OF ANALOGY.
§ 1. The word Analogy, as the name of a mode of reasoning, is generally
taken for some kind of argument supposed to be of an inductive nature,
but not amounting to a complete induction. There is no word, however,
which is used more loosely, or in a greater variety of senses, than
Analogy. It sometimes stands for arguments which may be examples of the
most rigorous Induction. Archbishop Whately, for instance, following
Ferguson and other writers, defines Analogy conformably to its primitive
acceptation, that which was given to it by mathematicians, Resemblance
of Relations. In this sense, when a country which has sent out colonies
is termed the mother country, the expression is analogical, signifying
that the colonies of a country stand in the same _relation_ to her in
which children stand to their parents. And if any inference be drawn
from this resemblance of relations, as, for instance, that obedience or
affection is due from colonies to the mother country, this is called
reasoning by analogy. Or if it be argued that a nation is most
beneficially governed by an assembly elected by the people, from the
admitted fact that other associations for a common purpose, such as
joint-stock companies, are best managed by a committee chosen by the
parties interested; this, too, is an argument from analogy in the
preceding sense, because its foundation is, not that a nation is like a
joint stock company, or Parliament like a board of directors, but that
Parliament stands in the same _relation_ to the nation in which a board
of directors stands to a joint stock company. Now, in an argument of
this nature, there is no inherent inferiority of conclusiveness. Like
other arguments from resemblance, it may amount to nothing, or it may be
a perfect and conclusive induction. The circumstance in which the two
cases resemble, may be capable of being shown to be the _material_
circumstance; to be that on which all the consequences, necessary to be
taken into account in the particular discussion, depend. In the example
last given, the resemblance is one of relation; the _fundamentum
relationis_ being the management by a few persons, of affairs in which a
much greater number are interested along with them. Now, some may
contend that this circumstance which is common to the two cases, and the
various consequences which follow from it, have the chief share in
determining all the effects which make up what we term good or bad
administration. If they can establish this, their argument has the force
of a rigorous induction; if they cannot, they are said to have failed in
proving the analogy between the two cases; a mode of speech which
implies that when the analogy can be proved, the argument founded on it
cannot be resisted.
§ 2. It is on the whole more usual, however, to extend the name of
analogical evidence to arguments from any sort of resemblance, provided
they do not amount to a complete induction: without peculiarly
distinguishing resemblance of relations. Analogical reasoning, in this
sense, may be reduced to the following formula:--Two things resemble
each other in one or more respects; a certain proposition is true of the
one; therefore it is true of the other. But we have nothing here by
which to discriminate analogy from induction, since this type will serve
for all reasoning from experience. In the strictest induction, equally
with the faintest analogy, we conclude because A resembles B in one or
more properties, that it does so in a certain other property. The
difference is, that in the case of a complete induction it has been
previously shown, by due comparison of instances, that there is an
invariable conjunction between the former property or properties and the
latter property; but in what is called analogical reasoning, no such
conjunction has been made out. There have been no opportunities of
putting in practice the Method of Difference, or even the Method of
Agreement; but we conclude (and that is all which the argument of
analogy amounts to) that a fact _m_, known to be true of A, is more
likely to be true of B if B agrees with A in some of its properties
(even though no connexion is known to exist between _m_ and those
properties), than if no resemblance at all could be traced between B and
any other thing known to possess the attribute _m_.
To this argument it is of course requisite, that the properties common
to A with B shall be merely not known to be connected with _m_; they
must not be properties known to be unconnected with it. If, either by
processes of elimination, or by deduction from previous knowledge of the
laws of the properties in question, it can be concluded that they have
nothing to do with _m_, the argument of analogy is put out of court. The
supposition must be that _m_ is an effect really dependent on some
property of A, but we know not on which. We cannot point out any of the
properties of A, which is the cause of _m_, or united with it by any
law. After rejecting all which we know to have nothing to do with it,
there remain several between which we are unable to decide: of which
remaining properties, B possesses one or more. This accordingly, we
consider as affording grounds, of more or less strength, for concluding
by analogy that B possesses the attribute _m_.
