BUCKLE, DRAPER, AND A SCIENCE OF HISTORY.

SECOND PAPER.

The word Science has been so indiscriminately applied to very diverse departments of our intellectual domain, that it has ceased to have any distinctive or well-defined signification. Meaning, appropriately, that which is certainly known, as distinguished from that which is matter of conjecture, opinion, thought, or plausible supposition merely, its application to any special branch of human inquiry signifies, in that sense, that the facts and principles relating to the given branch, or constituting it, are no longer subjects of uncertain investigation, but have become accurately and positively known, so as to be demonstrable to all intelligent minds and invariably recognized by them as true when rightly apprehended and understood. In the absence, however, of any clear conception of what constitutes knowledge, of where the dividing line between it and opinion lay, departments of the universe of intelligence almost wholly wanting in exactness and certainty have been dignified with the same title which we apply to departments most positively known. We hear of the Science of Mathematics, the Science of Chemistry, the Science of Medicine, the Science of Political Economy, and even of the Science of Theology.

This vague use of the word Science is not confined to general custom only, but appertains as well to Scientists and writers on scientific subjects. So general is this indistinct understanding of the meaning of this term, that there does not exist in the range of scientific literature a precise, compact, exhaustive, intelligible definition of it. In order, therefore, to approach our present subject with clear mental vision, we must gain an accurate conception of the character and constituents of Science.

In his History of the Inductive Sciences, Professor Whewell says:

'In the first place, then, I remark, that to the formation of science, two things are requisite:—Facts and Ideas; observation of Things without, and an inward effort of Thought; or, in other words, Sense and Reason. Neither of these elements, by itself, can constitute substantial general knowledge. The impression of sense, unconnected by some rational and speculative principle, can only end in a practical acquaintance with individual objects; the operations of the rational faculties, on the other hand, if allowed to go on without a constant reference of external things, can lead only to empty abstraction and barren ingenuity. Real speculative knowledge demands the combination of the two ingredients—right reason and facts to reason upon. It has been well said, that true knowledge is the interpretation of nature; and therefore it requires both the interpreting mind, and nature for its subject, both the document, and ingenuity to read it aright. Thus invention, acuteness, and connection of thought, are necessary on the one hand, for the progress of philosophical knowledge; and on the other hand, the precise and steady application of these faculties to facts well known and clearly conceived.'

This explanation of the nature of Science, more elaborately expanded in The Philosophy of the Inductive Sciences, is limited by its author to the Physical Sciences only. In addition to this circumscribed application, it is moreover indistinct by reason of the use of the word Ideas, a word to which so many different significations have been attached by different writers that its meaning is vague and undefined—to convey the impression of Laws or Principles. The same defect exists in the detailed exposition is perhaps the most extended and complete extant.

But even when we gain a clear conception of the proposition which Professor Whewell only vaguely apprehends and therefore does not clearly state, namely—that Science is an assemblage of Facts correlated by Laws or Principles, a system in which the mutual relations of the Facts are known, and the Laws or Principles established by them are discovered;—when we understand this ever so distinctly, we are still at the beginning of a knowledge of what constitutes Science. When do we know that we have a Fact? How are we to be sure that our proof is not defective? By what means shall it be certain, beyond the cavil of a doubt, that the right Laws or Principles, and no more than those warranted by the Facts, are deduced? These and some other questions must be definitely settled before we can thoroughly comprehend the nature of Science, and the consideration of which brings us, in the first place, to the examination of the characteristics of Scientific Methods.

The intellectual development of the world has proceeded under the operation of three Methods. Two of these, identical in their mode of action, but arriving, nevertheless, at widely different results, from the different points at which they take their departure, are not commonly discriminated, but are both included in the technical term Deductive Method. The other is denominated the Inductive. A brief analysis of these Methods will clear the way for an understanding of the nature of Science, particularly in its application to the subject of History, with which we are at present especially concerned.

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.

