Chapter 18: The Five Special Methods of Observation and Experiment.13

=1. THE AIM OF THE FIVE METHODS.=

The primary forms of induction have been divided into _simple enumeration_, _analogy_ and _analysis_ . Conditioning these forms are the two laws, _uniformity of nature_ and _universal causation_. Since these laws are always concerned with causes, we may refer to them as together expressing the fundamental “_fact of causation_.” Wherever there is a causal connection, no matter how slight, these laws obtain.

Though “the fact of causation” probably conditions all forms of induction, it is most conspicuous in the third form; namely, Analysis. Here the main aim is to establish a causal connection of some kind; an aim which may be accomplished through the medium of observation and experiment. Incident to this notion, John Stewart Mill formulated five experimental methods of induction. These are known according to the following distinctive titles:

1. The Method of Agreement.

2. The Method of Difference.

3. The Joint Method of Agreement and Difference.

4. The Method of Concomitant Variations.

5. The Method of Residues.

=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_

{ 1. Greater expense to candidate,
Direct { 2. Greater interest shown,
primary { 3. Better men nominated,
{ 4. “Bumper” crops.

_Second trial._

{ 1. Greater expense to candidate,
Direct { 2. Greater interest shown,
primary { 3. Better men nominated,
{ 4. Crops below average.

_Third trial._

{ 1. No greater expense,
Direct { 2. Greater interest shown,
primary { 3. Better men nominated,
{ 4. Crops average.

_Fourth trial._

{ 1. No greater expense,
Direct { 2. No greater interest,
primary { 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 matter of 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_.

=3. METHOD OF DIFFERENCE.=

(1) Principle stated.

Says Mill, “If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ is the effect or the cause of an indispensable part of the cause, of the phenomenon.”

To put this in simple terms: _Whatever is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur, other circumstances remaining the same, is probably the cause or the effect of the phenomenon._

(2) Method symbolized.

Using the same symbols as were used in “Agreement.”

_Antecedents_ _Consequents_
A B C D P
‒ B C D ‒

or

P A B C D
‒ ‒ B C D

In the first instance A is probably the cause of the phenomenon, since it is present when the phenomenon occurs and absent when it does not occur. For a similar reason, A is the effect in the second case.

(3) Concrete illustrations.

(A) A wise teacher in ascertaining the cause of John’s tardiness would have suggested at once a change of route. Using as symbols the initial letters of the key-words of the antecedents in the case, the following results:

s d h w t
s d h − ‒

(B) _First trial._

_Problem_: Unprepared home work.

_Antecedents_ _Consequents_

1. Length of lesson, }
2. Definiteness of lesson, } Work _not_ properly
3. Amount of interest shown, } prepared.
4. Physical condition the same. }

_Second trial._

1. _Length_ of lesson the same, }
2. _Lesson made more definite_, } Work _properly_ prepared.
3. _Interest_ the same, }
4. Physical _condition_ the same. }

The foregoing symbolized:

L D I C W
L ‒ I C ‒

It is seen that indefiniteness of lesson assignment is the cause of the unprepared home work.

(4) Advantages and disadvantages of the Method of Difference.

The main difficulty attending the use of the method of difference is the _complexity_ of phenomenon. The very nature of the method insists as an essential requirement that _only one material antecedent shall be varied at a time_. In life the variations are more or less confused, and it is often not only impossible to observe cases of a single variation, but frequently error comes through _overlooking_ antecedents which are material to the case under investigation. For these reasons the Method of Difference is more a method of _experiment_ than it is a method of observation. By controlling the circumstances it becomes possible to vary but _one_ antecedent at a time, and also to bring into prominence _all_ of the _material_ antecedents.

Bacon claims that _all “crucial instances”_ are merely applications of the Method of Difference. By crucial instance he means any fact which will enable us to determine _at once_ which supposition is the correct one. For example, the physician may not know whether it is malaria or typhoid fever till he takes a blood test; such a test typifies “crucial instances.” The various tests in chemistry are likewise cases of crucial instances, and, in consequence, this science makes use of “Difference” more than any other method.

(5) Characteristic features of Method of Difference.

There are three distinguishing marks of the Method of Difference: these are, (1) The phenomenon does not always happen; (2) _One_ antecedent is variable; (3) The other antecedents are more or less invariable.

