Why the inductive and mathematical sciences, after their first rapid development at the cu

lmination of Greek civilization, advanced so slowly for two thousand years--and why in the following two hundred years a knowledge of natural and mathematical science has accumulated, which so vastly exceeds all that was previously known that these sciences may be justly regarded as the products of our own times--are questions which have interested the modern philosopher not less than the objects with which these sciences are more immediately con versant. Was it the employment of a new method of research, or in the exercise of greater virtue in the use of the old methods, that this singular modern phenomenon had its origin？ Was the long period one of arrested development, as in the modern era one of normal growth？ Or should we ascribe the characteristics of both periods to so-called historical accidents--to the influence of conjunctions in circumstances of which no explanation is possible, save in the omnipotence and wisdom of a guiding Providence？

The explanation which has become commonplace, that the ancients employed deduction chiefly in their scientific inquiries, while the moderns employ induction, proves to be too narrow, and fails upon close examination to point with sufficient distinctness the contrast that is evident between ancient and modern scientific doc- trines and inquires. For all knowledge is founded on observation, and proceeds from this by analysis and syn thesis, by synthesis and analysis, by induction and deduction, and if possible by verification, or by new appeals to observation under the guidance of deduction--by steps which are indeed correlative parts of one method; and the ancient sciences afford examples of every one of these methods, or parts of one method, which have been generalized from the examples of sciences.

A failure to employ or to employ adequately anyone of these partial methods, an imperfection in the arts and resources of observation and experiment, carelessness in observation, neglect of relevant facts, vagueness and carelessness in the reasoning, and the failure to draw the consequences of theory and test them by appeal to experiment and observation--these are the faults which cause all failures to ascertain truth, whether among the ancients or the moderns; but this statement does not explain why the modern is possessed of a greater virtue, and by what means he attained his superiority. Much less does it explain the sudden growth of science in recent times.

The attempt to discover the explanation of this phenomenon in the antithesis of "facts" and "theories" or "facts" and "ideas"--in the neglect among the ancients of the former, and their too exclusive attention to the latter proves also to be too narrow, as well as open to the charge of vagueness. For, in the first place, the antithesis is not complete, facts and theories are not coordinate species. Theories, if true, are facts--a particular class of facts indeed, generally complex ones, but still facts. Facts, on the other hand, even in the narrowest signification of the word, if they are at all complex, and if a logical connection subsists between their constituents, have all the positive attributes of theories.

Nevertheless, this distinction, however inadequate it may be to explain the source of the true method in science, is well founded, and connotes an important character in true method. A fact is a proposition of which the verification by an appeal to the primary sources of our knowledge or to experience is direct and simple. A theory, on the other hand, if true, has all the characteristics of a fact, except that its verification is possible only by indirect, remote, and difficult means. To convert theories into facts is to add simple verification, and the theory thus acquires the full characteristics of a fact.

The title that best expresses the ideas of this passage is ______.

A．Philosophy of Mathematics

B．The Recent Growth in Science

C．The Verification of Facts

D．Methods of Scientific Inquiry