A distinguished thinker, Stephen Pearl Andrews, from whose writings some of these suggestions concerning Methods have been borrowed, points out three sources of confusion in the minds even of the learned themselves, in connection with this subject. First, in the verbal point of view, the terms Induction and Deduction are applied in a way directly the opposite of that which their Etymology would indicate: In-duction is used for the De-rivation of a Law from Facts, and De-duction for the Intro-duction of new Facts under the Law. Secondly, the two terms Inductive and Deductive, which are alone usually spoken of, are not enough to designate all the processes involved in the several Scientific Methods; and, thirdly, these terms are sometimes used to denote Processes merely, and sometimes to designate Methods which are merely characterized by the predominance of one or the other of these Processes.

This intricate subject of Methods may be better understood after a statement of the following considerations. Induction, as a Process, occurs whenever Facts are used as an instrument by which to discover a Principle or Law of Nature. The Principle is derived from, or, as Scientists have chosen to conceive it, induced upon the Facts. Deduction, as a Process, occurs whenever a Principle or Law of Nature is used as an instrument by which to discover Facts. The new Facts are ranged under, or, as it is conceived, deduced from the Principle.

Each, of these Processes occurs in every Scientific Method; but different Methods are characterised by that one of these two Processes which is put first or takes the lead in the given Method. Thus, in both Methods which are included in the one generally called the Deductive, the main Process was Deduction, there being no perceptible Induction from Collected Facts in the proper Hypothetical or Anticipative Method, while in the true Deductive Method, as applied to Mathematics, the Inductive stage is so short and so slight that it is performed instinctively by all people and the Deductive stage at once reached. The other branch of the Hypothetical Method, that used by Aristotle and the Greek Scientists, was, as we have seen, in reality a first and imperfect attempt to use the Inductive Method. In this Method itself, on the other hand, the main Process is the Induction or derivation of a Principle or Law from accumulated Facts, while Deduction, or the bringing in of new Facts under the Law, is a subordinate or Secondary Process.

In reality, there is but one Method, having several stages or Processes, which Processes, preponderating at different epochs, have not been clearly apprehended as necessary complements of each other, and have, hence, been regarded as different Methods. In one phase of the Anticipative or Hypothetical stage,—the assumption of basic Principles as points to reason from,—the Observation and Collection of Facts, and the Induction therefrom, were processes so imperfectly performed, that they appeared to have no existence; in another phase, that employed by Aristotle, these Processes were apparent, but still imperfectly conducted, and hence, in both cases, the Law or Principle employed for the Deductive Process was liable to be defective, and therefore insufficient as a guide to the acquisition of certain knowledge. In the Inductive stage or Method, on the other hand, the Processes thus defectively employed in the former stage, the Hypothetical, are preëminently and disproportionately active, while the Deductive Process is given a very inferior position. The establishment of the just, reciprocal activity of these two Processes in intellectual investigation would secure the perfection of the one true Scientific Method.

The Inductive Method—preserving the term Method to avoid confusion—in which the mode of procedure from Facts to Principles predominates, and which is hence sometimes called the Empirical, or the Experimental, or the Positive, or the à posteriori Method, is that which now prevails in the world, which is extolled as if it were the only legitimate Method, and the only possible route to Scientific Discovery. That the just claims of the Inductive Method are very great is universally admitted, but let us not stultify ourselves by assuming a position in its defence which is in direct violation of the teachings of the Method itself,—namely, the assumption of a theory which is not verified by Facts. That the Inductive Method is vastly superior to the Anticipative or Hypothetical one, is abundantly proved; but that it is the only correct path to Scientific truth, that it is the best path to Scientific truth which will ever be known, or that in a rightly balanced Method it would be the main Process, is an averment for which there is no warrant. On the contrary, a very cursory examination of the Inductive Method will show defects which render it unavailable as the sole or the chief guide in Scientific inquiry.

