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The immediately preceding paragraphs contain in themselves a

complete programme of Inductive Method, a programme which it will be the main business of the following chapters to develop. It may not be out of place, however, to add, in conclusion, an illustration or two of the general process through which facts are generalized, and, as a further consequence, systematized and explained.

Let us take as our complex fact a door with its framework somewhat out of order. We proceed to analyse the obstruction by resolving the vague complex idea of a door out of order into the more simple ideas of a latch, a hinge, or fitting out of order. We find eventually that the upper hinge is to blame, and that its looseness has caused the door to lean and graze the floor: it presses against the floor, and so scrapes against it when moved. The problem is now reduced to a question of pressure and friction, and we may now proceed to explain the difficulty by showing how, according to the laws of pressure and friction, the obstruction necessarily came about. By this simplification the fact is generalized. It is generalized as a particular case of the operation of the general laws of pressure and friction. It is also systematized, or at least potentially correlated with a host of other facts; for, by connecting the phenomenon with all other phenomena of pressure and of friction, we have taken it out of its mere particularity and isolation.

Again-to take an illustration given by Dr. Venn* if we are attempting to explain the slipperiness of ice, we at once simplify and generalize the problem before us by displaying the fact of slipperiness as a specific variety of the forward and backward reactions that always take place between our feet and the surface of the ground against which they press. 'We slip,' we say, 'because the horizontal reaction to the impulse of the feet has fallen below a certain minimal amount.'

Once more, if we desire to explain the succulent habit of some desert-plant, we generalize the fact of succulence by showing it to be a specific form of 'xerophilous' adaptation, and by regarding this again as a special kind of that adaptive modification, in response to the influence of environment, which, gradually perfected through the process of natural selection, ultimately fits each species of plant to the conditions of its own particular habitat.

* 'The Principles of Empirical or Inductive Logic,' ch. xxi., p. 498.

XII.

APPLICATION OF THE INDUCTIVE PRINCIPLE TO

'INDUCTIONS IMPROPERLY SO-CALLED' AND

TO 'IMPERFECT INDUCTIONS.'

(i.) Inductive Inferences, improperly so-called (ch. xl.).

(ii.) The 'Imperfect Inductions':

(A) Enumerative Induction (ch. xli.).

(B) Argument from Analogy (ch. xlii.).

CHAPTER XL.

XII. (i.) INDUCTIVE INFERENCES, IMPROPERLY SO-CALLED.

THE essential distinction between popular and scientific explanation has been expressed in the familiar saying that Science is just organized common sense. This organization implies two thingsprinciple and method, the method being determined by the principle. And the principle whereby Science organizes common sense in the matter of the explanation of facts is just that of steadfast loyalty to the facts in so far as they are relevant to its scientific purpose. This principle gives to scientific investigation an ultimate standard or criterion-ultimate since the scientific aspiration and purpose does not extend beyond that of an adequate explanation of the facts of the sense-world. Hence, in inquiring whether any proposed method of dealing with the facts is scientifically adequate or not, we shall have to ask : In what sense does it provide an adequate Verification-test? This is the touchstone of Scientific Method, to which all else is subordinate.

For the purpose of carrying out this principle and applying this inductive standard in detail, we propose to adopt Mill's* Inductive Scheme, which may conveniently be laid out as follows:

'Inductions.'

Improperly so-called.

Properly so-called.

'Perfect Induction.' Parity of Reasoning. Colligation of Facts.

Imperfect Inductions.

Imperfect Enumeration.

Analogy.

Scientific Induction.

Under the head of Inductions improperly so-called Mill reckons three types:

1. 'Perfect Induction.'

2. 'Induction by Parity of Reasoning.'
3. Colligation.

* Vide J. S. Mill, 'A System of Logic, Book III.

1. 'Perfect Induction.'

Suppose that we have certain knowledge that all the instances belonging to a given class have been considered by us; then, if we find that a certain attribute is possessed by each of these instances, it is an act of 'perfect induction' to universalize-i.e., summarizethe discovery by stating that all the members of that class possess the attribute in question.

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.... All the months in the year have twenty-eight days or

more.'

Now, is there anything in this reasoning which could allow us to consider it as a form of Scientific Explanation or Induction ?

There is Scientific Explanation, as we have seen, only where a hypothetical conjecture is adequately verified. Two elements are here indispensable: the conjecture (going tentatively beyond the evidence), and the verification or the justifying of the conjecture.

Here, we might say, we have at least verification: the general proposition seems to admit of complete, final verification. But this confidence is illusory; for there has really been no conjecturing at all, and there is therefore nothing to verify. There has been no tentative supposition made, no uncertainty at any point of the reasoning, no temporary passage from the known to the unknown, which, when understood to mean a tentative passage from known facts to a hypothesis, is essential to all inductive procedure. In order that a scientific method may satisfy the criterion of Induction, not only must its verification-tests be adequate, but it must involve a verifiable conjecture. The legitimate hypothesis is the precondition of verification. 'Perfect Induction' lacks the legitimate hypothesis-lacks, indeed, the hypothetical element altogether. If it is something more than 'a mere short-hand registration of facts known,'* as Mill puts it, it is still essentially a self-contained deductive inference, and of the very simplest type. As such, it is no episode in a total process of Induction, and therefore not inductive in any sense of the word.'†

* J. S. Mill, 'A System of Logic, Book III., ch. ii.. § 1.

† For Jevons' defence of Perfect Induction, see 'Elementary Lessons in Logic,' p. 214. He appears to himself to be criticizing Mill, whereas he is only forcibly repeating Mill's own words. (Cf. 'A System of Logic,' ibid.: 'The operation may be very useful, as most forms of abridged notation are; but it is no part of the investigation of truth, though often bearing an important, part in the preparation of the materials for that investigation.')

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