Chapter II: Front Matter (2)

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.

DIARY OF FRANCES KRASINSKA;

OR, LIFE IN POLAND DURING THE EIGHTEENTH CENTURY.

Friday, _April 10th._

Easter week is over, and I am really sorry; I had found happiness in repose, and already have care and disquiet won their way into my heart and my mind.... How many sins I have committed! Poor humanity! poor nature, so frail and weak! Notwithstanding my promises and the resolutions which I fancied so strong, I yield to the least temptation.

For example, and it is indeed incredible, but a fact, that on Holy Thursday, the very day after my confession, I sinned, and sinned through pride. I should have worn black when I went to be present at the court ceremony, but I could not resist the seduction of a beautiful costume. Just as I was beginning my preparations, the Princess Lubomirska entered my room, accompanied by her maids, who brought me a charming dress of white velvet, with a long train, and trimmed with white roses; the headdress consisted of a garland of white roses, and a long white blonde veil. The taste and richness of this costume surpasses description! How could I resist the happiness of seeing myself so becomingly attired!

I asked the princess why she required me to wear so brilliant a costume to church; she replied that on Holy Thursday it was customary after the service to go into the great hall of the castle, where the king would wash the feet of twelve old men, in commemoration of the humility of our Saviour, and that he would also wait upon them at table. During this pious and edifying ceremony, a young girl belonging to one of the noblest families must make a collection for the poor; the king himself names the lady, and this year he was pleased to honor me by his selection; he at the same time announced that the results of my efforts should be given to the hospital for the poor under the Abbé Baudoin's charge.

I was very happy as I listened to the princess; but, must I confess it? I was not happy through the good action I was about to perform; I thought only of myself, of my beauty, of the charming costume, of the effect I should produce among all the other women dressed in black, and I rejoiced to think that I should be the most beautiful. What culpable vanity! And on Holy Thursday! But at least I frankly admit my sin, and humiliate myself for it.

My collection surpassed my hopes. I received nearly four thousand ducats. Prince Charles Radziwill said, as he put his hand to his purse: 'My dear (Panie Kochanku, his favorite expression), one must give something to so beautiful a lady;' and he threw five hundred gold pieces on my plate, which would have fallen from my hands had I not been aided in holding it. When I began my collection, I was very much embarrassed; I trembled all over, and blushed at each new offering I received; but by degrees I gained courage, and profited by my dancing master's lessons. The grand marshal of the court gave me his hand, and named each lord as he repeated the customary formula employed in handing them the plate; as for me, I could not have said a word; I found it quite enough to make a proper and becoming courtesy to each one. When the plate became too heavy, the marshal emptied it into a large bag, borne behind us.

I heard many compliments, and I was more looked at and admired than I ever had been before in my life. The prince royal said to me: 'If you had asked each of us to give you his heart, no one could have refused you.'

I replied: 'Affection is not solicited, it is inspired.'

He seemed pleased with my frankness. I cannot comprehend how a woman could solicit love, and say: Love me, admire me.... For a king I could not thus degrade myself. Tenderness is involuntary; one may seek to win it, one may gladly accept it when offered; but to solicit it, is even more ridiculous than criminal.

The washing of the feet is one of the most striking ceremonies of our religion. A king kneeling before those twelve aged men, and then standing behind them while they are at table, is a most touching and sublime spectacle. That ceremony can never pass from my memory. Augustus III, although no longer young, is still handsome; his gestures bear the impress of dignity and nobility: the prince royal, Charles, resembles him exactly.

On Good Friday we visited the sepulchre; all the court ladies were dressed in black; we made our stations in seven churches, and in each we said appropriate prayers. I was on my knees during a whole hour in the cathedral. On Holy Saturday the services were magnificent, and the organs pealed forth the most heavenly strains of music.

Tho princess's Easter collation (swiencone) was superb; until yesterday, the tables were continually covered with cakes and cold meats. It is just one year since I assisted at Madame Strumle's very modest collation; I was then a schoolgirl; who could have guessed that on the following Easter Monday I should be with the princess palatiness, that the prince royal would partake of the same collation with myself, and that we should eat out of the same plate!

One really finds a pleasure in eating meat after a Lent so rigorously observed; for all here are as particular as at Maleszow. During holy week, everything is cooked in oil, and on Good Friday a severe fast is adhered to, each one taking only food sufficient to keep him from starving.