The leading characteristic of the Inductive Method, that for which it is mainly admired, is its cautious, laborious, oftentimes tedious Observation and Collection of the Facts of Experience, and their careful Classification as a basis for the derivation of a Principle or Law applicable to the Phenomena grouped together. By this means, it is said, we secure precision and certainty, by which is intended, not only the certainty of that which is already observed and classified, but also the certainty of that which is deduced from the Law or Principle derived from these known Facts. It is just here, however, that the Inductive Method is lacking. Experience may testify a thousand, ten thousand, any indefinite number of times, to the repetition of the same Phenomena, and yet we can have no certainty of the recurrence of the same Phenomena, in the future, in the same way. All the Facts of Observation and Experience for thousands of years went to convince men that the earth was at rest and the sun and stars passing around it. A larger Experience showed them their error. How shall we know that our Observation has at any time included all the Facts necessary to establish a Law? The history of Science, even under the guidance of the Inductive Method, is a history of Principles announced as firmly established, which a little later were found to be defective and had to be adjusted to the advanced stage of human Experience. The very nature of the Inductive Method indicates its inadequacy for the largest and most important purposes of Science. It gives certainty, where it does give it, only up to the point of the present, it can never afford complete certainty for the future. The logical and rigid testimony of this Method can never be more than this;—Observation and Experience show that such has been the uniform operation of Nature in this particular so far as can be discovered, and in all probability it will always continue to be such. High Probability, amounting, it may be, at times, to an assurance of certainty, is the strongest proof which this Method can, from its very nature, produce. To establish a Principle or Law for a certainty beyond any possibility of doubt by the Inductive Method, it is essential that we should know that we are in possession of every Fact in the universe which has any relation to the given Principle, or rather that we should know that there are no Facts in the universe at variance with it. To know this, it is necessary to be in possession of all the Facts in the universe, since the Inductive Method has no mode of discovering when it has sifted out of the immense mass of Facts all those which exist in connection with any given Law. As we shall never be in possession of all the Facts of the universe, we shall never be able, by the Inductive Method, to possess certainty in respect to the future operations of Nature; and thus we discover the insufficiency of this Method as a perfect guide to the acquisition of knowledge.

The famed Inductive Method, like the Anticipative or Hypothetical, furnishes, in truth, only an assumption as a starting point for reasoning in the endeavor to establish other Facts than those already known. The verification of the Law or Principle assumed is, indeed, in the former Method, as complete as it can be, in the nature of the case, while in the latter it is not; but we have just seen that the strongest proof which Observation, Classification, and Induction can give is that of High Probability, on the supposition that a certain number of Facts from which a Law is derived include substantially all that the whole range of Phenomena belonging to the given sphere would represent. Any possible application of the Inductive Method is, therefore, only a nearer or more remote approximation to an Exactitude and Certainty which the Method itself can never fully attain.

The Inductive Method being thus defective as a Scientific guide, in the most important requirement of Science, it is unnecessary to enter into an exposition of minor defects, not the least of which is the slowness with which conclusions must necessarily be arrived at, when they are reached only by the gradual accumulation of Facts and the derivation of a Law from these. A Method or a Process which lacks that which is the very essence of Science—the power of making known, of introducing certainty into investigation, may be an important factor in the true Scientific Method, but cannot constitute the Method itself, or its leading feature. Let it not be understood, however, that in bringing the Inductive Method in Science to the ordeal of a critical examination, it is designed to detract from its just dues or to depreciate its true value. Science is preëminently severe in its probings; and that which, asserts its claim to the highest Scientific position, and affects to be the only guide to exact knowledge, cannot expect anything less than the most rigorous inquiry into the validity of such claim, and the most peremptory insistence upon the production of proper credentials before so lofty a seat be accorded it. If inquiry discovers deficiencies in its character, Science should rejoice that truth is vindicated, and that, by correctly understanding the nature and powers of their present guide, Scientific men may avoid being tempted to consider it as competent to conduct them into regions where the blind must inevitably be leading the blind, and both be in danger of the ditch. If the devotees of the Inductive Method have in their enthusiasm set up claims for it which cannot be substantiated, they must not blame the rigorous hand, which, in the service of Science, unmasks their idol and exhibits its defects, but rather impute to their own deviation from the severity of Scientific truth, the disappointment which they may experience. The question of Method lies at the foundation of all Science. Until it is thoroughly understood, until the exact character of all our Methods or Processes is definitely and rightly apprehended, there can be no full understanding of the true nature of Science, and, hence, no critical and exact line drawn between that which is Science and that which is not.

