_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.