A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

2. METHOD OF AGREEMENT.

(1) Principle stated. As stated by Mill the principle of the Method of Agreement is this: “If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstances in which alone all the instances agree is the cause (or effect) of the given phenomenon.”

This notion is given in clearer terms by Jevons and Creighton. Viz.: “The sole invariable antecedent of a phenomenon is probably its cause”; and “The sole invariable consequent of a phenomenon is probably its effect.”

It is known that an antecedent is anything which precedes; while a consequent is anything which follows. To be regarded as a cause, an antecedent must be invariable, and to be regarded as an effect, a consequent must likewise be invariable. Antecedents and consequents which are in no way constant could hardly have any causal connection.

(2) Method symbolized. Let P₁, P₂, P₃, P₄, etc., represent the phenomenon as it may appear the first, second, third, fourth, etc., times, and let A, B, C, etc., stand for the various antecedents, or the various consequents as the case may demand. These two forms may now be used to illustrate the two statements which summarize Agreement:

First statement.

Antecedents.   Consequents.

A B C D — P₁

A D E F — P₂

A L M N — P₃

A O P Q — P₄

Second statement.

P₁ — A B C D

P₂ — A D E F

P₃ — A L M N

P₄ — A O P Q

In the first case, the sole invariable antecedent is A, and, therefore, we infer that A is probably the cause of P. In the second case, the invariable consequent being A, is probably the effect of P.

(3) Concrete examples illustrating first statement.

The Problem: Cause of John’s tardiness.

On investigation the various antecedents are these: (1) John has his breakfast at seven; (2) after breakfast he carries his father’s dinner to him and (3) feeds the hens; and then (4) goes to school by the path through the woods and around the mill pond.

Phenomenon as a consequent. John is tardy. Determining to do away with the tardiness, the teacher brings about a variation in the antecedents, varying one at a time taken in the order indicated above.

To wit: (1) Varying the first antecedent.

John breakfasts at 6:30;

Other antecedents the same;

(Phenomenon) But John is tardy.

(2) Varying the second antecedent.

The younger brother carries the dinner;

Other antecedents the same;

(Phenomenon) John is tardy.

(3) Varying the third antecedent.

Another brother cares for the hens;

Other antecedents the same;

(Phenomenon) John is still tardy.

The teacher is now quite certain that the tardiness is due to the route through the woods and around the pond.

Using, as symbols, the initial letters of the italicized “key-words” of the antecedents as stated above, the case of tardiness may be symbolized as follows:

Key words Symbols

seven s

dinner d

hens h

woods w

tardy t₁, t₂, t₃

Antecedents Phenomenon

s d h w t₁

e d h w t₂

s b h w t₃

s d a w t₄

“w” standing for route through the woods, is seen to be the invariable antecedent.

(4) Concrete example illustrating the second statement.

The Problem: To determine the effect of direct primaries.

First trial.
Antecedent		Consequents
Direct primary		1. Greater expense to candidate,
		2. Greater interest shown,
		3. Better men nominated,
		4. “Bumper” crops.
Second trial.
Direct primary		1. Greater expense to candidate,
		2. Greater interest shown,
		3. Better men nominated,
		4. Crops below average.
Third trial.
Direct primary		1. No greater expense,
		2. Greater interest shown,
		3. Better men nominated,
		4. Crops average.
Fourth trial.
Direct primary		1. No greater expense,
		2. No greater interest,
		3. Better men nominated,
		4. Crops average.

It is seen that the invariable consequent is, “Better men nominated.” We may, therefore, conclude that this is a probable effect of “Direct primaries.”

(5) Distinguishing features of method of agreement. The essential characteristics of the method of agreement are three:

First, The phenomenon always occurs.

Second, There is at least one invariable antecedent.

Third, The other antecedents vary.

Giving attention to the attending symbolized illustrations it may be noted that “P,” the phenomenon, always happens; while in the case of the first symbolization, “D” is the invariable antecedent and “A, B, C, E, G, L, M, F, I” are the variable antecedents. “K” is the invariable antecedent of the second and “H, I, L, T, M, W, X, Y, Z, S” are the variable antecedents.

Antecedents   Consequents

1. A B C D E — P₁

A B C D G — P₂

L B C D M — P₃

A F G D M — P₄

L B C D  I  — P₅

2. H  I  K L T — P₁

K L M T W — P₂

M T L K W — P₃

X H K Y Z — P₄

T W L K S — P₅

(6) A Matter of Observation and Experiment.

On studying the problem relative to the tardiness of John, it appears that in obtaining the various antecedents the work would be largely a matter of observation. Carrying the father’s dinner, the route through the woods, etc., are facts which observation would make evident. However, when it becomes necessary to vary these antecedents with a view to finding the invariable one, the procedure is experimental as well as a matter of casual observation. Moreover, in connection with the direct primary problem the question would be largely a matterof experiment; though observation would obtain as a subsidiary condition. We may conclude from this that the method of agreement involves both observation and experiment; and since the student will discover that the other methods impose similar demands, we are justified in designating these five special methods of induction as those of observation as well as of experiment.

(7) Advantages and Disadvantages of the Method of Agreement.

The concrete cases given to illustrate the method of agreement present a simple combination of antecedents and consequents. In life, however, such simplicity does not usually obtain and in consequence the method of agreement gives rise to a few serious difficulties. These may be summarized as (a) Plurality of causes; (b) Immaterial antecedents; (c) Complexity of phenomena; (d) Uncertainty of conclusion.

(a) Plurality of causes is mentioned by Mill as constituting the “characteristic imperfection” of the method of agreement. As the term signifies, plurality of causes represents a condition where a given phenomenon has more than one cause, or where different causes produce the same effect. For example, “A poor crop” may be due to drought, neglect, pests, etc.; heat may be caused by friction, electricity, combustion. Unfavorable home conditions; ill health; dislike for teacher—any one of these might be followed by irregular attendance.

(b) Immaterial antecedents are those which precede a given phenomenon and yet, under the most favorable situations, have no causal connection with said phenomenon.For example, the various antecedents of the heavy rain may have been a south wind, forgetting to take an umbrella, missing the car and having to walk, etc. Clearly these antecedents, with the exception of the first, are immaterial.

(c) The law of agreement demands that all the material antecedents receive consideration, but often the situation is too complex to make this possible; a fair illustration of such would be an attempt to ascertain all of the antecedents of “the high cost of living.”

(d) The law of agreement never precludes the possibility of error; as it is quite impossible to carry the analysis to the point of absolute certainty. Of all the methods, “agreement” is the least reliable. Despite the foregoing objections, however, the method is of positive value because of its suggestiveness; opening the door to plausible hypotheses it gives the investigators a working basis.