There can be no doubt that every such resemblance which can be pointed
out between B and A, affords some degree of probability, beyond what
would otherwise exist, in favour of the conclusion drawn from it. If B
resembled A in all its ultimate properties, its possessing the attribute
_m_ would be a certainty, not a probability: and every resemblance which
can be shown to exist between them, places it by so much the nearer to
that point. If the resemblance be in an ultimate property, there will be
resemblance in all the derivative properties dependent on that ultimate
property, and of these _m_ may be one. If the resemblance be in a
derivative property, there is reason to expect resemblance in the
ultimate property on which it depends, and in the other derivative
properties dependent on the same ultimate property. Every resemblance
which can be shown to exist, affords ground for expecting an indefinite
number of other resemblances: the particular resemblance sought will,
therefore, be oftener found among things thus known to resemble, than
among things between which we know of no resemblance.[24]
For example, I might infer that there are probably inhabitants in the
moon, because there are inhabitants on the earth, in the sea, and in the
air: and this is the evidence of analogy. The circumstance of having
inhabitants is here assumed not to be an ultimate property, but (as is
reasonable to suppose) a consequence of other properties; and depending,
therefore, in the case of the earth, on some of its properties as a
portion of the universe, but on which of those properties we know not.
Now the moon resembles the earth in being a solid, opaque, nearly
spherical substance, appearing to contain, or to have contained, active
volcanoes; receiving heat and light from the sun, in about the same
quantity as our earth; revolving on its axis; composed of materials
which gravitate, and obeying all the various laws resulting from that
property. And I think no one will deny that if this were all that was
known of the moon, the existence of inhabitants in that luminary would
derive from these various resemblances to the earth, a greater degree of
probability than it would otherwise have: though the amount of the
augmentation it would be useless to attempt to estimate.
If, however, every resemblance proved between B and A, in any point not
known to be immaterial with respect to _m_, forms some additional
reason for presuming that B has the attribute _m_; it is clear, _è
contra_, that every dissimilarity which can be proved between them,
furnishes a counter-probability of the same nature on the other side. It
is not indeed unusual that different ultimate properties should, in some
particular instances, produce the same derivative property; but on the
whole it is certain that things which differ in their ultimate
properties, will differ at least as much in the aggregate of their
derivative properties, and that the differences which are unknown will
on the average of cases bear some proportion to those which are known.
There will, therefore, be a competition between the known points of
agreement and the known points of difference in A and B; and according
as the one or the other may be deemed to preponderate, the probability
derived from analogy will be for or against B's having the property _m_.
The moon, for instance, agrees with the earth in the circumstances
already mentioned; but differs in being smaller, in having its surface
more unequal, and apparently volcanic throughout, in having, at least on
the side next the earth, no atmosphere sufficient to refract light, no
clouds, and (it is therefore concluded) no water. These differences,
considered merely as such, might perhaps balance the resemblances, so
that analogy would afford no presumption either way. But considering
that some of the circumstances which are wanting on the moon are among
those which, on the earth, are found to be indispensable conditions of
animal life, we may conclude that if that phenomenon does exist in the
moon, (or at all events on the nearer side,) it must be as an effect of
causes totally different from those on which it depends here; as a
consequence, therefore, of the moon's differences from the earth, not of
the points of agreement. Viewed in this light, all the resemblances
which exist become presumptions against, not in favour of, the moon's
being inhabited. Since life cannot exist there in the manner in which it
exists here, the greater the resemblance of the lunar world to the
terrestrial in other respects, the less reason we have to believe that
it can contain life.
There are, however, other bodies in our system, between which and the
earth there is a much closer resemblance; which possess an atmosphere,
clouds, consequently water (or some fluid analogous to it), and even
give strong indications of snow in their polar regions; while the cold,
or heat, though differing greatly on the average from ours, is, in some
parts at least of those planets, possibly not more extreme than in some
regions of our own which are habitable. To balance these agreements, the
ascertained differences are chiefly in the average light and heat,
velocity of rotation, density of material, intensity of gravity, and
similar circumstances of a secondary kind. With regard to these planets,
therefore, the argument of analogy gives a decided preponderance in
favour of their resembling the earth in any of its derivative
properties, such as that of having inhabitants; though, when we consider
how immeasurably multitudinous are those of their properties which we
are entirely ignorant of, compared with the few which we know, we can
attach but trifling weight to any considerations of resemblance in which
the known elements bear so inconsiderable a proportion to the unknown.
