(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 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.