Inductive investigation, as we have seen, consists in the union of hypothesis and experiment, deductive reasoning being the link by which experimental results are made to confirm or confute the hypothesis. Now when we consider this relation between hypothesis and experiment it is obvious that we may classify our knowledge under four heads.
(1) We may be acquainted with facts which have not yet been brought into accordance with any hypothesis. Such facts constitute what is called Empirical Knowledge.
(2) Another extensive portion of our knowledge consists of facts which having been first observed empirically, have afterwards been brought into accordance with other facts by an hypothesis concerning the general laws applying to them. This portion of our knowledge may be said to be explained, reasoned, or generalised.
(3) In the third place comes the collection of facts, minor in number, but most important as regards their scientific interest, which have been anticipated by theory and afterwards verified by experiment.
(4) Lastly, there exists knowledge which is accepted solely on the ground of theory, and is incapable of experimental confirmation, at least with the instrumental means in our possession.
It is a work of much interest to compare and illustrate the relative extent and value of these four groups of knowledge. We shall observe that as a general rule a great branch of science originates in facts observed accidentally, or without distinct consciousness of what is to be expected. As a science progresses, its power of foresight rapidly increases, until the mathematician in his library acquires the power of anticipating nature, and predicting what will happen in circumstances which the eye of man has never examined.
Empirical Knowledge.
By empirical knowledge we mean such as is derived directly from the examination of detached facts, and rests entirely on those facts, without corroboration from other branches of knowledge. It is contrasted with generalised and theoretical knowledge, which embraces many series of facts under a few comprehensive principles, so that each series serves to throw light upon each other series of facts. Just as, in the map of a half-explored country, we see detached bits of rivers, isolated mountains, and undefined plains, not connected into any complete plan, so a new branch of knowledge consists of groups of facts, each group standing apart, so as not to allow us to reason from one to another.
Before the time of Descartes, and Newton, and Huyghens, there was much empirical knowledge of the phenomena of light. The rainbow had always struck the attention of the most careless observers, and there was no difficulty in perceiving that its conditions of occurrence consisted in rays of the sun shining upon