The earliest evolution of that which has been called Science,—the Mathematics, which we dismiss for the instant, excepted,—took place under the operation of a Method, which, ordinarily confounded with the true Deductive one, is now better known among rigorous Scientists as the Hypothetical or Anticipative Method. This has two modes of expression, one of which consists in the assumption of Laws or Principles, which have not been adequately verified, or in the erection of fanciful hypotheses, as the starting points of reasoning for the purpose of establishing other Facts. The second and most common operation referred to this Method, which is, however, strictly speaking, an imperfect application of the Inductive Method, is to draw conclusions from Facts which these do not warrant—sometimes conclusions not related to the Facts, oftener those which, being so related, are a step beyond the legitimate inferences which the Facts authorize, though in the same direction. This results in the establishment of Laws or Principles as true, which are by no means proven, many of which are subsequently found to be incorrect. It is to this operation of the Hypothetical Method that Professor Whewell, who does not discriminate the two, refers when he describes the defect in the physical speculations of the Greek philosophers to have been, 'that though they had in their possession Facts and Ideas, the Ideas were not distinct and appropriate to the Facts.' The main cause of defect in the mental process here employed is the tendency of the human mind to generalize at too early a stage of the investigation, and consequently upon a too narrow basis of Facts.

This Method characterized the intellectual activity of the race from the earliest beginnings of thought up to a period which is commonly said to have commenced with the publication of the Novum Organum of Lord Bacon. It was of course fruitless of Scientific results, as it was not a Scientific, but an absolutely Unscientific Method, since certainty is the basis of all Science, and since a Method which attempts to deduce Facts from Principles which are not ascertained to be Principles, or Principles from an insufficient accumulation of Facts, cannot insure certainty.

It is common to aver that the Anticipative or Hypothetical Method failed to secure distinct and established verities, and thus to answer the purpose of a guide to knowledge, because it neglected Facts, disregarded experience, and endeavored to spin philosophy out of the unverified thoughts of men. Professor Whewell, in the two able and valuable works to which we have referred, has shown that this was not the case among the Greeks, at least, whose Philosophy 'did, in its opinions, recognize the necessity and paramount value of observation; did, in its origin, proceed upon observed Facts, and did employ itself to no small extent in classifying and arranging phenomena;' and furthermore, 'that Aristotle, and other ancient philosophers, not only asserted in the most pointed manner that all our knowledge must begin from experience, but also stated, in language much resembling the habitual phraseology of the most modern schools of philosophizing, that particular facts must be collected; that from these, general principles must be obtained by induction; and that these principles, when of the most general kind, are axioms.'

The confusion of thought which has existed and, to a considerable extent, still exists, even among Scientific men, in relation to the nature of this Method, arises from the want of an understanding of its twofold mode of operation, as just explained. The assertion of those who ascribe the failure of this Method to its neglect of Facts, is true; the averment of Professor Whewell that it was neither from a lack of Facts nor Ideas, but because the Ideas were not distinct and appropriate to the Facts, is not less so. But the former statement applies to that phase of the Method which assumed unverified Laws or Principles, or fanciful hypotheses, as the starting points of reasoning without reference to Facts; while the latter refers to the process, which, while it collected Facts and derived Laws therefrom, did not stop at the inferences which were warranted by the Facts. This last was the mode of applying the Method most in vogue with Aristotle and the Greek Scientists; while the first was preëminently, almost exclusively, the process of the Greek Philosophers and the mediæval Schoolmen.

But while the endeavor to arrive at certain knowledge by the Deductive Method, by attempting to reason from Principles to Facts, from Generals to Particulars, failed so completely as far as the Anticipative or Hypothetical branch, of the Method was concerned, the same mode of procedure was productive of the most satisfactory results when applied to Mathematics, and furnished a rapid and easy means of arriving at the ulterior Facts of this department of the universe with precision and certainty. We have thus the curious exhibition of the same process leading into utter confusion when applied to one set of phenomena, and into exactitude and surety when applied to another; and behold the Scientific world condemning as utterly useless for other departments of investigation, and throwing aside, a Method which is still retained in the only Science that is called exact, and in which proof amounts to demonstration, in the strict sense of the term. This anomaly will be recurred to and explained farther on.

Soon after the invention of printing, with its resulting multiplication of books and increased intellectual activity, the mind of Europe began to emerge from the deep darkness in which it had been shrouded for centuries, and a number of great intellects engaged in the search after knowledge by the close and laborious examination of the actual existences and operations of nature around them. Leonardo da Vinci and Galileo in Italy; Copernicus, Kepler, and Tycho Brahe in Central Europe; and Gilbert in England, peered into the hidden depths of the universe, collected Facts, and established those Principles which are the foundations of the magnificent structures of modern Astronomy and Physics. About the same time, Francis Bacon put forth the formal and elaborate statement of that Method of acquiring knowledge which is often called after him the Baconian, but more commonly the Inductive Method; substantially the Method pursued by the great scientific dicoverers whom we have just named.

