9. SUMMARY.
(1) The fundamental fact of causation underlies the three forms of induction, but is most conspicuous in the method of analysis and may be ascertained by recourse to one of the experimental methods.
(2) The principle of the method of agreement may be summed up in the two statements: The sole invariable antecedent of a phenomenon is probably its cause and the sole invariable consequent of a phenomenon is probably its effect. These two statements may be symbolized and illustrated.
The essential characteristics of the method of agreement are the phenomenon always occurs; there is at least one invariable antecedent; the other antecedents vary.
The method of agreement together with the other four methods may justly be termed methods of experiment as well as methods of observation.
The difficulties of the method of agreement are in the main plurality of causes, immaterial antecedents, complexity of phenomenon and uncertainty of conclusion. These difficulties may be summarized as involving a phenomenon which may have several causes; may be preceded by conditions of no causal consequence; may be so involved as to prevent exhaustive examination; and may give unreliable conclusions.
Agreement is valuable chiefly in furnishing to the investigator plausible hypotheses.
(3) The principle of difference is this: “Whatever is invariably present when the phenomenon occurs and invariablyabsent when the phenomenon does not occur, other circumstances remaining the same, is probably the cause or the effect of the phenomenon.”
Like agreement, difference admits of symbolization and illustration by concrete examples.
The chief difficulties attending difference are: in nature varying one antecedent at a time is infrequent, and it is easy to overlook antecedents which are closely related to the case under investigation.
Difference is the most common method of the experimental sciences. The characteristic features of difference are, the phenomenon does not always occur, one antecedent is variable, while the others are invariable.
The methods of agreement and difference are complementary processes. Agreement attempts to eliminate all the antecedents but one, while difference aims to eliminate one only. Agreement is a method of observation, while difference is a method of experiment. The conclusion of the method of difference gives greater certainty than that of the method of agreement.
(4) The joint method may be stated in this way: Among many instances if one circumstance is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur, this circumstance is probably the cause or the effect of the phenomenon.
The instances of the joint method are more numerous and more varied than those of either agreement or difference.
The joint method has the distinguishing characteristics of both agreement and difference.
Because it furnishes greater opportunities for multiplying and varying the instances involved, the joint method presents fewer objections than either of the two separate methods.
The positive branch of the joint method suggests the hypothesis, while the negative branch proves it. This makes the method somewhat ideal.
(5) The principle of concomitant variations may be stated as follows: If when one phenomenon varies alone, and another also varies alone, the one is either the cause or the effect of the other. This is the method of fluctuation, and is used when it isimpossible to make the phenomenon disappear altogether, as in the case of difference.
The chief function of concomitant variations is to establish exact quantitative relations between cause and effect.
(6) The principle of residues is this: Subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents, and what is left of the phenomenon is the effect of the remaining antecedent.
The most valuable feature of residues is its suggestiveness; an attempt to explain the “residual phenomenon” has led to many important scientific discoveries.
(7) The five methods are concerned with the establishment of causal connections between phenomena. Agreement suggests the connection while difference proves it. The other methods are modified applications of difference, necessitated by some peculiar form which the phenomenon may take. A statement of the one principle involved is: “If the conjunction between two phenomena is invariable then there is a causal connection.”
All of the methods are forms of inductive thinking.