Of Inductions Improperly So Called.
§ 1. Induction, then, is that operation of the mind, by which we infer
that what we know to be true in a particular case or cases, will be true
in all cases which resemble the former in certain assignable respects. In
other words, Induction is the process by which we conclude that what is
true of certain individuals of a class is true of the whole class, or that
what is true at certain times will be true in similar circumstances at all
times.
This definition excludes from the meaning of the term Induction, various
logical operations, to which it is not unusual to apply that name.
Induction, as above defined, is a process of inference; it proceeds from
the known to the unknown; and any operation involving no inference, any
process in which what seems the conclusion is no wider than the premises
from which it is drawn, does not fall within the meaning of the term. Yet
in the common books of Logic we find this laid down as the most perfect,
indeed the only quite perfect, form of induction. In those books, every
process which sets out from a less general and terminates in a more
general expression—which admits of being stated in the form, “This and
that A are B, therefore every A is B”—is called an induction, whether any
thing be really concluded or not: and the induction is asserted not to be
perfect, unless every single individual of the class A is included in the
antecedent, or premise: that is, unless what we affirm of the class has
already been ascertained to be true of every individual in it, so that the
nominal conclusion is not really a conclusion, but a mere re-assertion of
the premises. If we were to say, All the planets shine by the sun’s light,
from observation of each separate planet, or All the Apostles were Jews,
because this is true of Peter, Paul, John, and every other apostle—these,
and such as these, would, in the phraseology in question, be called
perfect, and the only perfect, Inductions. This, however, is a totally
different kind of induction from ours; it is not an inference from facts
known to facts unknown, but a mere short-hand registration of facts known.
The two simulated arguments which we have quoted, are not generalizations;
the propositions purporting to be conclusions from them, are not really
general propositions. A general proposition is one in which the predicate
is affirmed or denied of an unlimited number of individuals; namely, all,
whether few or many, existing or capable of existing, which possess the
properties connoted by the subject of the proposition. “All men are
mortal” does not mean all now living, but all men past, present, and to
come. When the signification of the term is limited so as to render it a
name not for any and every individual falling under a certain general
description, but only for each of a number of individuals, designated as
such, and as it were counted off individually, the proposition, though it
may be general in its language, is no general proposition, but merely that
number of singular propositions, written in an abridged character. The
operation may be very useful, as most forms of abridged notation are; but
it is no part of the investigation of truth, though often bearing an
important part in the preparation of the materials for that investigation.
As we may sum up a definite number of singular propositions in one
proposition, which will be apparently, but not really, general, so we may
sum up a definite number of general propositions in one proposition, which
will be apparently, but not really, more general. If by a separate
induction applied to every distinct species of animals, it has been
established that each possesses a nervous system, and we affirm thereupon
that all animals have a nervous system; this looks like a generalization,
though as the conclusion merely affirms of all what has already been
affirmed of each, it seems to tell us nothing but what we knew before. A
distinction, however, must be made. If in concluding that all animals have
a nervous system, we mean the same thing and no more as if we had said
“all known animals,” the proposition is not general, and the process by
which it is arrived at is not induction. But if our meaning is that the
observations made of the various species of animals have discovered to us
a law of animal nature, and that we are in a condition to say that a
nervous system will be found even in animals yet undiscovered, this indeed
is an induction; but in this case the general proposition contains more
than the sum of the special propositions from which it is inferred. The
distinction is still more forcibly brought out when we consider, that if
this real generalization be legitimate at all, its legitimacy probably
does not require that we should have examined without exception every
known species. It is the number and nature of the instances, and not their
being the whole of those which happen to be known, that makes them
sufficient evidence to prove a general law: while the more limited
assertion, which stops at all known animals, can not be made unless we
have rigorously verified it in every species. In like manner (to return to
a former example) we might have inferred, not that all _the_ planets, but
that all _planets_, shine by reflected light: the former is no induction;
the latter is an induction, and a bad one, being disproved by the case of
double stars—self-luminous bodies which are properly planets, since they
revolve round a centre.