The prince royal has fasted so much that he has become quite thin. I noticed this yesterday, and my eyes involuntarily rested upon his features with a more tender expression than usual: as he was talking with the prince palatine, I did not think he was paying any attention to me, but thoughts springing from the heart never escape him, he is so good, so quick in understanding; soon after, he thanked me for my solicitude. I grew very red, and promised myself in future to keep a strict guard over the expression of my eyes.

A woman's part, especially that of an unmarried girl, is very difficult; not only must she measure out her words and watch the tones of her voice, but she must also command the expression of her countenance. I must ask, of what use are governesses and their lessons in such cases? The princess is quite right when she says, that ten governesses, let them be as watchful as they may, cannot guard a young girl who does not know how to guard herself.

Wednesday, _April 15th._

We leave Warsaw to-morrow; I am going with the prince and princess to their estate at Opole. My father has written to the princess to say that I may remain with her so long as my presence may be agreeable to her. I hope she will never be dissatisfied with me; I endeavor to please her in every possible way. She inspires me with infinite fear and respect; she controls me entirely, and I am always ready to yield to the lightest expression of her will; when she smiles upon me, when she looks at me kindly, it seems to me as if heaven were opening before me. If I should ever reach an advanced age, I would like to inspire the same feelings which I experience toward her. The prince royal himself is afraid of the princess.

Would any one believe that I am glad to think that I shall not now go to Maleszow? I dread the home of my childhood; it seems to me as if I should profane it were I to visit it with a heart so filled with unrest and disquietude!

Ought I to regret the past? Will a life of torment be the price of a single ray of happiness enlightening the highest pinnacle of human felicity? If the wish which I dare not express should ever be accomplished, I will surely be equal to my position; but I will also know how to bear the shipwreck of my dearest hopes.... Great God, how can I write, how dare I confide to paper what I fear to confess to myself! When I think of him, I tremble lest any one should divine my feelings, and yet I write!... If my journal were to fall into any one's hands I should be deemed mad, or at least most foolishly presumptuous; I must shut it up under four locks.

CASTLE OF OPOLE, Friday, _April 24th._

We have been here nearly a week; the situation of the castle is very agreeable, but I am no longer gay, and nothing pleases me. The trees should already be green, and they are still bare; it should be warm, and the air freezes me. I desired to embroider, but the indispensable silks were wanting; I tried the piano, but it was not in tune: it will be necessary to send to Lublin for the organist. There is quite a large library here, but I dare not ask the princess for the key. The prince has several new works; he paid in my presence six gold ducats for ten little volumes of M. Voltaire's works: Voltaire is now the most celebrated writer in France. The princess forbids my reading his books, and I am sure I am quite content. But what I cannot endure is, that I am not permitted to read a romance lately come from Paris, entitled _La Nouvelle Héloïse_. It is by a certain Rousseau, and has made a great sensation here. I picked up one volume, and read a few pages of the preface, but what did I see? Rousseau himself says: 'A mother will forbid her daughter to read it.' The princess is quite right, and I laid the book aside with a flutter at my heart which still continues.

The physicians in Warsaw have ordered the princess to ride on horseback during her sojourn in the country; they say this exercise will be excellent for her health. She laughed at the prescription, and had not the faintest intention of trying it; but the prince palatine will hear of no jesting where physicians are concerned.

He has bought a pretty mare, very gentle and well trained, as also a most comfortable saddle; but the princess still refuses to mount the animal. She was with great difficulty persuaded yesterday to mount a donkey, and thus make the circuit of the garden. She will be obliged to repeat this exercise every day. As for me, who have no fear of horses, I had a most burning desire to try the mare; I spoke of it yesterday evening; but the princess chid me, and told me with quite a severe air, that it was the most improper thing in the world for a young lady. I must of course renounce my desire; but I do it with real regret, for I already saw myself in fancy riding through the forests, going to the chase, climbing the steep mountain sides with _him_, and admiring his strength and skill....

The castle has become more lively; several persons have come from the city and the neighborhood to present their homage to the palatine. They might perhaps afford me amusement; and yet I do not even find a passing distraction in their presence. I have seen Michael Chronowski, my father's former chamberlain; how the poor young man is changed! The prince palatine, in consequence of my father's recommendation, placed him at the bar in Lublin. They say he is doing very well, but he is thin, bent, and old before his time; his face is strangely colored, and he has some frightful scars. He has not danced once since Barbara's wedding. The time for mazourkas and cracoviennes is past: they have been replaced by law cases, pleading, chicanery, and all its tiresome accompaniments; his language is so learned that one can no longer understand him.