The following symbolizations will make these three characteristics evident:

_Antecedents_ _Consequents_

(1) A B C P
A ‒ C ‒
(2) ‒ B C ‒
X B C P
(3) L M T K P
L M ‒ K ‒

AGREEMENT AND DIFFERENCE COMPARED.

(a) The methods of Agreement and Difference are complementary as may be discerned by comparing their characteristic features: In Agreement the phenomenon _always occurs_; in Difference the phenomenon _does not always occur_: In Agreement there is one _invariable_ antecedent; whereas in Difference there is one _variable_ antecedent: In Agreement the other antecedents are more or less _variable_; but in Difference the other antecedents are more or less _invariable_.

(b) According to Mill the Method of Agreement insists that what _can be eliminated_ is _not_ connected; whereas the Method of Difference implies that what _cannot be eliminated is_ connected.

(c) The Method of Agreement is more a method of observation, since it is chiefly concerned with the _discovery of causes_. The Method of Difference is distinctly a method of experiment, because its usual aim is to _discover effects_.

(d) The Method of Agreement is so called because the object is to compare several instances to determine in what respect they _agree_; but in the case of Difference instances are compared to determine in what respects they _differ_.

(e) The conclusions of the Method of Difference involve greater certainty than those of Agreement and, therefore, the former method should be adopted when there is a choice.

=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 instances in 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, }
Lack of interest, } Much whispering.
_Seated near a friend._ }

2. More work, }
Lack of interest, } Much whispering.
_Seated near a friend._ }

3. More work, }
More interest, } Much whispering.
_Seated near a friend._ }

4. More work, }
More interest, } Not much whispering.
_Not seated near a friend._ }

5. More work, }
Lack of interest, } Not much whispering.
_Not seated near a friend._ }

6. Insufficient work, }
Lack of interest, } Not much whispering.
_Not seated near a 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, }
Faulty assignment of lesson, } Poor recitation.
_Fear of teacher._ }

2. Lesson made shorter, }
Faulty assignment of lesson, } Poor recitation.
_Fear of teacher._ }

3. Lesson made shorter, }
A more careful assignment, } Poor recitation.
_Fear of teacher._ }

4. Lesson made shorter, }
A more careful assignment, } Good recitation.
_Removal of fear of teacher._ }

5. Lesson made shorter, }
Faulty assignment, } Good recitation.
_No fear of teacher._ }

6. Lesson long, }
Faulty assignment, } Good recitation.
_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 of the 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.

=5. METHOD OF CONCOMITANT VARIATIONS.=

(1) Principle stated.

Mill’s statement is this: “Whatever phenomenon varies in any manner whenever another phenomenon varies in a particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.”

To put it differently: _If when one phenomenon varies alone, another also varies alone, the one is either the cause or the effect of the other._

(2) Concomitant Variations symbolized.

Circumstances Phenomenon
A P
A + a P + p
(A + a) − a (P + p) − p

It is evident from this that little “a” is the cause or the effect of little “p.” To put it in concrete form:

Let A = X number of calories of heat,

And P = 68° F., the original temperature of room,

And a = candle burning in room for ½ hour,

And p = 2° F.

Then

_Antecedents_ _Consequent_

X no. of cal. of heat in room = 68° F. temp. of room
X no. of cal. of heat + burning candle = 68° + 2° = 70°
X (no. of cal. of heat + burning candle) = (68° + 2°) − 2° = 68°
− burning candle

As large “A” is increased and decreased by little “a” so large “P” appears to be increased and decreased by little “p.” This strongly suggests a causal connection between little “a” and little “p.”

(3) Other concrete illustrations.

_Problem_: To ascertain nature of sound.

_Antecedent_ _Consequent_

Bell rung when within a glass jar filled Loud sound.
with air,
Some of the air pumped out of the jar, Sound not so loud.
More air pumped into jar again, Sound louder again.

The conclusion must be that air has something to do with the production of sound.

_Problem_: To find best feed for egg production.