Our examination of the Methods in use thus far in our past search after knowledge has developed these facts:—that prior to an era which is commonly said to commence with Bacon, the Method of intellectual investigation was mainly by attempting to proceed from Principles to Facts, and that the attempt exhibits three distinct phases: one, in which the Induction stage is so simple and so short as to be instinctively and correctly performed by all people, and the Deductive stage at once reached—this furnishes the Mathematics, the only Science in which hitherto the true Deductive Method has prevailed; a second, in which Principles are assumed to reason from, without any previous effort at Induction, such as existed, being unconsciously made from the supposed Facts or Knowledge which the mind was in possession of; and a third, in which Facts were collected, classified, and Induction therefrom as a basis of further investigation attempted, but in which the Laws or Principles assumed as established by the Facts were not rigorously and accurately derived from Facts; or, in other words, in which the Facts were not strictly used for the purpose of deriving from them just such Laws or Principles only as they actually established, but were wrenched to the attempted support of Laws, Principles, or Ideas more or less fanciful or unrelated to the Facts. These two last phases are included in what is known among Scientists as the Anticipative or Hypothetical Method; while the three phases are commonly undiscriminated and collectively termed the Deductive Method. It was also developed that the results of this period of intellectual activity were fruitless of definite Scientific achievements, except so far as the true Deductive Method had been employed. It was furthermore seen that since Bacon's time, the opposite Method of procedure, namely, from Facts to Principles, has been chiefly in vogue; that under its impulse distinctness and clearness have been brought to pervade those stores of knowledge which were already in our possession, thus fulfilling one of the requisites of a perfect Scientific Method, while, however, the other necessary requirement, that of furnishing a certain guide to future discoveries, has been only proximately attained by it.

It is obvious from this exhibition of the characteristics of the two leading Scientific Methods, or the two leading Processes of the one Method, in whichever light we may choose to view them, that so far from being the best or the only true Method or Process of intellectual investigation, the Inductive is far inferior to the true Deductive Method or Process, in all the essentials of a Scientific guide. The Inductive can give us only a high degree of precision and definiteness, with only proximate certainty for the future as the result of a slow mode of procedure; while the true Deductive Method gives us perfect precision, exactitude, and complete certainty, as the result of a rapid mode. The true Deductive Method—brought into disrepute by being confounded with the Anticipative or Hypothetical, which differs from it only in this, that the Principles from which the latter reasons are true, while those of the former are doubtful—has thus far prevailed in Mathematics alone, and Mathematics is, up to our day, the only recognized Exact Science, the only Science in which Demonstration, in the strict sense of that term, is now possible,—the fruits of the Inductive Method being known as the Inexact Sciences, in which only Probable Reasoning prevails.

It is necessary to say, in the strict sense of the term, because the same laxity exists in the use of the word Demonstration, as in that of Science, and hence it has lost the distinctive meaning which attaches to it, in its legitimate use, as signifying a mode of reasoning in which the self-evident truths or axioms, with which we start, and every step in the deduction, 'are not only perfectly definite, but incapable of being apprehended differently—if really apprehended, they must be apprehended alike by all and at all times.' It is because this Method of proof exists only in Mathematics, that this alone is denominated the Exact Science, or its branches, the Exact Sciences; Sciences whose Laws or Principles, and the Facts connected with or deduced from them, are irresistible conclusions of thought, in all minds, which conclusions rest upon universally recognized axioms; while the Inexact Sciences, including all except Mathematics, the Sciences in which the Inductive Method prevails, are systems of Laws or Principles, with their related Facts, of the truth of which there is great probability, but of which there is, nevertheless, no complete certainty; whose conclusions are not based upon universally undeniable axioms, or are not themselves irresistible to the human mind.

The superiority of the Deductive Method, both in its mode of advancing to the discovery of new truth and in the precision, clearness, and certainty which accompany its findings, must now easily become apparent. Whether we regard Induction and Deduction as correlative Processes belonging to one Method, each of which has been disproportionately in vogue at different epochs, or as distinctive Methods, having each their own Deductive and Inductive Processes, in either aspect, Induction is only a preparative labor, leading in the more important work of the application of the Law or Principle derived. It is only, indeed, for the purpose of discovering this Law that Observation, Classification, and Induction are undertaken. It has been the triumphant boast of the Inductive Method, that it guarded, by means of these preliminary steps, in the most careful manner, against error in establishing its Laws. To the extent of its capacity it has done so. But we have already seen, that deriving its Principles, as it was obliged to, from less than all the Facts which appertained to the Principles, these must inevitably have been lacking in some particulars; it being impossible to make the whole out of less than all its parts.

