have already got by induction-explain the facts,-more of the facts, all of the facts? Does it extend to cases where I cannot observe the cause already in operation, but the results of which seem to be in conformity with this as the cause? What is its probability, its generality? This is frequently to be tested by deduction-Material Deduction. This means taking the conception formulated in the hypothesis, or taking the limited uniformity, and calculating with this as a basis what should happen in certain circumstances, or in a sphere wider than that already embraced by us. This is experimental rather than observational. Newton might apply the conception of gravity to the motion of the moon to discover whether attraction subsisted between it and the earth. Observation of the facts corresponded with the results of the deduction that is, what ought to be the hypothesis or limited law extended to this new sphere. And so with the moon and the sun. Doubtless this is the way in which science progresses, and this was not a form of method, at least explicitly contemplated by the modern founder of Inductive Method-Lord Bacon. At the same time it is not just to say that Bacon limited scientific method simply to observation and induction from facts and laws of increasing generality. His Prerogative Instances, especially the Migrantes and Crucial, show how he could look at characteristic facts, and specially select them. Modern Deductive Method is in no way incompatible with Baconianism. Bacon's denunciation of "the anticipation of nature," as opposed to "the interpretation of nature," was eminently sound. In warning men against projecting their mere "conceits" into the course of nature, and thinking they find them there, Bacon did an incalculable service to science. Facts are the first thing -conceptions, hypotheses, modes of explanation may follow. He fully admits the value of hypotheses-that is, of questions to put to nature. The most and best questioning man will be the discoverer in the end, provided he has caution, zeal, application, as Newton had. But testing, verification, deduction are in the end to appear before the bar of Observation; and it is because of the harmony which subsists between the most laborious, the most ingenious deductive results and the facts as tested by observation, that Deduction as a method has its value-in relation, at least, to the

physical universe. We use deduction when we cannot observe the cause, but only suppose it. All the same, the result of the deduction, in order to have any validity, must harmonise with the facts, or supposed effects as observed by us. If Newton showed that there was attraction between the earth and the moon, by reasoning deductively, the criterion of this reasoning was the harmony between the actual motions and positions and the result of the deduction. And so it is in all cases where a conclusion arrived at deductively reaches full verification or certainty; otherwise, the supposition involved is only a probable hypothesis. Of this we have an illustration in the supposition that the brighter parts of the moon consist of mountains. These, in themselves, are beyond direct observation: yet this hypothesis explains certain appearances which those parts present. They are found(1.) to cast shadows when the sun's rays fall upon them obliquely; (2.) in the interior illuminated border of the moon there are points illuminated before the others, thus showing them to be higher. The hypothesis, thus, of a mountainous surface is rendered highly probable. The facts we observe, are as if there were mountains of a great elevation.

§ 626. The rules of Induction are, as it seems to me, not really by themselves rules of discovery; they are rather rules of guidance and verification or testing in the process of discovery. The discoverer must start with an hypothesis-a question to put to nature or the facts. This is the guiding spirit of investigation: if, with this in his mind, he tests its applicability according to the canons of induction, he will do well either in finding in it a probable solution, or in casting it aside as useless. And, certainly, before he can vindicate his theory to the world, he must show that his hypothesis has fulfilled those conditions.

As to the value of the rules of Induction in the matter of culture, they are wholly secondary as compared with the high abstract training, the precision of logical thinking, the orderliness of thought, the power of consecution, which are developed by the study of Formal or General Logic. Compared to this, their influence is weak and unsteady as is the swaying chaos of fact in the world compared with the grasp of the universal laws which regulate concepts, proposi

tions, and reasonings. And while in the world of physical phænomena-definite, visible, tangible, or to be reached by microscope or telescope they are valuable and important, they cannot for a moment be placed on the same high level as those laws which regulate all human thinking in its very essence, its very possibility-form, in fact, the conditions of any concept, any judgment, any reasoning whatever. These are the first things to be studied, and the man who knows not these in their grounds and basis, is, whatever he may know of rules applied to so-called phænomena, a mere empiric.

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CHAPTER XXXVI.

QUASI-SYLLOGISMS-EXAMPLE-ARISTOTELIC ENTHYMEME.

§ 627. What is known as Reasoning from Example has an apparent likeness to Analogy. In Example the process is from one particular to another particular, similar to the former. Thus we may say :

Socrates (a philosopher) was modest; therefore Diogenes (a philosopher) was modest. In this there is really no valid inference the one particular does not necessarily imply the other.

If, further, we explicate what is apparently involved in the one premiss, we should have Socrates is modest; therefore all philosophers are modest, which is a paralogism. We need somehow to connect modest and philosopher into a universal proposition,-All philosophers are modest,—and this is not provided for by the terms of the propositions or data given us. Yet this is typical of the reasoning from Example set forth by Aristotle.

His reasoning from Example (πapádayμa) is really a complex process, consisting (1.) of an inference so-called, from one single case to every case of the same kind; (2.) of a syllogism properly constituted, in which the supposed universal conclusion of the first reasoning becomes the major proposition of the second. Aristotle defines Example as that in which, among three notions, the extreme is affirmed of the middle through a term similar to the third. But we must know, he adds, that the middle is with the third term, and that the first is with the similar term.

1 Cf. Duncan, Inst. Log., L. iv. c. vii. § 2.

Thus, to take his own illustration, which may be put thus:

(a) The war by the Thebans (neighbours) against the Phocians was destructive;

Therefore the war by the Athenians (neighbours) against the Thebans will be destructive.

This implies the reasoning

(b) The war waged by the Thebans against the Phocians was destructive (A is A);

That was a war against neighbours (▲ is B);

Therefore every war against neighbours is destructive (B is A).

Then we have the following:

Every war against neighbours is destructive;

The war of the Athenians against the Thebans would be a war against neighbours;

Therefore this war would be destructive.

§ 628. The latter reasoning is perfect; but the major, every war against neighbours is destructive, depends on the preceding reasoning, if it can be called such, which it is not in any proper sense. It may be brought under the head of Imperfect Induction; but it is a thoroughly weak case. The point to be established, which is not, but is simply assumed or left to be inferred from the nature of the case as known to us, is the connection between the destructiveness of the war and its being between neighbours. As Aristotle himself points. out, the reasoning in the former case is really only of rhetorical import or influence-fitted to persuade, but not cogent enough for conviction.

Or, to take another illustration :

(a) A (a statesman) is patriotic;

Therefore B (a statesman) is patriotic.

This implies the reasoning—