Chapter 33

FORMAL OR ARISTOTELIAN INDUCTION.--INDUCTIVE ARGUMENT.

The distinction commonly drawn between Deduction and Induction is that Deduction is reasoning from general to particular, and Induction reasoning from particular to general.

But it is really only as modes of argumentation that the two processes can be thus clearly and fixedly opposed. The word Induction is used in a much wider sense when it is the title of a treatise on the Methods of Scientific Investigation. It is then used to cover all the processes employed in man's search into the system of reality; and in this search deduction is employed as well as induction in the narrow sense.

We may call Induction in the narrow sense Formal Induction or Inductive Argument, or we may simply call it Aristotelian Induction inasmuch as it was the steps of Inductive argument that Aristotle formulated, and for which he determined the conditions of validity.

Let us contrast it with Deductive argument. In this the questioner's procedure is to procure the admission of a general proposition with a view to forcing the admission of a particular conclusion which is in dispute. In Inductive argument, on the other hand, it is a general proposition that is in dispute, and the procedure is to obtain the admission of particular cases with a view to forcing the admission of this general proposition.

Let the question be whether All horned animals ruminate. You engage to make an opponent admit this. How do you proceed? You ask him whether he admits it about the various species. Does the ox ruminate? The sheep? The goat? And so on. The bringing in of the various particulars is the induction ([Greek: epagoge]).

When is this inductive argument complete? When is the opponent bound to admit that all horned animals ruminate? Obviously, when he has admitted it about every one. He must admit that he has admitted it about every one, in other words, that the particulars enumerated constitute the whole, before he can be held bound in consistency to admit it about the whole.

The condition of the validity of this argument is ultimately the same with that of Deductive argument, the identity for purposes of predication of a generic whole with the sum of its constituent parts. The Axiom of Inductive Argument is, _What is predicated of every one of the parts is predicable of the whole._ This is the simple converse of the Axiom of Deductive argument, the _Dictum de Omni_, "What is predicated of the whole is predicable about every one of the parts". The Axiom is simply convertible because for purposes of predication generic whole and specific or individual parts taken all together are identical.

Practically in inductive argument an opponent is worsted when he cannot produce an instance to the contrary. Suppose he admits the predicate in question to be true of this, that and the other, but denies that this, that and the other constitute the whole class in question, he is defeated in common judgement if he cannot instance a member of the class about which the predicate does not hold. Hence this mode of induction became technically known as _Inductio per enumerationem simplicem ubi non reperitur instantia contradictoria_. When this phrase is applied to a generalisation of fact, Nature or Experience is put figuratively in the position of a Respondent unable to contradict the inquirer.

Such in plain language is the whole doctrine of Inductive Argument. Aristotle's Inductive Syllogism is, in effect, an expression of this simple doctrine tortuously in terms of the Deductive Syllogism. The great master was so enamoured of his prime invention that he desired to impress its form upon everything: otherwise, there was no reason for expressing the process of Induction syllogistically. Here is his description of the Inductive Syllogism:--

"Induction, then, and the Inductive Syllogism, consists in syllogising one extreme with the middle through the other extreme. For example, if B is middle to A and C, to prove through C that A belongs to B."[1]

This may be interpreted as follows: Suppose a general proposition is in dispute, and that you wish to make it good by obtaining severally the admission of all the particulars that it sums up. The type of a general proposition in Syllogistic terminology is the Major Premiss, All M is P. What is the type of the particulars that it sums up? Obviously, the Conclusion, S is P. This particular is contained in the Major Premiss, All M is P; its truth is accepted as contained in the truth of All M is P. S is one of the parts of the generic whole M; one of the individuals or species contained in the class M. If you wish, then, to establish P of All M by Induction, you must establish P of all the parts, species, or individuals contained in M, that is, of all possible S_s:_ you must make good that this, that and the other S is P, and also that this, that and the other S constitute the whole of M. You are then entitled to conclude that All M is P: you have syllogised one Extreme with the Middle through the other Extreme. The formal statement of these premisses and conclusion is the Inductive Syllogism.

This, that and the other S is P, _Major_. This, that and the other S is all M, _Minor_. [.'.] All M is P, _Conclusion_. This, that and the other magnet (_i.e._, magnets individually) attract iron. This, that and the other magnet (_i.e._, the individuals separately admitted) are all magnets. [.'.] All magnets attract iron.

This, that and the other S being simply convertible with All M, you have only to make this conversion and you have a syllogism in Barbara where this, that and the other S figures as the Middle Term.

The practical value of this tortuous expression is not obvious. Mediaeval logicians shortened it into what was known as the Inductive Enthymeme: "This, that and the other, therefore all," an obvious conclusion when this, that and the other constitute all. It is merely an evidence of the great master's intoxication with his grand invention. It is a proof also that Aristotle really looked at Induction from the point of view of Interrogative Dialectic. His question was, When is a Respondent bound to admit a general conclusion? And his answer was, When he has admitted a certain number of particulars, and cannot deny that those particulars constitute the whole whose predicate is in dispute. He was not concerned primarily with the analysis of the steps of an inquirer generalising from Nature.

[Footnote 1: [Greek: epagoge men oun esti kai ho ex epagoges syllogismos to dia tou eterou thateron akron to meso syllogisasthai; Oion ei ton A G meson to B, dia tou G deixai to A to B hyparchon.] (An. Prior., ii. 23.)]