again, the hypothesis of a law with which the process starts
contains more than is present in the particular data: according
to Jevons, it is the hypothesis of a law of a cause from which
induction deduces particular effects; and according to Sigwart,
it is a hypothesis of the ground from which the particular data
necessarily follow according to universal laws. Lastly, Wundt’s
view is an interesting piece of eclecticism, for he supposes that
induction begins in the form of Aristotle’s inductive syllogism,
S–P, S–M, M–P, and becomes an inductive method in the form
of Jevons’s inverse deduction, or hypothetical deduction, or
analysis, M–P, S–M, S–P. In detail, he supposes that, while
an “inference by comparison,” which he erroneously calls an
affirmative syllogism in the second figure, is preliminary to
induction, a second “inference by connexion,” which he
erroneously calls a syllogism in the third figure with an indeterminate
conclusion, is the inductive syllogism itself. This is like
Aristotle’s inductive syllogism in the arrangement of terms;
but, while on the one hand Aristotle did not, like Wundt, confuse
it with the third figure, on the other hand Wundt does not, like
Aristotle, suppose it to be practicable to get inductive data so
wide as the convertible premise, “All S is M, and all M is S,”
which would at once establish the conclusion, “All M is P.”
Wundt’s point is that the conclusion of the inductive syllogism
is neither so much as all, nor so little as some, but rather the
indeterminate “M and P are connected.” The question therefore
arises, how we are to discover “All M is P,” and this question
Wundt answers by adding an inductive method, which involves
inverting the inductive syllogism in the style of Aristotle into a
deductive syllogism from a hypothesis in the style of Jevons,
thus:—
| (1) | (2) | |
| S is P. | Every | M is P. |
| S is M. | S is M. | |
| ∴M and P are connected. | ∴ | S is P. |
He agrees with Jevons in calling this second syllogism analytical deduction, and with Jevons and Sigwart in calling it hypothetical deduction. It is, in fact, a common point of Jevons, Sigwart and Wundt that the universal is not really a conclusion inferred from given particulars, but a hypothetical major premise from which given particulars are inferred, and that this major contains presuppositions of causation not contained in the particulars.
It is noticeable that Wundt quotes Newton’s discovery of the centripetal force of the planets to the sun as an instance of this supposed hypothetical, analytic, inductive method; as if Newton’s analysis were a hypothesis of the centripetal force to the sun, a deduction of the given facts of planetary motion, and a verification of the hypothesis by the given facts, and as if such a process of hypothetical deduction could be identical with either analysis or induction. The abuse of this instance of Newtonian analysis betrays the whole origin of the current confusion of induction with deduction. One confusion has led to another. Mill confused Newton’s analytical deduction with hypothetical deduction; and thereupon Jevons confused induction with both. The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences. But we can easily extricate ourselves from these confusions by comparing induction with different kinds of deduction. The point about induction is that it starts from experience, and that, though in most classes we can experience only some particulars individually, yet we infer all. Hence induction cannot be reduced to Aristotle’s inductive syllogism, because experience cannot give the convertible premise, “Every S is M, and every M is S”; that “All A, B, C are magnets” is, but that “All magnets are A, B, C” is not, a fact of experience. For the same reason induction cannot be reduced to analytical deduction of the second kind in the form, S–P, M–S, ∴ M–P; because, though both end in a universal conclusion, the limits of experience prevent induction from such inference as:—
| Every experienced magnet attracts iron. |
| Every magnet whatever is every experienced magnet. |
| ∴Every magnet whatever attracts iron. |
Still less can induction be reduced to analytical deduction of the first kind in the form—P–M, S–P, ∴ S–M, of which Newton has left so conspicuous an example in his Principia. As the example shows, that analytic process starts from the scientific knowledge of a universal and convertible law (every M is P, and every P is M), e.g. a mechanical law of all centripetal force, and ends in a particular application, e.g. this centripetal force of planets to the sun. But induction cannot start from a known law. Hence it is that Jevons, followed by Sigwart and Wundt, reduces it to deduction from a hypothesis in the form “Let every M be P, S is M, ∴ S is P.” There is a superficial resemblance between induction and this hypothetical deduction. Both in a way use given particulars as evidence. But in induction the given particulars are the evidence by which we discover the universal, e.g. particular magnets attracting iron are the origin of an inference that all do; in hypothetical deduction, the universal is the evidence by which we explain the given particulars, as when we suppose undulating aether to explain the facts of heat and light. In the former process, the given particulars are the data from which we infer the universal; in the latter, they are only the consequent facts by which we verify it. Or rather, there are two uses of induction: inductive discovery before deduction, and inductive verification after deduction. But neither use of induction is the same as the deduction itself: the former precedes, the latter follows it. Lastly, the theory of Mill, though frequently adopted, e.g. by B. Erdmann, need not detain us long. Most inductions are made without any assumption of the uniformity of nature; for, whether it is itself induced, or a priori or postulated, this like every assumption is a judgment, and most men are incapable of judgment on so universal a scale, when they are quite capable of induction. The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in Physical Realism, and afterwards in Venn’s Empirical Logic. The axiom of contradiction is not a major premise of a judgment: the dictum de omni et nullo is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction. Induction, in fact, is no species of deduction; they are opposite processes, as Aristotle regarded them except in the one passage where he was reducing the former to the latter, and as Bacon always regarded them. But it is easy to confuse them by mistaking examples of deduction for inductions. Thus Whewell mistook Kepler’s inference that Mars moves in an ellipse for an induction, though it required the combination of Tycho’s and Kepler’s observations, as a minor, with the laws of conic sections discovered by the Greeks, as a major, premise. Jevons, in his Principles of Science, constantly makes the same sort of mistake. For example, the inference from the similarity between solar spectra and the spectra of various gases on the earth to the existence of similar gases in the sun, is called by him an induction; but it really is an analytical deduction from effect to cause, thus:—
| Such and such spectra are effects of various gases. |
| Solar spectra are such spectra. |
| ∴Solar spectra are effects of those gases. |
In the same way, to infer a machine from hearing the regular tick of a clock, to infer a player from finding a pack of cards arranged in suits, to infer a human origin of stone implements, and all such inferences from patent effects to latent causes, though they appear to Jevons to be typical inductions, are really deductions which, besides the minor premise stating the particular effects, require a major premise discovered by a previous induction and stating the general kind of effects of a general kind of cause. B. Erdmann, again, has invented an induction from particular predicates to a totality of predicates which he calls “ergänzende Induction,” giving as an example, “This body has the colour, extensibility and specific gravity of magnesium; therefore it is magnesium.” But this inference contains the tacit major, “What has a given colour, &c., is magnesium,” and is a syllogism of recognition. A deduction is often like an induction, in inferring from particulars; the difference is that