§ 2. There are several processes used in mathematics which require to be
distinguished from Induction, being not unfrequently called by that name,
and being so far similar to Induction properly so called, that the
propositions they lead to are really general propositions. For example,
when we have proved with respect to the circle, that a straight line can
not meet it in more than two points, and when the same thing has been
successively proved of the ellipse, the parabola, and the hyperbola, it
may be laid down as a universal property of the sections of the cone. The
distinction drawn in the two previous examples can have no place here,
there being no difference between all _known_ sections of the cone and
_all_ sections, since a cone demonstrably can not be intersected by a
plane except in one of these four lines. It would be difficult, therefore,
to refuse to the proposition arrived at, the name of a generalization,
since there is no room for any generalization beyond it. But there is no
induction, because there is no inference: the conclusion is a mere summing
up of what was asserted in the various propositions from which it is
drawn. A case somewhat, though not altogether, similar, is the proof of a
geometrical theorem by means of a diagram. Whether the diagram be on paper
or only in the imagination, the demonstration (as formerly observed(101))
does not prove directly the general theorem; it proves only that the
conclusion, which the theorem asserts generally, is true of the particular
triangle or circle exhibited in the diagram; but since we perceive that in
the same way in which we have proved it of that circle, it might also be
proved of any other circle, we gather up into one general expression all
the singular propositions susceptible of being thus proved, and embody
them in a universal proposition. Having shown that the three angles of the
triangle ABC are together equal to two right angles, we conclude that this
is true of every other triangle, not because it is true of ABC, but for
the same reason which proved it to be true of ABC. If this were to be
called Induction, an appropriate name for it would be, induction by parity
of reasoning. But the term can not properly belong to it; the
characteristic quality of Induction is wanting, since the truth obtained,
though really general, is not believed on the evidence of particular
instances. We do not conclude that all triangles have the property because
some triangles have, but from the ulterior demonstrative evidence which
was the ground of our conviction in the particular instances.
There are nevertheless, in mathematics, some examples of so-called
Induction, in which the conclusion does bear the appearance of a
generalization grounded on some of the particular cases included in it. A
mathematician, when he has calculated a sufficient number of the terms of
an algebraical or arithmetical series to have ascertained what is called
the _law_ of the series, does not hesitate to fill up any number of the
succeeding terms without repeating the calculations. But I apprehend he
only does so when it is apparent from _a priori_ considerations (which
might be exhibited in the form of demonstration) that the mode of
formation of the subsequent terms, each from that which preceded it, must
be similar to the formation of the terms which have been already
calculated. And when the attempt has been hazarded without the sanction of
such general considerations, there are instances on record in which it has
led to false results.
It is said that Newton discovered the binomial theorem by induction; by
raising a binomial successively to a certain number of powers, and
comparing those powers with one another until he detected the relation in
which the algebraic formula of each power stands to the exponent of that
power, and to the two terms of the binomial. The fact is not improbable:
but a mathematician like Newton, who seemed to arrive _per saltum_ at
principles and conclusions that ordinary mathematicians only reached by a
succession of steps, certainly could not have performed the comparison in
question without being led by it to the _a priori_ ground of the law;
since any one who understands sufficiently the nature of multiplication to
venture upon multiplying several lines of symbols at one operation, can
not but perceive that in raising a binomial to a power, the co-efficients
must depend on the laws of permutation and combination: and as soon as
this is recognized, the theorem is demonstrated. Indeed, when once it was
seen that the law prevailed in a few of the lower powers, its identity
with the law of permutation would at once suggest the considerations which
prove it to obtain universally. Even, therefore, such cases as these, are
but examples of what I have called Induction by parity of reasoning, that
is, not really Induction, because not involving inference of a general
proposition from particular instances.