Besides the competition between analogy and diversity, there may be a
competition of conflicting analogies. The new case may be similar in
some of its circumstances to cases in which the fact _m_ exists, but in
others to cases in which it is known not to exist. Amber has some
properties in common with vegetable, others with mineral products. A
painting of unknown origin, may resemble, in certain of its characters,
known works of a particular master, but in others it may as strikingly
resemble those of some other painter. A vase may bear some analogy to
works of Grecian, and some to those of Etruscan, or Egyptian art. We are
of course supposing that it does not possess any quality which has been
ascertained, by a sufficient induction, to be a conclusive mark either
of the one or of the other.
§ 3. Since the value of an analogical argument inferring one resemblance
from other resemblances without any antecedent evidence of a connexion
between them, depends on the extent of ascertained resemblance, compared
first with the amount of ascertained difference, and next with the
extent of the unexplored region of unascertained properties; it follows
that where the resemblance is very great, the ascertained difference
very small, and our knowledge of the subject-matter tolerably extensive,
the argument from analogy may approach in strength very near to a valid
induction. If, after much observation of B, we find that it agrees with
A in nine out of ten of its known properties, we may conclude with a
probability of nine to one, that it will possess any given derivative
property of A. If we discover, for example, an unknown animal or plant,
resembling closely some known one in the greater number of the
properties we observe in it, but differing in some few, we may
reasonably expect to find in the unobserved remainder of its properties,
a general agreement with those of the former; but also a difference
corresponding proportionately to the amount of observed diversity.
It thus appears that the conclusions derived from analogy are only of
any considerable value, when the case to which we reason is an adjacent
case; adjacent, not as before, in place or time, but in circumstances.
In the case of effects of which the causes are imperfectly or not at all
known, when consequently the observed order of their occurrence amounts
only to an empirical law, it often happens that the conditions which
have coexisted whenever the effect was observed, have been very
numerous. Now if a new case presents itself, in which all these
conditions do not exist, but the far greater part of them do, some one
or a few only being wanting, the inference that the effect will occur,
notwithstanding this deficiency of complete resemblance to the cases in
which it has been observed, may, though of the nature of analogy,
possess a high degree of probability. It is hardly necessary to add
that, however considerable this probability may be, no competent
inquirer into nature will rest satisfied with it when a complete
induction is attainable; but will consider the analogy as a mere
guide-post, pointing out the direction in which more rigorous
investigations should be prosecuted.
It is in this last respect that considerations of analogy have the
highest scientific value. The cases in which analogical evidence affords
in itself any very high degree of probability, are, as we have observed,
only those in which the resemblance is very close and extensive; but
there is no analogy, however faint, which may not be of the utmost value
in suggesting experiments or observations that may lead to more positive
conclusions. When the agents and their effects are out of the reach of
further observation and experiment, as in the speculations already
alluded to respecting the moon and planets, such slight probabilities
are no more than an interesting theme for the pleasant exercise of
imagination; but any suspicion, however slight, that sets an ingenious
person at work to contrive an experiment, or affords a reason for trying
one experiment rather than another, may be of the greatest benefit to
science.
On this ground, though I cannot accept as positive doctrines any of
those scientific hypotheses which are unsusceptible of being ultimately
brought to the test of actual induction, such, for instance, as the two
theories of light, the emission theory of the last century, and the
undulatory theory which predominates in the present, I am yet unable to
agree with those who consider such hypotheses to be worthy of entire
disregard. As is well said by Hartley (and concurred in by a thinker in
general so diametrically opposed to Hartley's opinions as Dugald
Stewart), "any hypothesis which has so much plausibility as to explain a
considerable number of facts, helps us to digest these facts in proper
order, to bring new ones to light, and make _experimenta crucis_ for the
sake of future inquirers."[25] If an hypothesis both explains known
facts, and has led to the prediction of others previously unknown, and
since verified by experience, the laws of the phenomenon which is the
subject of inquiry must bear at least a great similarity to those of the
class of phenomena to which the hypothesis assimilates it; and since the
analogy which extends so far may probably extend farther, nothing is
more likely to suggest experiments tending to throw light upon the real
properties of the phenomenon, than the following out such an hypothesis.
But to this end it is by no means necessary that the hypothesis be
mistaken for a scientific truth. On the contrary, that illusion is in
this respect, as in every other, an impediment to the progress of real
knowledge, by leading inquirers to restrict themselves arbitrarily to
the particular hypothesis which is most accredited at the time, instead
of looking out for every class of phenomena between the laws of which
and those of the given phenomenon any analogy exists, and trying all
such experiments as may tend to the discovery of ulterior analogies
pointing in the same direction.