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 anything 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 reassertion 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, cannot 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
cannot 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 an 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 cannot 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[2]) 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 an 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
cannot 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 _à 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 _à 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, cannot but perceive that in raising a binomial to a
power, the coefficients must depend on the laws of permutation and
combination: and as soon as this is recognised, 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 cannot 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 anything of the nature of an induction in this process? Did he
infer anything 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 anything 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,[3] "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 connexion. 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 endeavouring
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 recognised 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 cannot 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
cannot 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 anything 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 cannot 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 afterwards 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."[4] 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 skilful 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, and facts were disclosed which were not
reconcileable 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 excentrics 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 afterwards 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."[5]
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.[6]
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, towards 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 connexion 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, re-stating his opinions, but without (as far as I can
perceive) adding anything 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_.[7] 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, cannot 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 connexion 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 everything 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.