§ 3. There remains a third improper use of the term Induction, which it is
of real importance to clear up, because the theory of Induction has been,
in no ordinary degree, confused by it, and because the confusion is
exemplified in the most recent and elaborate treatise on the inductive
philosophy which exists in our language. The error in question is that of
confounding a mere description, by general terms, of a set of observed
phenomena, with an induction from them.
Suppose that a phenomenon consists of parts, and that these parts are only
capable of being observed separately, and as it were piecemeal. When the
observations have been made, there is a convenience (amounting for many
purposes to a necessity) in obtaining a representation of the phenomenon
as a whole, by combining, or as we may say, piecing these detached
fragments together. A navigator sailing in the midst of the ocean
discovers land: he can not at first, or by any one observation, determine
whether it is a continent or an island; but he coasts along it, and after
a few days finds himself to have sailed completely round it: he then
pronounces it an island. Now there was no particular time or place of
observation at which he could perceive that this land was entirely
surrounded by water: he ascertained the fact by a succession of partial
observations, and then selected a general expression which summed up in
two or three words the whole of what he so observed. But is there any
thing of the nature of an induction in this process? Did he infer any
thing that had not been observed, from something else which had? Certainly
not. He had observed the whole of what the proposition asserts. That the
land in question is an island, is not an inference from the partial facts
which the navigator saw in the course of his circumnavigation; it is the
facts themselves; it is a summary of those facts; the description of a
complex fact, to which those simpler ones are as the parts of a whole.
Now there is, I conceive, no difference in kind between this simple
operation, and that by which Kepler ascertained the nature of the
planetary orbits: and Kepler’s operation, all at least that was
characteristic in it, was not more an inductive act than that of our
supposed navigator.
The object of Kepler was to determine the real path described by each of
the planets, or let us say by the planet Mars (since it was of that body
that he first established the two of his three laws which did not require
a comparison of planets). To do this there was no other mode than that of
direct observation: and all which observation could do was to ascertain a
great number of the successive places of the planet; or rather, of its
apparent places. That the planet occupied successively all these
positions, or at all events, positions which produced the same impressions
on the eye, and that it passed from one of these to another insensibly,
and without any apparent breach of continuity; thus much the senses, with
the aid of the proper instruments, could ascertain. What Kepler did more
than this, was to find what sort of a curve these different points would
make, supposing them to be all joined together. He expressed the whole
series of the observed places of Mars by what Dr. Whewell calls the
general conception of an ellipse. This operation was far from being as
easy as that of the navigator who expressed the series of his observations
on successive points of the coast by the general conception of an island.
But it is the very same sort of operation; and if the one is not an
induction but a description, this must also be true of the other.
The only real induction concerned in the case, consisted in inferring that
because the observed places of Mars were correctly represented by points
in an imaginary ellipse, therefore Mars would continue to revolve in that
same ellipse; and in concluding (before the gap had been filled up by
further observations) that the positions of the planet during the time
which intervened between two observations, must have coincided with the
intermediate points of the curve. For these were facts which had not been
directly observed. They were inferences from the observations; facts
inferred, as distinguished from facts seen. But these inferences were so
far from being a part of Kepler’s philosophical operation, that they had
been drawn long before he was born. Astronomers had long known that the
planets periodically returned to the same places. When this had been
ascertained, there was no induction left for Kepler to make, nor did he
make any further induction. He merely applied his new conception to the
facts inferred, as he did to the facts observed. Knowing already that the
planets continued to move in the same paths; when he found that an ellipse
correctly represented the past path, he knew that it would represent the
future path. In finding a compendious expression for the one set of facts,
he found one for the other: but he found the expression only, not the
inference; nor did he (which is the true test of a general truth) add any
thing to the power of prediction already possessed.
