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 can not, 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 can not 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 connection 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 can not 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 favor 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.
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 favor of, the moon’s being inhabited. Since life can not 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 favor
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 connection
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 co-existed 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 can not accept as positive truths 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.”(183) 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 further, 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.