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.