§ 4. The descriptive operation which enables a number of details to be
summed up in a single proposition, Dr. Whewell, by an aptly chosen
expression, has termed the Colligation of Facts. In most of his
observations concerning that mental process I fully agree, and would
gladly transfer all that portion of his book into my own pages. I only
think him mistaken in setting up this kind of operation, which according
to the old and received meaning of the term, is not induction at all, as
the type of induction generally; and laying down, throughout his work, as
principles of induction, the principles of mere colligation.
Dr. Whewell maintains that the general proposition which binds together
the particular facts, and makes them, as it were, one fact, is not the
mere sum of those facts, but something more, since there is introduced a
conception of the mind, which did not exist in the facts themselves. “The
particular facts,” says he,(102) “are not merely brought together, but
there is a new element added to the combination by the very act of thought
by which they are combined.... When the Greeks, after long observing the
motions of the planets, saw that these motions might be rightly considered
as produced by the motion of one wheel revolving in the inside of another
wheel, these wheels were creations of their minds, added to the facts
which they perceived by sense. And even if the wheels were no longer
supposed to be material, but were reduced to mere geometrical spheres or
circles, they were not the less products of the mind alone—something
additional to the facts observed. The same is the case in all other
discoveries. The facts are known, but they are insulated and unconnected,
till the discoverer supplies from his own store a principle of connection.
The pearls are there, but they will not hang together till some one
provides the string.”
Let me first remark that Dr. Whewell, in this passage, blends together,
indiscriminately, examples of both the processes which I am endeavoring to
distinguish from one another. When the Greeks abandoned the supposition
that the planetary motions were produced by the revolution of material
wheels, and fell back upon the idea of “mere geometrical spheres or
circles,” there was more in this change of opinion than the mere
substitution of an ideal curve for a physical one. There was the
abandonment of a theory, and the replacement of it by a mere description.
No one would think of calling the doctrine of material wheels a mere
description. That doctrine was an attempt to point out the force by which
the planets were acted upon, and compelled to move in their orbits. But
when, by a great step in philosophy, the materiality of the wheels was
discarded, and the geometrical forms alone retained, the attempt to
account for the motions was given up, and what was left of the theory was
a mere description of the orbits. The assertion that the planets were
carried round by wheels revolving in the inside of other wheels, gave
place to the proposition, that they moved in the same lines which would be
traced by bodies so carried: which was a mere mode of representing the sum
of the observed facts; as Kepler’s was another and a better mode of
representing the same observations.
It is true that for these simply descriptive operations, as well as for
the erroneous inductive one, a conception of the mind was required. The
conception of an ellipse must have presented itself to Kepler’s mind,
before he could identify the planetary orbits with it. According to Dr.
Whewell, the conception was something added to the facts. He expresses
himself as if Kepler had put something into the facts by his mode of
conceiving them. But Kepler did no such thing. The ellipse was in the
facts before Kepler recognized it; just as the island was an island before
it had been sailed round. Kepler did not _put_ what he had conceived into
the facts, but _saw_ it in them. A conception implies, and corresponds to,
something conceived: and though the conception itself is not in the facts,
but in our mind, yet if it is to convey any knowledge relating to them, it
must be a conception _of_ something which really is in the facts, some
property which they actually possess, and which they would manifest to our
senses, if our senses were able to take cognizance of it. If, for
instance, the planet left behind it in space a visible track, and if the
observer were in a fixed position at such a distance from the plane of the
orbit as would enable him to see the whole of it at once, he would see it
to be an ellipse; and if gifted with appropriate instruments and powers of
locomotion, he could prove it to be such by measuring its different
dimensions. Nay, further: if the track were visible, and he were so placed
that he could see all parts of it in succession, but not all of them at
once, he might be able, by piecing together his successive observations,
to discover both that it was an ellipse and that the planet moved in it.
The case would then exactly resemble that of the navigator who discovers
the land to be an island by sailing round it. If the path was visible, no
one I think would dispute that to identify it with an ellipse is to
describe it: and I can not see why any difference should be made by its
not being directly an object of sense, when every point in it is as
exactly ascertained as if it were so.