The characteristic of this Method is the precise Observation of Facts or Phenomena and the Induction (drawing in) or accumulation of these accurate Observations as the basis of knowledge. (This is seemingly the first or etymological reason for the use of the term Induction; a term subsequently transferred, as we shall see, to the establishment of the Laws, from which then ulterior Facts are to be deduced.) When a sufficient number of Facts have been accumulated and classified in any sphere of investigation, and these are found uniformly to reveal the same Law or Principle, it is assumed that all similar Phenomena are invariably governed by this Principle or Law, which, in reality deduced or derived, is, by this inversion of terms, said to be induced from the observed Facts. The Law so established has thenceforth two distinct functions: I, all the Facts of subsequent Observation, by the primitive Method of observation, are ranged under the Law which, to this extent, serves merely as a superior mode of classification; and, II, the Law itself, now assumed to be known and infallible, becomes an instrument of prevision and the consequent discovery through it of new Facts, the same which were meant by the expression 'ulterior Facts' above used. It is this deduction of new Facts from an established Law which constitutes the true and legitimate Deductive Method of Science, the third of the three Methods above stated and the one which, as has been pointed out, is often erroneously confounded with the Anticipative or Hypothetical Method.

The mode of investigation by the Inductive Method is, therefore, in general, similar to that which Aristotle and the Greek Scientists adopted. It first Observes and Collects Facts; then it resorts to Classification for the purpose of discovering the Law by which the observed Facts are regulated; then derives from this Classification a General Law, presumed to be applicable to all similar Facts, although they have not yet been observed; and, finally, deduces from the General Law thus established, new Facts and Particulars, by bringing them in under the Law.

The Inductive Method is, therefore, almost identical in its mode of procedure with one of the processes anciently adopted for the acquisition of knowledge under the Anticipative or Hypothetical Method. It failed of fruitful results, in this earlier age, because, as we have seen, men were not content with adhering rigorously and patiently to the logical, irresistible conclusions which Facts evolved, but sought to wrench from them Principles, which required for their establishment a wider or different range of phenomena. On the revival of this Method among the modern Scientists, it was conceived, especially by Bacon, that a rigid adhesion to the legitimate deductions of Facts and a faithful exclusion from the domain of knowledge of everything which did not logically and inevitably result from the Observation and Classification of Facts, was the only safe way to arrive at certainty in any department of thought. It is this fidelity to conclusions rigorously derived from Facts, and the severe exclusion of everything not clearly substantiated by Observation, Classification, and Induction, which has given us the body of proximately definite knowledge that we now possess, and which, so far as it has been persevered in, has been productive of such beneficial intellectual results.

Under the guidance of this Inductive Method new Sciences have been gradually generated, whose foundations and Principles are capable of such a degree of satisfactory proof as the Method itself affords. During the present century, Auguste Comte, a distinguished French philosopher, often denominated the Bacon of our epoch, the special champion of the Inductive Method, has undertaken, for our day, the task which his illustrious English predecessor attempted for his, namely—an Inventory and Classification of our intellectual stores. He endeavored to bring the Scientific world up to the practical recognition of that which they had theoretically maintained since Bacon's time,—that nothing deserves to be considered as true, which cannot be undoubtedly, conclusively established by inference, from the Facts of Experience,—a theory to which they had never strictly adhered. He insisted that all Theological, Metaphysical, and Transcendental Speculations were wholly beyond the range of exact inquiry, and should therefore be excluded from the domain in which human knowledge was to be sought; and that investigation should be confined to those regions of thought and activity which were within the limits of precise apprehension. Upon this clear, logical and right application of the Inductive Method, Comte based his Classification of our existing knowledge. He denominated as Positive Sciences those systems of Principles and correlated Facts, comprising Mathematics, Astronomy, Physics, Chemistry, Biology, Sociology, and their derivative domains, which were founded on the exact Observation of Phenomena, and set aside all other realms of the universe of thought as departments in which exact knowledge was impossible, and whose intellectual examination was therefore fruitless. The Philosophy based on this critical Method was denominated by its founder Positivism. All modern Scientists, with rare exceptions, whether they are disciples of Comte or not, are theoretical Positivists in their modes of investigation, in their unwillingness to accept theories not proven, in their partiality for Facts, and in their devotion to the Inductive Method, although the nature of proof is still but dimly comprehended by them as a body, and much laxity creeps into their practical efforts at demonstration. Under the influence of Positivism, however, the Scientific field is being rapidly cleared of unestablished theories which formerly mingled with it, claiming to be an integral part of its area, and the boundaries of Science are becoming more closely defined. The Inductive Method is enthusiastically eulogized as the source of the success of modern Scientific investigators, as the true Scientific Method, and—except among a few of the most advanced thinkers—as the final word of wisdom in regard to the manner of establishing definite and exact knowledge. The Deductive, often called the à priori Method—in which term the Anticipative or Hypothetical and the true Deductive Method, seen in Mathematical investigations, are not sufficiently discriminated—is, on the other hand, almost everywhere denounced as essentially false, the source of all error; and we are assured that the attempt to work it was the fault of the old world, prior to Bacon, and the cause of its failure to secure great intellectual results.