The Inductive Method has obtained an importance greatly exaggerated, for the reason that it has been brought into comparison, for the most part, with the Anticipative or Hypothetical, the bastard Deductive Method only, and its superiority over this exhibited in the most detailed manner, while the right application of the Deductive Method, except in Mathematics, has not been considered possible. The reason of this can be made obvious.

The immense superiority of Mathematical Reasoning, as Demonstration is often called, over all other kinds, is universally known and recognized. For in this mode of reasoning there is no room for doubt or uncertainty. It starts from Principles of whose truth there can be no doubt, because it is impossible for the human mind to apprehend them in more than one way, and proceeds by steps, every one of which can likewise be apprehended in only one way. Hence all men arrive inevitably at the same conclusion at the close of the chain of reasoning. It is, therefore, a Method of proof which sets out from a precise, definite, universally established Law or Principle which really contains the conclusion in itself, and which can be developed to the end through a series of necessary and irresistible convincements; while in the Inductive Method we are obliged to start from this or that admitted Fact or Truth assumed after Observation, Classification, and Induction, which may have been rigorously performed, but which, nevertheless, could not, in the nature of the case, prove the Fact or Truth with complete certainty, and which is not, perhaps, universally admitted, and proceed by merely probable inferences drawn from various, diverse, and often uncertain relations, until we reach a conclusion. Such reasoning may be sufficient to incline the mind to a particular conclusion, as against those which tend to any other conclusion, but they are never quite sufficient, as in Demonstrative or true Deductive reasoning, to necessitate the conclusion, and render any other impossible.

A Method of Scientific investigation which proceeds from self-evident truths to necessary results by undeniable steps, would of course be preferable to one which, starting from truths whose precision and certainty might be doubtful, advances by more or less probable inferences to a more or less probable conclusion, did there not exist some powerful cause for a contrary action. A difficulty thus far insurmountable has, indeed, stood in the way of the adoption of the Deductive Method in any department of investigation, save the one already referred to. This Method, we have seen, leads to truth or error accordingly as the Principles or Laws from which it commences its reasoning process are true or false. In the Mathematics, the basic truths, being of a simple character, were arrived at by easy and instinctive mental processes, and the Method achieved in this department great success. But the other domains of human knowledge being more complex, involving more qualities or characteristics than mere Number and Form and Force, which are all that come within the scope of Mathematics, their fundamental bases or truths were not so easily attainable. Hence, when Principles or Ideas which men believed to contain all the fundamentals of a specific domain of thought were adopted as starting points of reasoning, they were generally lacking in some important element, which caused the conclusion to be in some way incorrect. We have seen the historical results of this mode of procedure in what is denominated the Anticipative or Hypothetical Method. The failure of this to secure good results, and the absence of any standard by which to be certain when a Law or Principle was fundamental, exact, and inclusive, when it was a valid basis to reason from, led to the abandonment of the Deductive Method, except in its application to Mathematics, where true starting points were known. The Observation and Classification of Facts was then resorted to, first, in a loose way, in Greece, and afterward, in a more rigorous way, in the world at large, for the purpose of endeavoring to discover, by the only mode considered effective—the examination of Phenomena—the fundamental Principles, which, like those of Mathematics, should include all the essentials of the special domain under consideration. These being discovered, might furnish, it was instinctively felt, starting points from which to work the Deductive Process, with the same success as that which attended its application to Mathematics.

The Inductive Principle, considered either as a Process or a Method, is valuable, therefore, mainly as it furnishes proper starting points for the activity of the Deductive Principle. Thus far in the history of the Natural Sciences it has been the best and safest guide in affording such starting points. But the indications are numerous all about us that the progress of Scientific discovery will ere long bring us to a stage, where the Laws or Principles which underlie every department of the Universe being fully revealed, the function of the Inductive Principle as a guide to fundamental bases, will be at an end, and the Deductive Method once more assume the leadership, opening to us all departments of investigation, with the rapidity, precision, and certainty which characterize Mathematical research and Demonstrative Reasoning.

