The first in this class of passages is taken from Whewell's Philosophy of the Inductive Sciences. No one probably was ever much better fitted by training and attainment than that eminent writer for the investigation he here undertakes. We must, however, caution the reader against supposing that Dr. Whewell means to introduce him into a world of Platonism. The ideas he speaks of may be illustrated in this way. Suppose a person constructs a right line according to Euclid's definition and draws it evenly between its extreme points, his mind has immediately an impression of rightness or straightness, which he attaches to all lines actually so constructed or conceived of as theoretically possible. This idea of straightness is absolute and universal. So, again, looking at two such lines, he knows that they, cannot, in the nature of things inclose a space, and this idea likewise is universal and absolutely true. With the nature of these ideas as a psychological question, the reader need not concern himself for our present purpose. It is sufficient to observe they are brought into activity by a practical occasion. Whether they were wholly or partially pre-existent--or whether they represent a state of our Reason evoked by the occasion--are points which make no difference to their exact strength of validity. We find as a matter of fact in going through life that this particular class of ideas is so very true that it enables us to gauge the material universe. Yet notably enough, Hume in his Treatise (I. 247, seq.) reduces applied mathematics to a species of probability. Other ideas having various degrees of validity and practical necessity are involved in the diverse processes which pertain to the inductive sciences. Dr. Whewell's work was written for the purpose of elucidating them, which he does at great length. To some such ideas, principles, and beliefs we shall advert by and bye. All that seems now necessary is to remark that the distinguished author's general division (Book IX.) where our extract will be found, is concerned with the Philosophy of Biology, and that the paragraphs quoted are sections of its chapter VI., "On the Idea of Final Causes."