Subject to the indispensable condition which has just been stated, I do
not conceive that the part which conceptions have in the operation of
studying facts, has ever been overlooked or undervalued. No one ever
disputed that in order to reason about any thing we must have a conception
of it; or that when we include a multitude of things under a general
expression, there is implied in the expression a conception of something
common to those things. But it by no means follows that the conception is
necessarily pre-existent, or constructed by the mind out of its own
materials. If the facts are rightly classed under the conception, it is
because there is in the facts themselves something of which the conception
is itself a copy; and which if we can not directly perceive, it is because
of the limited power of our organs, and not because the thing itself is
not there. The conception itself is often obtained by abstraction from the
very facts which, in Dr. Whewell’s language, it is afterward called in to
connect. This he himself admits, when he observes (which he does on
several occasions), how great a service would be rendered to the science
of physiology by the philosopher “who should establish a precise, tenable,
and consistent conception of life.”(103) Such a conception can only be
abstracted from the phenomena of life itself; from the very facts which it
is put in requisition to connect. In other cases, no doubt, instead of
collecting the conception from the very phenomena which we are attempting
to colligate, we select it from among those which have been previously
collected by abstraction from other facts. In the instance of Kepler’s
laws, the latter was the case. The facts being out of the reach of being
observed, in any such manner as would have enabled the senses to identify
directly the path of the planet, the conception requisite for framing a
general description of that path could not be collected by abstraction
from the observations themselves; the mind had to supply hypothetically,
from among the conceptions it had obtained from other portions of its
experience, some one which would correctly represent the series of the
observed facts. It had to frame a supposition respecting the general
course of the phenomenon, and ask itself, If this be the general
description, what will the details be? and then compare these with the
details actually observed. If they agreed, the hypothesis would serve for
a description of the phenomenon: if not, it was necessarily abandoned, and
another tried. It is such a case as this which gives rise to the doctrine
that the mind, in framing the descriptions, adds something of its own
which it does not find in the facts.
Yet it is a fact surely, that the planet does describe an ellipse; and a
fact which we could see, if we had adequate visual organs and a suitable
position. Not having these advantages, but possessing the conception of an
ellipse, or (to express the meaning in less technical language) knowing
what an ellipse was, Kepler tried whether the observed places of the
planet were consistent with such a path. He found they were so; and he,
consequently, asserted as a fact that the planet moved in an ellipse. But
this fact, which Kepler did not add to, but found in, the motions of the
planet, namely, that it occupied in succession the various points in the
circumference of a given ellipse, was the very fact, the separate parts of
which had been separately observed; it was the sum of the different
observations.
Having stated this fundamental difference between my opinion and that of
Dr. Whewell, I must add, that his account of the manner in which a
conception is selected, suitable to express the facts, appears to me
perfectly just. The experience of all thinkers will, I believe, testify
that the process is tentative; that it consists of a succession of
guesses; many being rejected, until one at last occurs fit to be chosen.
We know from Kepler himself that before hitting upon the “conception” of
an ellipse, he tried nineteen other imaginary paths, which, finding them
inconsistent with the observations, he was obliged to reject. But as Dr.
Whewell truly says, the successful hypothesis, though a guess, ought
generally to be called, not a lucky, but a skillful guess. The guesses
which serve to give mental unity and wholeness to a chaos of scattered
particulars, are accidents which rarely occur to any minds but those
abounding in knowledge and disciplined in intellectual combinations.
How far this tentative method, so indispensable as a means to the
colligation of facts for purposes of description, admits of application to
Induction itself, and what functions belong to it in that department, will
be considered in the chapter of the present Book which relates to
Hypotheses. On the present occasion we have chiefly to distinguish this
process of Colligation from Induction properly so called; and that the
distinction may be made clearer, it is well to advert to a curious and
interesting remark, which is as strikingly true of the former operation,
as it appears to me unequivocally false of the latter.
