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

by George Hastings McNair

4. THE JOINT METHOD OF AGREEMENT AND DIFFERENCE.

(1) Principle stated.

The uncertainty of the conclusions of Agreement and the impossibility at times of employing directly the Method of Difference, give rise to the use of the combination of Agreement and Difference known as the Joint Method. As stated by Mill, the principle conditioning the Joint Method is this: “If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instancesin which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ is the effect or the cause or an indispensable part of the cause, of the phenomenon.” More briefly the notion may be stated in this wise: 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.

This principle differs from the one underlying the Method of Difference in that the instances considered are more varied and more numerous. The principle of Difference requires but two sets of instances, while the Joint Method demands at least three; two when the phenomenon occurs and one when it does not occur. A study of the symbolizations and illustrations will clarify this distinction.

(2) Joint Method symbolized.

If we use circumstances and phenomenon in place of antecedents and consequent, then one symbolization may be made to stand for ascertaining either the invariable antecedent, or the invariable consequent.

	Circumstances	Phenomenon
1.	A B C D	P₁
2.	A D E F	P₂
3.	A L M N	P₃
4.	A O P Q	P₄
5.	O P Q	—
6.	L M N	—
7.	D E F	—
8.	B C D	—

It is obvious that the first, second, third and fourth groups of instances illustrate the principle of Agreement; whereas the first and eighth, the second and seventh, the third and sixth, and the fourth and fifth illustrate in each case, the principle of Difference.

(3) Concrete Examples illustrating Joint Method.

The problem: Too much whispering.

	Antecedents		Consequent
1.	Insufficient work,		Much whispering.
	Lack of interest,
	Seated near a friend.
2.	More work,		Much whispering.
	Lack of interest,
	Seated near a friend.
3.	More work,		Much whispering.
	More interest,
	Seated near a friend.
4.	More work,		Not much whispering.
	More interest,
	Not seated near friend.
5.	More work,		Not much whispering.
	Lack of interest,
	Not seated near friend.
6.	Insufficient work,		Not much whispering.
	Lack of interest,
	Not seated near friend.

From this it may be concluded that the undue amount of whispering is caused by seating particular friends near each other.

The problem: Poor recitations.

	Antecedents		Consequent
1.	Long lesson,		Poor recitation.
	Faulty assignment of lesson,
	Fear of teacher.
2.	Lesson made shorter,		Poor recitation.
	Faulty assignment,
	Fear of teacher.
3.	Lesson made shorter,		Poor recitation.
	A more careful assignment,
	Fear of teacher.
4.	Lesson made shorter,		Good recitation.
	A more careful assignment,
	Removal of fear of teacher.
5.	Lesson made shorter,		Good recitation.
	Faulty assignment,
	No fear of teacher.
6.	Lesson long,		Good recitation.
	Faulty assignment,
	No fear of teacher.

Fear of teacher is the cause of the poor recitation.

(4) Distinguishing features.

Being a combination of Agreement and Difference the Joint Method possesses the characteristics of each, though more or less modified. The distinguishing marks may be summarized as follows:

(1) Of the first group of instances:

(1) The phenomenon must always occur,

(2) One antecedent must be invariable,

(3) The other antecedents must be more or less variable.

(2) Of the second group of instances:

(1) The phenomenon must never occur,

(2) One antecedent must be variable,

(3) The other antecedents must be more or less invariable.

Briefly, the one principle concerned is this: There must be an invariable conjunction between the phenomenon involved and the antecedent suspected of being the cause.

(5) Advantages and Disadvantages of the Joint Method.

Since the Joint Method permits a consideration of the negative aspect of the question as well as the affirmative, the opportunities for testing the many instances concerned are doubled. In consequence, the conclusions of the Joint Method are more positive than those of the other methods. It follows that this same opportunity to multiply the instances would tend to lessen the other objections raised against the Method of Agreement; viz., plurality of causes, immaterial antecedents, complexity of phenomenon.

The student must regard the given illustrative symbolizations and concrete examples as being of the simplest form; in life such are the exceptions rather than the rule. When investigating questions, like the cause ofthe high cost of living, the effect of high tariff, the reason for the typhoid epidemic, etc., there is often a confusion of circumstances which makes the Joint Method unsatisfactory, even though it furnishes a larger opportunity for the multiplication of instances.

The strongest case which the Joint Method is able to present is when the negative instances repeat the positive in every detail, with the one exception of the variable antecedent. To wit:

Strong Argument:
	Circumstances	Phenomenon
	A B C	P₁
	A L M	P₂
	– L M	—
	– B C	—
Weak Argument:
	A B C	P₁
	A L M	P₂
	– R S	—
	– T K	—

Despite the disadvantages, the conditions of the Joint Method are more or less ideal; since the positive branch of the argument suggests the hypothesis, while the negative branch proves the accuracy or inaccuracy of such.