This desideratum must necessarily result whenever a Unitary Law shall be discovered in Science; whenever the Sciences, and the Phenomena within the different Sciences, shall be basically connected. All the present conditions and tendencies of knowledge indicate that the attainment of this crowning intellectual goal was predestined to our epoch. It has been the grand work of the Inductive Method to arrange Facts under Principles, and these latter as Facts or Truths under a smaller number of Principles, and these in turn under a still smaller number, until all the Phenomena of the different domains of thought which are reckoned as Sciences are included within a few Principles which lie at the foundation of each domain. The connection of these few Principles by a still more fundamental Law, is all that is necessary to the completion of the work of the centuries and the establishment of a Universal or Unitary Science. Already those recognized as leaders in the Scientific world watch expectantly the signs of the times and await the advent of the Grand Discovery which is to usher in a new intellectual era, 'We have reached the point,' says Agassiz, in one of his Atlantic Monthly articles, 'where the results of Science touch the very problem of existence, and all men listen for the solving of that mystery. When it will come, and how, none can say; but this much, at least, is certain, that all our researches are leading up to that question, and mankind will never rest till it is answered.'

'All the Phenomena of Physics,' says Professor Silliman, in his First Principles of Philosophy, 'are dependent on a limited number of general laws, of which they are the necessary consequences. However various and complex may be the phenomena, their laws are few, and distinguished for their exceeding simplicity. All of them may be represented by numbers and algebraic symbols, and these condensed formulæ enable us to conduct investigations with the certainty and precision of pure Mathematics. As in geometry, all the properties of figures are deduced from a few axioms and definitions; so when the general laws of Physics are known, we may deduce from them, by a series of rigorous reasonings, all the phenomena to which they give rise.'

Auguste Comte, in his elaborate and encyclopædic Course of Positive Philosophy, tells us that 'these three laws [the Law of Inertia, the Law of the Equality of action and reaction, and the Law of the Composition of forces] are the experimental basis of the Science of Mechanics. From them the mind may proceed to the logical construction of the Science, without further reference to the external world. * * * We cannot, however, conceive of any case which is not met by these three laws of Kepler, of Newton, and of Galileo, and their expression is so precise that they can be immediately treated in the form of analytical equations easily obtained.' While also exhibiting the small number of Principles which lie at the foundation of other domains of our intellectual accumulations, Comte remarks: 'The ultimate perfection of the Positive system would be (if such perfection could be hoped for) to represent all phenomena as particular aspects of a single general fact;—such as Gravitation, for instance.'

These are a few specimens of what may be found in the books, pointing out the gradual approach of Scientific investigation to the discovery of a Unitary Law, and the expectation among Scientists of the advent, at some period not far distant, of a new Science, the greatest among Sciences, a true Pantology or Universology. Upon the apprehension of this Law, which must establish the true basis of every domain of thought or activity, and show it to be identical or analogous in the several domains, we shall be placed, in relation to the whole universe, precisely where we now stand in relation to Mathematics, Mechanics, and Physics; that is, the General Law or Laws of every domain of investigation will become known, as we now know those of these Sciences, and, to adopt the words of the French writer, 'from them the mind may proceed to the logical construction of the Science [being now the Science of the whole Universe], without further reference to the external world;' or to use the language of Professor Silliman, 'when the general laws of [the Universe] are known, we may deduce from them, by a series of rigorous reasonings, all the phenomena to which they give rise.' Thus, upon the discovery of a Unitary Law, linking the Sciences together, and showing the identity of their starting points or bases, the Deductive Principle, considered either as a Method or a Process, must once more take the lead, and the Inductive occupy its legitimate position as a subordinate and corroborative auxiliary. Under the guidance of this new adjustment of the Deductive and Inductive Principles, a full, exact, complete, definite, Scientific Classification of our knowledge will become possible, and the true boundaries of every domain of intellectual examination may be critically and clearly established. In the absence of such a Classification, it is only by viewing departments of the Universe with reference to the Method or Process employed in the investigation of their Phenomena, that we are able to estimate their present relations to Science, and to ascertain proximately their Scientific or Unscientific character. We proceed, then, to examine the connection of History, in its present development, with Science, a task to which the foregoing brief and incomplete consideration of the subject of Method has been a necessary preliminary.

