In instances in which the number of particular cases is limited, the necessary existence of a logical flaw in the syllogistic translation of the process is not so evident. But in truth, such a flaw exists in all cases of Induction proper: (for Induction by mere enumeration can hardly be called Induction). I will, however, consider for a moment the instance of a celebrated proposition which has often been taken as an example of Induction, and in which the number of particular cases is, or at least is at present supposed to be, limited. Kepler's laws, for instance the law that the planets describe ellipses, may be regarded as examples of Induction. The law was inferred, we will suppose, from an examination of the orbits of Mars, Earth, Venus. And the syllogistic illustration which Aristotle gives, will, with the necessary addition to it, stand thus,
Mars, Earth, Venus describe ellipses.
Mars, Earth, Venus are planets.
Assuming the convertibility of this last proposition, and its universality, (which is the necessary addition in order to make Aristotle's syllogism valid) we say
All the planets are as Mars, Earth, Venus.
Whence it follows that all the planets describe ellipses.
If, instead of this assumed universality, the astronomer had made a real enumeration, and had established the fact of each particular, he would be able to say
Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe ellipses.
Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the planets.
And he would obviously be entitled to convert the second proposition, and then to conclude that
All the planets describe ellipses.
But then, if this were given as an illustration of Induction by means of syllogism, we should have to remark, in the first place, that the conclusion that "all the planets describe ellipses," adds nothing to the major proposition, that "S., J., M., E., V., m., do so." It is merely the same proposition expressed in other words, so long as S., J., M., E., V., m., are supposed to be all the planets. And in the next place we have to make a remark which is more important; that the minor, in such an example, must generally be either a very precarious truth, or, as appears in this case, a transitory error. For that the planets known at any time are all the planets, must always be a doubtful assertion, liable to be overthrown to-night by an astronomical observation. And the assertion, as received in Kepler's time, has been overthrown. For Saturn, Jupiter, Mars, Earth, Venus, Mercury, are not all the planets. Not only have several new ones been discovered at intervals, as Uranus, Ceres, Juno, Pallas, Vesta, but we have new ones discovered every day; and any conclusion depending upon this premiss that A, B, C, D, E, F, G, H, to Z are all the planets, is likely to be falsified in a few years by the discovery of A´, B´, C´, &c. If, therefore, this were the syllogistic analysis of Induction, Kepler's discovery rested upon a false proposition; and even if the analysis were now made conformable to our present knowledge, that induction, analysed as above, would still involve a proposition which to-morrow may show to be false. But yet no one, I suppose, doubts that Kepler's discovery was really a discovery—the establishment of a scientific truth on solid grounds; or, that it is a scientific truth for us, notwithstanding that we are constantly discovering new planets. Therefore the syllogistic analysis of it now discussed (namely, that which introduces simple enumeration as a step) is not the right analysis, and does not represent the grounds of the Inductive Truth, that all the planets describe ellipses.