As a compensation, however, we have here one very agreeable visitor, Prince Martin Lubomirski, the prince palatine's cousin, though much younger than he. I had already met him in society at Warsaw. The princess, who is severe, and who never overlooks the least defect, criticizes him a little; but I find his manners very agreeable: he owns in the neighborhood the estate of Janowiec, and has given us all a most pressing invitation to visit his castle. It is possible we may go there; I should be charmed, for no one talks more agreeably. He is gay, fond of pleasantry, and a great friend to the prince royal; he often speaks of him, and always well and worthily; he appreciates him and knows how to praise him.... My heart swells with pleasure while I listen.

CASTLE OF JANOWIEC, Friday, _May 1st, 1760._

We came here two days ago, and Prince Martin says he will not let us soon depart. Everything is more beautiful at Janowiec than at Opole; no one can be more generous, more hospitable, or more amiable than Prince Martin. The princess says he scatters gold and silver about as if he expected it to grow. He is now having a wide avenue cut through the forest surrounding the castle. I can see from the windows of my room immense trees falling beneath the axes of hundreds of laborers; at the end of the avenue, a pavilion is being built, at which they work so rapidly that one can see it grow from hour to hour. The prince sent to Warsaw and to various other places for his workmen; he pays them double wages, and he has made a bet with the palatine that the pavilion will be entirely finished in four weeks. I am quite sure he will win. The forest is to be transformed into an enclosed park. The whole neighborhood abounds in wild beasts; but he has had many elks and bears taken to people his wonderful park. There must be some mystery lurking behind all these preparations. I feel, rather than guess it.

I like Janowiec better than any other place; the situation is charming, and the castle magnificent. It stands upon a mountain overlooking the Vistula; its architecture belongs to a very ancient period. From the castle the whole city may be seen, with the granaries of Kazimierz, and also Pulawy, belonging to the Princess Czartoryski. The apartments are large, very numerous, and gorgeously furnished; but I believe that my boudoir is the most delightful room in the castle. It is situated at the top of a tower, and while I am in it I can fancy myself a real heroine of romance. It has three windows, all opening in different directions, and each with a most enchanting view. I generally sit by the window overlooking the new avenue and the pavilion, which rises as if built by fairies. The panels of my cabinet are adorned with paintings, representing Olympus. 'Venus alone was wanting,' said the prince, with that grace for which he is distinguished, 'but you have come to finish the picture.'

I feel here an incomprehensible sense of well-being, I am soothed by such sweet presentiments, I fancy myself on the eve of some very happy event.

Sunday, _May 3d._

I do not think I ever rose so early before in my whole life; the castle clock has just struck three, and I am already at my writing. I took a walk before daylight through the long corridors of the castle: had any one seen me, I should have been taken for an ancestral shade, come to visit the domain of its descendants. Prince Martin, following an old and excellent custom, has built a gallery, containing the portraits of all the most distinguished members of his family; all the memories of the race of Lubomirski may be found in this gallery. He sent to Italy for an artist to execute the portraits, and he called to his aid a learned man fully acquainted with the history of the Lubomirski family and of our country. After much deliberation and many discussions, the project was finally carried into effect in 1756, as announced by the main inscription. It is to be regretted, says the princess, that these pictures are in fresco, and not in oil colors, as they would then have been more solid and transportable.

Let what will happen in the future, at present this gallery is truly magnificent. Yesterday, Prince Martin, with the palatine and the palatiness, gave me a historical account of each picture; I immediately determined to transfer them to my journal. With this intention I rose before day and visited the gallery on tiptoe while all were still sleeping. I will write down all I have been told, and all I have seen.

In the four corners of the hall are the arms of the Lubomirski family, Srzeniawa, received on the occasion of a battle gained by one of the ancestors on the banks of the Srzeniawa, not far from Cracow. The first picture represents the division of the property between the three brothers Lubomirski; a division which was made according to law, during the reign of Wladislas I, and signed February 1st, 1088. Nearly all the other pictures are family portraits; women rendered illustrious by noble deeds, and men distinguished in political, civil, military, or religious careers, especially during the reigns of Sigismund III, of John Casimir, and of John III, Sobieski, There are several copies of the portrait of Barbara Tarlo, who brought the castle of Janowiec as a dowry to a Lubomirski.