100 lbs. beef scraps, }
100 lbs. wheat, } 30 doz. eggs.
100 lbs. oats, }
100 lbs. corn, }

50 lbs. beef scraps, }
100 lbs. wheat, } 27 doz. eggs.
100 lbs. oats, }
100 lbs. corn, }

90 lbs. beef scraps, }
100 lbs. wheat, } 28 doz. eggs.
100 lbs. oats, }
100 lbs. corn, }

Since the variation in the amount of beef scraps is accompanied by a like variation in the number of eggs produced, it may be assumed that beef scraps are essential to large egg production.

(4) Distinguishing features.
The phenomenon always occurs but in varying degrees;
One antecedent varies in degree;
The other antecedents are invariable.

(5) Advantages and disadvantages.

Concomitant Variations is applicable in cases when it is impossible to use Difference. Recourse is made to the latter when the phenomenon can be made to appear or disappear at will, but there are times when it is impossible to cause the phenomenon to disappear altogether. For example, in the case of the varying degrees of heat in the room it would be scientifically impossible to take _all_ of the heat out of the room; or in experimenting with gravitation, to do away with its influence entirely, is beyond the power of man. It is thus evident that Concomitant Variations may be used in cases where the conditions forbid doing away entirely with the phenomenon.

The special function of Concomitant Variations seems to be to establish the exact quantitative relation between the varying cause and the varying effect. To illustrate: As a general law it is known that bodies attract each other in varying degrees according to their distances apart and according to their relative sizes; by Concomitant Variations this law has been given definite quantitative value and reads like this: “Bodies attract each other directly as the product of their masses, and inversely as the square of the distance between them.” This illustration suggests that the variation between antecedent and consequent may be _direct_ or _inverse_.

The error most common in this method is the assumption that the quantitative relation between two varying phenomena will always be according to a _constant ratio_. For example, when being reduced from a high temperature to 39⅕° F., water steadily contracts; but at 39⅕° F. it commences to expand until it becomes ice. Thus the ratio of contraction of water is constant only within certain limits. In any event the established ratio of variation can with absolute safety be applied only to the _instances investigated_. Another disadvantage incident to this method, is the situation of two elements varying together constantly, and yet having no causal connection whatever.

=6. THE METHOD OF RESIDUES.=

(1) Principle stated.

As stated by Mill the principle of residue is this: “Subtract from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”

In simpler form the notion 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 antecedents_.

(2) Principle symbolized.

_Antecedent_ _Consequent_

A x
B y
C z

The total cause of the phenomenon xyz is ABC. But it is known that the cause of x is the antecedent A; whereas the cause of y is the antecedent B; hence it is concluded that the cause of z is the antecedent C.

(3) Concrete illustrations.

_Problem_: To find the weight of coal.

_Antecedents_ _Consequents_

Weight of driver, }
Weight of wagon, } = 4200 lbs.
Weight of coal. }

Weight of driver, } = { 200 lbs. } = 2200 lbs.
Weight of wagon, } { 2000 lbs. }

Hence we may conclude that the weight of coal is 4200 lbs. − 2200 lbs., or 2000 lbs.

Perhaps the most noted instance in history of the application of this method, was the one which resulted in the discovery of Neptune. In calculating the orbit of Uranus, it was found that the combined attractions of the sun and the known planets did not account for the path which Uranus took. There was some unknown influence at work. Assuming that this unaccountable attraction was due to the presence of another planet beyond the orbit of Uranus, an Englishman by the name of Adams, and later the Frenchman Leverrier, were able to indicate by the principle of Residues, the spot where this planet should be. By directing the telescope toward this point, Neptune was discovered.

(4) Distinguishing features:
The phenomenon always occurs,
The antecedents are usually invariable,
Some of the antecedents are known to be the cause of a part of
the phenomenon.

(5) Advantages and disadvantages.

The Method of Residues gives three distinct results: First, it tells _what_ is left over after all the other parts of the phenomenon have been explained. Second, it tells _how much_ is left over, and third, it calls attention to the _unexplained parts_ of the phenomenon. For example, in the first concrete illustration, by subtracting the known quantities from the total quantity, what is left over is found to be coal; not only so but we are able to calculate the exact amount of coal. This illustrates the first and second results of the Method of Residues. (Like concomitant variations it is seen that residues is serviceable in given _definite quantitative values_.) The discovery of Neptune illustrates well the third result of this method; i. e., after accounting for every other force, it was found that there was yet a force at work which had never been explained. It is this third feature of _unexplained residues_ which has placed “Science in its present advanced state.” “Most of the phenomena which nature presents are complicated; and when the effects of all known causes are estimated with exactness, and subducted, the residual facts are constantly appearing in the form of phenomena altogether new, and leading to the most important conclusions.” So says John Herschel. Almost all of the discoveries in astronomy have come about in this way. If a heavenly body does not behave as it should according to the established theory, then either the theory is wrong or there is some _residual phenomenon_ which needs to be explained. Its suggestiveness is, therefore, the most important function of this method, though this very feature is the one which makes evident its greatest disadvantage. The unexplained residual phenomenon may be very complex and, therefore, a careless observer is apt to overlook a lurking element which in reality is the true cause.

