INFERENCE FROM ANALOGY.
The word Analogy was appropriated by Mill, in accordance with the
usage of the eighteenth century, to designate a ground of inference
distinct from that on which we proceed in extending a law, empirical
or scientific, to a new case. But it is used in various other senses,
more or less similar, and in order to make clear the exact logical
sense, it is well to specify some of these. The original word
[Greek: analogia], as employed by Aristotle, corresponds to the word
Proportion in Arithmetic: it signified an equality of ratios, [Greek:
isotes logon]: two compared with four is analogous to four compared
with eight. There is something of the same meaning in the technical
use of the word in Physiology, where it is used to signify similarity
of function as distinguished from similarity of structure, which is
called homology: thus the tail of a whale is analogous to the tail
of a fish, inasmuch as it is similarly used for motion, but it
is homologous with the hind legs of a quadruped; a man's arms are
homologous with a horse's fore legs, but they are not analogous
inasmuch as they are not used for progression. Apart from these
technical employments, the word is loosely used in common speech for
any kind of resemblance. Thus De Quincey speaks of the "analogical"
power in memory, meaning thereby the power of recalling things by
their inherent likeness as distinguished from their casual connexions
or their order in a series. But even in common speech, there is a
trace of the original meaning: generally when we speak of analogy we
have in our minds more than one pair of things, and what we call
the analogy is some resemblance between the different pairs. This
is probably what Whately had in view when he defined analogy as
"resemblance of relations".
In a strict logical sense, however, as defined by Mill, sanctioned
by the previous usage of Butler and Kant, analogy means more than
a resemblance of relations. It means a preponderating resemblance
between two things such as to warrant us in inferring that the
resemblance extends further. This is a species of argument distinct
from the extension of an empirical law. In the extension of an
empirical law, the ground of inference is a coincidence frequently
repeated within our experience, and the inference is that it has
occurred or will occur beyond that experience: in the argument from
analogy, the ground of inference is the resemblance between two
individual objects or kinds of objects in a certain number of points,
and the inference is that they resemble one another in some other
point, known to belong to the one, but not known to belong to the
other. "Two things go together in many cases, therefore in all,
including this one," is the argument in extending a generalisation:
"Two things agree in many respects, therefore in this other," is the
argument from analogy.
The example given by Reid in his _Intellectual Powers_ has become the
standard illustration of the peculiar argument from analogy.
We may observe a very great similitude between this earth
which we inhabit, and the other planets, Saturn, Jupiter,
Mars, Venus and Mercury. They all revolve round the sun,
as the earth does, although at different distances and in
different periods. They borrow all their light from the sun,
as the earth does. Several of them are known to revolve
round their axis like the earth, and by that means have like
succession of day and night. Some of them have moons, that
serve to give them light in the absence of the sun, as our
moon does to us. They are all, in their motions, subject to
the same law of gravitation as the earth is. From all this
similitude it is not unreasonable to think that these planets
may, like our earth, be the habitation of various orders of
living creatures. There is some probability in this conclusion
from analogy.[1]
The argument from analogy is sometimes said to range through all
degrees of probability from certainty to zero. But this is true only
if we take the word analogy in its loosest sense for any kind of
resemblance. If we do this, we may call any kind of argument an
argument from analogy, for all inferences turn upon resemblance. I
believe that if I throw my pen in the air it will come down again,
because it is like other ponderable bodies. But if we use the word in
its limited logical sense, the degree of probability is much nearer
zero than certainty. This is apparent from the conditions that
logicians have formulated of a strict argument from analogy.
1. The resemblance must be preponderating. In estimating the value of
an argument from analogy, we must reckon the points of difference
as counting against the conclusion, and also the points in regard
to which we do not know whether the two objects agree or differ. The
numerical measure of value is the ratio of the points of resemblance
to the points of difference _plus_ the unknown points. Thus, in the
argument that the planets are inhabited because they resemble the
earth in some respects and the earth is inhabited, the force of the
analogy is weakened by the fact that we know very little about the
surface of the planets.
2. In a numerical estimate all circumstances that hang together as
effects of one cause must be reckoned as one. Otherwise, we might make
a fallaciously imposing array of points of resemblance. Thus in Reid's
enumeration of the agreements between the earth and the planets, their
revolution round the sun and their obedience to the law of gravitation
should count as one point of resemblance. If two objects agree in _a_,
_b_, _c_, _d_, _e_, but _b_ follows from _a_, and _d_ and _e_ from
_c_, the five points count only as two.