In different stages of the progress of knowledge, philosophers have
employed, for the colligation of the same order of facts, different
conceptions. The early rude observations of the heavenly bodies, in which
minute precision was neither attained nor sought, presented nothing
inconsistent with the representation of the path of a planet as an exact
circle, having the earth for its centre. As observations increased in
accuracy, facts were disclosed which were not reconcilable with this
simple supposition: for the colligation of those additional facts, the
supposition was varied; and varied again and again as facts became more
numerous and precise. The earth was removed from the centre to some other
point within the circle; the planet was supposed to revolve in a smaller
circle called an epicycle, round an imaginary point which revolved in a
circle round the earth: in proportion as observation elicited fresh facts
contradictory to these representations, other epicycles and other
eccentrics were added, producing additional complication; until at last
Kepler swept all these circles away, and substituted the conception of an
exact ellipse. Even this is found not to represent with complete
correctness the accurate observations of the present day, which disclose
many slight deviations from an orbit exactly elliptical. Now Dr. Whewell
has remarked that these successive general expressions, though apparently
so conflicting, were all correct: they all answered the purpose of
colligation; they all enabled the mind to represent to itself with
facility, and by a simultaneous glance, the whole body of facts at the
time ascertained: each in its turn served as a correct description of the
phenomena, so far as the senses had up to that time taken cognizance of
them. If a necessity afterward arose for discarding one of these general
descriptions of the planet’s orbit, and framing a different imaginary
line, by which to express the series of observed positions, it was because
a number of new facts had now been added, which it was necessary to
combine with the old facts into one general description. But this did not
affect the correctness of the former expression, considered as a general
statement of the only facts which it was intended to represent. And so
true is this, that, as is well remarked by M. Comte, these ancient
generalizations, even the rudest and most imperfect of them, that of
uniform movement in a circle, are so far from being entirely false, that
they are even now habitually employed by astronomers when only a rough
approximation to correctness is required. “L’astronomie moderne, en
détruisant sans retour les hypothèses primitives, envisagées comme lois
réelles du monde, a soigneusement maintenu leur valeur positive et
permanente, la propriété de représenter commodément les phénomènes quand
il s’agit d’une première ébauche. Nos ressources à cet égard sont même
bien plus étendues, précisément à cause que nous ne nous faisons aucune
illusion sur la réalité des hypothèses; ce qui nous permet d’employer sans
scrupule, en chaque cas, celle que nous jugeons la plus avantageuse.”(104)
Dr. Whewell’s remark, therefore, is philosophically correct. Successive
expressions for the colligation of observed facts, or, in other words,
successive descriptions of a phenomenon as a whole, which has been
observed only in parts, may, though conflicting, be all correct as far as
they go. But it would surely be absurd to assert this of conflicting
inductions.
The scientific study of facts may be undertaken for three different
purposes: the simple description of the facts; their explanation; or their
prediction: meaning by prediction, the determination of the conditions
under which similar facts may be expected again to occur. To the first of
these three operations the name of Induction does not properly belong: to
the other two it does. Now, Dr. Whewell’s observation is true of the first
alone. Considered as a mere description, the circular theory of the
heavenly motions represents perfectly well their general features: and by
adding epicycles without limit, those motions, even as now known to us,
might be expressed with any degree of accuracy that might be required. The
elliptical theory, as a mere description, would have a great advantage in
point of simplicity, and in the consequent facility of conceiving it and
reasoning about it; but it would not really be more true than the other.