=7. THE GENERAL PURPOSE AND UNITY OF THE FIVE METHODS.=

Thinking has been defined as the deliberative process of affirming and denying connections. It is obvious that these five methods are a matter of affirming and denying connections between antecedents and consequents. As soon as the looked for connections are established, the antecedents and consequents are known to be related to each other as causes and effects. In this attempt to find and prove connections the Method of Agreement is chiefly valuable in suggesting workable hypotheses, and the method of difference in verifying, through experiment, the correctness or incorrectness of these hypotheses.

In substance the principle conditioning both methods is this: “_If a single antecedent is invariably present when the phenomenon is present and invariably absent when the phenomenon is absent then this antecedent is the cause of the phenomenon._” To put it still more briefly: _Between two phenomena there is a causal connection, if the conjunction between the two is invariable._ It is the business of Agreement to _single out the one antecedent_ and of Difference to show, by presenting the negative as well as the affirmative side of the case, that the _conjunction of the one antecedent and the particular phenomenon is invariable_. The Joint Method is merely a combination of Agreement and Difference carried into more varied and complex situations. The methods of Concomitant Variations and Residues are merely modifications of Difference; the former being used when the _chief feature is the fluctuation_ of the phenomenon, and the latter when it is desired to find _what is left over_.

_Agreement suggests the hypothesis, “difference” proves it; the joint method is “difference” more or less complicated, concomitant variations is “difference” applied to fluctuating phenomena, residues is “difference” used to find what and how much is left over._

Agreement is the method of observation and belongs to the physician and nature student. Difference and the Joint Method are experimental devices which are used by the physicist and chemist. Concomitant Variations is the method of unstable phenomena and naturally attaches itself to the economist and statistician. Residues is the method of “lurking exceptions” and is favored by the astronomer and mathematician. Residues, being the method of “what is left over,” is the most common in daily affairs.[14]

_All the five methods are forms of inductive thinking which lead to the establishment of causal connections by means of the principle of the invariable conjunction of phenomena._

=8. OUTLINE.=

THE FIVE SPECIAL METHODS OF OBSERVATION AND EXPERIMENT.

(1) Aim of Five Methods.
Fundamental fact of causation.

Aim of analysis.
{ agreement
{ difference
Methods of { joint
{ concomitant variations
{ residues

(2) Method of Agreement.
Principle stated
Method symbolized
Method illustrated
Distinguishing features of method
A matter of observation and experiment
Advantages and disadvantages

(3) Method of Difference.
Principle stated
Method symbolized
Method illustrated
Advantages and disadvantages
Characteristic features
Agreement and Difference compared

(4) The Joint Method of Agreement and Difference
Principle stated
Method symbolized
Concrete illustrations
Distinguishing features
Advantages and disadvantages

(5) Method of Concomitant Variations
Principle stated
Method symbolized
Concrete illustrations
Distinguishing features
Advantages and disadvantages

(6) The Method of Residues
Principle stated
Method symbolized
Concrete illustrations
Distinguishing features
Advantages and disadvantages

(7) General Purpose and Unity of Five Methods
One fundamental principle

=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 invariably absent 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 is impossible 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.

=10. REVIEW QUESTIONS.=

(1) Explain “the fundamental fact of causation.”

(2) Show that the fact of causation is most conspicuous in induction
by analysis.

(3) Name the five special inductive methods of observation and
experiment.

(4) State, symbolize, and illustrate the method of agreement.

(5) Give examples of antecedents which do not function as causes.

(6) Show that the “special methods” are a matter of both observation
and experiment.

(7) Give the distinguishing features of the method of agreement;
illustrate by reference to the symbols.