3. If the object to which we infer is known to possess some property
incompatible with the property inferred, the general resemblance
counts for nothing. The moon has no atmosphere, and we know that air
is an indispensable condition of life. Hence, however much the moon
may resemble the earth, we are debarred from concluding that there are
living creatures on the moon such as we know to exist on the earth. We
know also that life such as it is on the earth is possible only within
certain limits of temperature, and that Mercury is too hot for life,
and Saturn too cold, no matter how great the resemblance to the earth
in other respects.
4. If the property inferred is known or presumed to be a concomitant
of one or more of the points of resemblance, any argument from analogy
is superfluous. This is, in effect, to say that we have no occasion to
argue from general resemblance when we have reason to believe that a
property follows from something that an object is known to possess.
If we knew that any one of the planets possessed all the conditions,
positive and negative, of life, we should not require to reckon up
all the respects in which it resembles the earth in order to create
a presumption that it is inhabited. We should be able to draw the
conclusion on other grounds than those of analogy. Newton's famous
inference that the diamond is combustible is sometimes quoted as an
argument from analogy. But, technically speaking, it was rather,
as Professor Bain has pointed out, of the nature of an extended
generalisation. Comparing bodies in respect of their densities and
refracting powers, he observed that combustible bodies refract more
than others of the same density; and observing the exceptionally high
refracting power of the diamond, he inferred from this that it was
combustible, an inference afterwards confirmed by experiment. "The
concurrence of high refracting power with inflammability was an
empirical law; and Newton, perceiving the law, extended it to the
adjacent case of the diamond. The remark is made by Brewster that had
Newton known the refractive powers of the minerals _greenockite_ and
_octohedrite_, he would have extended the inference to them, and would
have been mistaken."[2]
From these conditions it will be seen that we cannot conclude with any
high degree of probability from analogy alone. This is not to deny, as
Mr. Jevons seems to suppose, that analogies, in the sense of general
resemblances, are often useful in directing investigation. When
we find two things very much alike, and ascertain that one of them
possesses a certain property, the presumption that the other has
the same is strong enough to make it worth while trying whether as a
matter of fact it has. It is said that a general resemblance of the
hills near Ballarat in Australia to the Californian hills where gold
had been found suggested the idea of digging for gold at Ballarat.
This was a lucky issue to an argument from analogy, but doubtless many
have dug for gold on similar general resemblances without finding that
the resemblance extended to that particular. Similarly, many of
the extensions of the Pharmacopeia have proceeded upon general
resemblances, the fact that one drug resembles another in certain
properties being a sufficient reason for trying whether the
resemblance goes further. The lucky guesses of what is known as
natural sagacity are often analogical. A man of wide experience in any
subject-matter such as the weather, or the conduct of men in war, in
business, or in politics, may conclude to the case in hand from some
previous case that bears a general resemblance to it, and very often
his conclusions may be perfectly sound though he has not made a
numerical estimate of the data.
The chief source of fallacy in analogical argument is ignoring the
number of points of difference. It often happens that an amount of
resemblance only sufficient for a rhetorical simile is made to do duty
as a solid argument. Thus the resemblance between a living body
and the body politic is sometimes used to support inferences from
successful therapeutic treatment to State policy. The advocates of
annual Parliaments in the time of the Commonwealth based their case on
the serpent's habit of annually casting its skin.
Wisest of beasts the serpent see,
Just emblem of eternity,
And of a State's duration;
Each year an annual skin he takes,
And with fresh life and vigour wakes
At every renovation.
Britain! that serpent imitate.
Thy Commons House, that skin of State,
By annual choice restore;
So choosing thou shall live secure,
And freedom to thy sons inure,
Till Time shall be no more.
Carlyle's saying that a ship could never be taken round Cape Horn if
the crew were consulted every time the captain proposed to alter
the course, if taken seriously as an analogical argument against
Representative Government, is open to the objection that the
differences between a ship and a State are too great for any argument
from one to the other to be of value. It was such fallacious analogies
as these that Heine had in view in his humorous prayer, "Heaven defend
us from the Evil One and from metaphors".
[Footnote 1: Hamilton's _Reid_, p. 236.]
[Footnote 2: Bain's _Logic_, ii. 145.]
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Transcriber's Note:
page 113: 'aneo symplokes' corrected to 'aneu symplokes'
End of Project Gutenberg's Logic, Inductive and Deductive, by William Minto