has not been accompanied by a corresponding advance in the theory of reasoning.  Physicists speak familiarly of Scientific Method, but they could not readily describe what they mean by that expression.  Profoundly engaged in the study of particular classes of natural phenomena, they are usually too much engrossed in the immense and ever accumulating details of their special sciences to generalize upon the methods of reasoning which they unconsciously employ.  Yet few will deny that these methods of reasoning ought to be studied, especially by those who endeavor to introduce scientific order into less successful and methodical branches of knowledge.”