(8) Exemplify the plurality of causes; immaterial antecedents;
complexity of phenomenon.

(9) Show that the conclusions of agreement are largely hypothetical.

(10) State, symbolize, and illustrate the method of difference.

(11) Show by illustration that, in the method of difference, only one
antecedent should be varied at a time.

(12) Show that difference is naturally a method of experiment.

(13) Explain Bacon’s use of the term “crucial instances.”

(14) Name and explain the characteristic features of the method of
difference.

(15) Show that agreement and difference are complementary.

(16) Explain and illustrate the joint method.

(17) What inference may be drawn from the following instances:

_Antecedents_ _Consequents_

A L M T p q r g
B L M E z q r x
B C M E r z x y
A M T H p q g o

(18) “Mr. Darwin, in his experiment on cross and self fertilization
in the vegetable kingdom, placed a net about one hundred flower
heads, thus protecting them from the bees. He at the same time
placed one hundred other flower heads of the same variety of
plant where they would be exposed to the bees. He obtained
the following result: The protected flowers failed to yield
a single seed. The others yielded about 2,720 seeds. Thus
cross-fertilization was proved.” (Hibben).

What method did Darwin employ? Symbolize the experiment.

(19) Summarize the distinguishing marks of the joint method.

(20) Show that the joint method is more ideal than either agreement
or difference.

(21) State and give concrete illustrations of the law of concomitant
variations.

(22) What is the chief function of concomitant variations? Illustrate.

(23) Give instances where it would be impossible to use difference,
but easy to use concomitant variations.

(24) Explain this: “The quantitative variation between antecedent and
consequent may be either direct or inverse.”

(25) State and explain by illustration the method of residues.

(26) What are the advantages and disadvantages of the principle of
residues?

(27) State the principle which virtually sums up the five methods.

(28) Write briefly on the practical applications of the five methods
to the ordinary walks of life.

=11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=

(1) Trace the connection between the method of agreement and
induction by simple enumeration.

(2) Show that Mill’s methods may properly be termed “Inductive
Methods of Scientific Investigation.”

(3) How may it be shown by “agreement” that the high cost of living
is due to the tendency to spend more than we earn?

(4) Assume that you are a member of the Board of Health, and that you
desire to ascertain the cause of the diphtheria epidemic by means
of the principle of agreement.

(5) What is the error involved in coming to the conclusion that to
sit at table where there are thirteen, may mean the death of
_one_ of the thirteen before the end of the year.

(6) Indicate how it could be shown, by the method of difference, that
the mosquito is responsible for the propagation of yellow fever.

(7) “Another experiment similar to this was tried by Plateau, who put
some food of which cockroaches are fond on a table and surrounded
it with a low circular wall of cardboard. He then put some
cockroaches on the table; they evidently scented the food, and
made straight for it. He then removed their antennae.” (Hibben).
Complete and give with explanations the method used.

(8) “In some cases it is impossible to remove an element which is
supposed to be the cause of an effect under investigation.”
Explain and illustrate.

(9) “Extreme care must be taken that, in the withdrawing of any
element, no other element is inadvertently introduced.” Tyndale
supposed he had proved _spontaneous generation_, when, after
sealing in a jar of boiled water a wisp of baked hay, he found,
after many days, indications of life within the bottle. In
transferring the hay to the bottle, he carried the former across
the room. What element was inadvertently introduced?

(10) “The attempt to determine the numerical relations according to
which two phenomena vary, requires the utmost caution as soon as
our inference outsteps the limits of our observations.” (Fowler).
Explain this in connection with the law of concomitant variations.

(11) “When the effects of all known causes are estimated with
exactness and subducted, the _residual facts_ are constantly
appearing in the form of phenomena altogether new, and leading
to the most important conclusions.” Make clear by illustration
this quotation which has reference to the principle of residues.

(12) Explain “invariable conjunction of phenomena.”

(13) Investigate by means of one of the five methods the following
problems:

(1) “All vegetables which grow to root should be planted during
the last two days of the waxing moon.”

(2) “In this section the _south_ wind is the _storm_ wind.”

(3) “Mischief is the outcome of misdirected energy.”

(4) “Bad boys usually receive unjust treatment.”

(5) “An ounce of prevention is worth a pound of cure.”