Different descriptions, therefore, may be all true: but not, surely,
different explanations. The doctrine that the heavenly bodies moved by a
virtue inherent in their celestial nature; the doctrine that they were
moved by impact (which led to the hypothesis of vortices as the only
impelling force capable of whirling bodies in circles), and the Newtonian
doctrine, that they are moved by the composition of a centripetal with an
original projectile force; all these are explanations, collected by real
induction from supposed parallel cases; and they were all successively
received by philosophers, as scientific truths on the subject of the
heavenly bodies. Can it be said of these, as was said of the different
descriptions, that they are all true as far as they go? Is it not clear
that only one can be true in any degree, and the other two must be
altogether false? So much for explanations: let us now compare different
predictions: the first, that eclipses will occur when one planet or
satellite is so situated as to cast its shadow upon another; the second,
that they will occur when some great calamity is impending over mankind.
Do these two doctrines only differ in the degree of their truth, as
expressing real facts with unequal degrees of accuracy? Assuredly the one
is true, and the other absolutely false.(105)
In every way, therefore, it is evident that to explain induction as the
colligation of facts by means of appropriate conceptions, that is,
conceptions which will really express them, is to confound mere
description of the observed facts with inference from those facts, and
ascribe to the latter what is a characteristic property of the former.
There is, however, between Colligation and Induction, a real correlation,
which it is important to conceive correctly. Colligation is not always
induction; but induction is always colligation. The assertion that the
planets move in ellipses, was but a mode of representing observed facts;
it was but a colligation; while the assertion that they are drawn, or
tend, toward the sun, was the statement of a new fact, inferred by
induction. But the induction, once made, accomplishes the purposes of
colligation likewise. It brings the same facts, which Kepler had connected
by his conception of an ellipse, under the additional conception of bodies
acted upon by a central force, and serves, therefore, as a new bond of
connection for those facts; a new principle for their classification.
Further, the descriptions which are improperly confounded with induction,
are nevertheless a necessary preparation for induction; no less necessary
than correct observation of the facts themselves. Without the previous
colligation of detached observations by means of one general conception,
we could never have obtained any basis for an induction, except in the
case of phenomena of very limited compass. We should not be able to affirm
any predicates at all, of a subject incapable of being observed otherwise
than piecemeal: much less could we extend those predicates by induction to
other similar subjects. Induction, therefore, always presupposes, not only
that the necessary observations are made with the necessary accuracy, but
also that the results of these observations are, so far as practicable,
connected together by general descriptions, enabling the mind to represent
to itself as wholes whatever phenomena are capable of being so
represented.
§ 5. Dr. Whewell has replied at some length to the preceding observations,
restating his opinions, but without (as far as I can perceive) adding any
thing material to his former arguments. Since, however, mine have not had
the good fortune to make any impression upon him, I will subjoin a few
remarks, tending to show more clearly in what our difference of opinion
consists, as well as, in some measure, to account for it.
Nearly all the definitions of induction, by writers of authority, make it
consist in drawing inferences from known cases to unknown; affirming of a
class, a predicate which has been found true of some cases belonging to
the class; concluding because some things have a certain property, that
other things which resemble them have the same property—or because a thing
has manifested a property at a certain time, that it has and will have
that property at other times.
It will scarcely be contended that Kepler’s operation was an Induction in
this sense of the term. The statement, that Mars moves in an elliptical
orbit, was no generalization from individual cases to a class of cases.
Neither was it an extension to all time, of what had been found true at
some particular time. The whole amount of generalization which the case
admitted of, was already completed, or might have been so. Long before the
elliptic theory was thought of, it had been ascertained that the planets
returned periodically to the same apparent places; the series of these
places was, or might have been, completely determined, and the apparent
course of each planet marked out on the celestial globe in an
uninterrupted line. Kepler did not extend an observed truth to other cases
than those in which it had been observed: he did not widen the _subject_
of the proposition which expressed the observed facts. The alteration he
made was in the predicate. Instead of saying, the successive places of
Mars are so and so, he summed them up in the statement, that the
successive places of Mars are points in an ellipse. It is true, this
statement, as Dr. Whewell says, was not the sum of the observations
_merely_; it was the sum of the observations _seen under a new point of
view_.(106) But it was not the sum of _more_ than the observations, as a
real induction is. It took in no cases but those which had been actually
observed, or which could have been inferred from the observations before
the new point of view presented itself. There was not that transition from
known cases to unknown, which constitutes Induction in the original and
acknowledged meaning of the term.