A number of Classifications of human knowledge have been attempted, none of which were exact or complete, or could have been, for a reason which was stated above, and none of which are now considered to be satisfactory by the Scientific world. Bacon and D'Alembert, men of vigorous and vast intellectual capacity, were admirably adapted to such a work, so far as it could be performed in their day. But the state of knowledge and Scientific progress was not sufficiently advanced, at that time, to render any Classification which could be made of more than temporary value, and those furnished by these illustrious thinkers now appertain only to the archæology of Science.

The Classification of Auguste Comte, in the absence of a more exact, complete, and inclusive one, still holds the highest rank, and is the only one which now claims the attention of the general Thinker. It is very restricted in its application, professing to include only the domain which Comte calls abstract or general Science, which has for its object the discovery of the laws which regulate Phenomena in all conceivable cases within their domain, and excluding the sphere of what he denominates concrete, particular, or descriptive Science, whose function it is to apply these laws to the history of existing beings. This throws such Natural Sciences as Botany, Zoology, Mineralogy, Geology, etc., out of his range. He also excludes the domain of practical Knowledge, comprising what is included under the terms, the Applied Sciences, the Arts, the Mechanical Sciences, etc. A Classification, far more detailed and comprehensive in its scope than anything yet published, is in preparation by Professor P. H. Vander Weyde, of the Cooper Institute—advanced sheets of which, so far as it is elaborated, have been kindly furnished to the writer by the author—the incomplete state of which, however, prevents a further consideration here.

The Principle which Comte adopted to guide him in his Classification was the following: 'All observable phenomena may be included within a very few natural categories, so arranged as that the study of each category may be grounded on the principal laws of the preceding, and serve as the basis of the next ensuing. This order is determined by the degree of simplicity, or, what comes to the same thing, of generality of their phenomena. Hence results their successive dependence, and the greater or lesser facility for being studied.' In accordance with this Principle, Comte establishes what he denominates the Hierarchy of the Sciences. Mathematics stands at the base of this, as being that Science whose Phenomena are the most general, the most simple, and the most abstract of all. Astronomy comes next, wherein the Static and Dynamic properties of the heavenly bodies complicate the nature of the investigation; in Physics, Phenomena must be considered in the midst of the still greater complications of Weight, Light, Heat, Sound, etc.; Chemistry has additional characteristics to trace in its subjects; Biology adds the intricacies of vital Phenomena to all below it; and Sociology, the sixth and last of Comte's Hierarchy—all other departments of thought other than those previously excluded from his survey, being regarded as out of the bounds of human cognition—deals with the still more complicated problem of the relations of men to each other in society.

This Classification is admirable for the purpose of showing the mutual interdependence of the branches of Knowledge included in it; but aside from its covering only a small part of our intellectual domain, it is also defective in not distinguishing with sufficient clearness that which is properly Science, from that which is merely Theory or Plausible Conjecture. Biology and Sociology are classed with Mathematics as Positive Sciences, as if the Laws or Principles which correlated the Phenomena of the former were established as certainly and definitely as those of the latter; while there is no prominence given to the different nature of proof in Mathematics and that in every other department of investigation—except in so far as Mathematical Phenomena and Processes enter into the latter—if, indeed, the founder of Positivism has even anywhere distinctly stated it. Chemistry, Biology, and Sociology, leaving Astronomy and Physics aside for the present, are not yet Positive Sciences, in any such sense as Mathematics. The lack of exact analysis is apparent in all of Comte's generalizations, otherwise magnificent and masterly as they undoubtedly are. In respect to the matter under consideration, it renders his Classification unavailing for determining with sufficient precision and exactitude the character of any intellectual domain. History, while it is the source whence the proof of his fundamental positions is drawn, finds no place in his Scientific schedule. Even had it been otherwise, the defect just alluded to would have rendered it useless for our present purposes, until a prior Classification had first been made, exhibiting the radical difference between the various domains, which are all indiscriminately grouped under the name of Science. After such a Classification, based on the nature of proof as involved in Method, the Principle which guided Comte in the establishment of the Hierarchy of the Sciences will enable us, in a concluding paper, to estimate with proximate certainty the character of a possible Science of History, and to ascertain how far the labors of Mr. Buckle and Professor Draper have aided toward the creation of such a Science.