Old definitions, it is true, can not prevail against new knowledge: and if
the Keplerian operation, as a logical process, be really identical with
what takes place in acknowledged induction, the definition of induction
ought to be so widened as to take it in; since scientific language ought
to adapt itself to the true relations which subsist between the things it
is employed to designate. Here then it is that I am at issue with Dr.
Whewell. He does think the operations identical. He allows of no logical
process in any case of induction, other than what there was in Kepler’s
case, namely, guessing until a guess is found which tallies with the
facts; and accordingly, as we shall see hereafter, he rejects all canons
of induction, because it is not by means of them that we guess. Dr.
Whewell’s theory of the logic of science would be very perfect if it did
not pass over altogether the question of Proof. But in my apprehension
there is such a thing as proof, and inductions differ altogether from
descriptions in their relation to that element. Induction is proof; it is
inferring something unobserved from something observed: it requires,
therefore, an appropriate test of proof; and to provide that test, is the
special purpose of inductive logic. When, on the contrary, we merely
collate known observations, and, in Dr. Whewell’s phraseology, connect
them by means of a new conception; if the conception does serve to connect
the observations, we have all we want. As the proposition in which it is
embodied pretends to no other truth than what it may share with many other
modes of representing the same facts, to be consistent with the facts is
all it requires: it neither needs nor admits of proof; though it may serve
to prove other things, inasmuch as, by placing the facts in mental
connection with other facts, not previously seen to resemble them, it
assimilates the case to another class of phenomena, concerning which real
Inductions have already been made. Thus Kepler’s so-called law brought the
orbit of Mars into the class ellipse, and by doing so, proved all the
properties of an ellipse to be true of the orbit: but in this proof
Kepler’s law supplied the minor premise, and not (as is the case with real
Inductions) the major.
Dr. Whewell calls nothing Induction where there is not a new mental
conception introduced, and every thing induction where there is. But this
is to confound two very different things, Invention and Proof. The
introduction of a new conception belongs to Invention: and invention may
be required in any operation, but is the essence of none. A new conception
may be introduced for descriptive purposes, and so it may for inductive
purposes. But it is so far from constituting induction, that induction
does not necessarily stand in need of it. Most inductions require no
conception but what was present in every one of the particular instances
on which the induction is grounded. That all men are mortal is surely an
inductive conclusion; yet no new conception is introduced by it. Whoever
knows that any man has died, has all the conceptions involved in the
inductive generalization. But Dr. Whewell considers the process of
invention which consists in framing a new conception consistent with the
facts, to be not merely a necessary part of all induction, but the whole
of it.
The mental operation which extracts from a number of detached observations
certain general characters in which the observed phenomena resemble one
another, or resemble other known facts, is what Bacon, Locke, and most
subsequent metaphysicians, have understood by the word Abstraction. A
general expression obtained by abstraction, connecting known facts by
means of common characters, but without concluding from them to unknown,
may, I think, with strict logical correctness, be termed a Description;
nor do I know in what other way things can ever be described. My position,
however, does not depend on the employment of that particular word; I am
quite content to use Dr. Whewell’s term Colligation, or the more general
phrases, “mode of representing, or of expressing, phenomena:” provided it
be clearly seen that the process is not Induction, but something radically
different.
What more may usefully be said on the subject of Colligation, or of the
correlative expression invented by Dr. Whewell, the Explication of
Conceptions, and generally on the subject of ideas and mental
representations as connected with the study of facts, will find a more
appropriate place in the Fourth Book, on the Operations Subsidiary to
Induction: to which I must refer the reader for the removal of any
difficulty which the present discussion may have left.