Occasions in which only two events, isolated from all other events, are causally connected with each other are rare. More often than not, two events mixed among many need to be detected as causally connected, and others need to be ignored as insignificant, if not irrelevant. Francis Bacon (1561—1626) is credited with an early attempt to formulate in simple rules the way the mind functions in such detectivelike exercise. After enrichment by several other philosophers and scientists, including Isaac Newton, the refined, final form of these rules, totaling five in number, is known today as Mill’s Methods of Experimental Inquiry,2 after the British philosopher J. S. Mill (1806—1873). These are summarized below.
1. Method of Agreement
Mill writes, “If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.”
Mill’s statement being somewhat abstract, it needs some elaboration. Suppose a group of seven students went to a weekend (free!) beer-tasting party, and four of them became sick after drinking. Let us call the four students A, B, C, and D and the brand names of beer available l, m, n, p, r. The next day, when recovered, the students got together and pooled their information (see Table 4.1).
In the above example, the two events causally connected are drinking beer m and getting sick. It would be reasonable if they
found brand m to be the culprit and “hated” that beer and, from that day on, lost no chance to say so.
2. Method of Difference
Mill writes, “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, or an inseparable part of the cause, of the phenomenon.”
Extending the Method of Agreement, suppose subsequent to the four students blaming beer m, student A met another student, say E, who went to the party that night but did not get sick. On being asked by student A, E told A that he drank beers l, p, and r, but not m. “No wonder you did not suffer like us. That accursed beer m should be banished,” is what A could say (see Table 4.2).
The event that made the difference was the drinking of beer m in one case and not drinking it in another. And the causal connection is between the above difference and the event of getting sick. Drink beer m, and get sick; don’t drink m, and don’t get sick
3. Joint Methods of Agreement and Difference
The evidence from the above two methods constitutes the present one. It may be formulated as
The above two pieces of evidence can be summarized as
- When H is yes, t is yes.
- When His no, t is no.
The causal connection, obviously, is between H and t (t is an “inseparable” part of H). Though in the above demonstration we have chosen three terms (H J K, t u v) as the greatest number of terms, and two terms (J K, u v) as the least, in principle, these numbers can vary, and the method will still apply.
Example:
In this example, two terms and one term are used to establish the causal connection between H and t, though by a slightly different path.
4. Method of Residue
We may often find a cause as one of many bundled together. Likewise, we may also find the corresponding effect as one of many bundled together. Each of the bundles can be likened to the ends of electrical cables, consisting of many wires, the cables to be connected together. If all but one wire from the first cable are connected to all but one wire from the second cable, that the remaining wires from each are to be mutually connected is logical. That is the kind of logic involved in the Method of Residue.
Considering small numbers for convenience, although the method remains the same, an electrician is required to connect two cables, each consisting of three wires, one black, one green, and one white. He does his job as a routine, connecting black to black, green to green, and white to white. Now, suppose the first cable consists of black, green, and white wires, but the second cable consists of blue, red, and yellow wires. The job is now not so obvious. A little pause and some inquiry are necessary; according to his local “code,” the black wire is hot, the white wire is neutral, and the green wire is grounded. If he finds on inquiry that, by the code of the foreign country from which the second cable was imported, blue is neutral and yellow is ground, then he connects the white wire of the first cable with the blue wire of the second and the green of the first with the yellow of the second. Yet to be connected are the hot black wire in the first cable and the hot red wire in the second cable. This last connection is the connection between residues, which is now obvious to the electrician. Likewise, in terms of logic, we can identify which particular cause in the bundle of causes is responsible for a particular effect in the bundle of effects; this is done by relating the residue in the bundle of causes with the residue in the bundle of effects.
Mill writes, “Subduct from any phenomenon such part as is known by previous induction to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”
This may be symbolized as below:
L M N — x y z
L is known to be the cause of x. M is known to be the cause of y. Thus, Nis the cause of z.
It may be noted that, unlike the three previous methods, wherein causal connection was self-sufficient, in this method, we need to mention cause and effect separately, thereby implying temporal relation. This is because the Method of Residue explicitly appeals to the previously established pair(s) of cause and effect. Also, note the assumption that, although the causes and effects occur in separate bundles, for a given effect, only one of the causes is responsible for the effect.
5. Method of Concomitant Variation
This method is similar to the Method of Residue in that a bundle of factors is causally related to another bundle of factors. Unlike the Method of Residue, however, we do not know beforehand the cause-and-effect relation between all but one pair of the wires in the first bundle and those in the second bundle. In this method, though only one of the members in the bundle of likely causes is responsible for a given effect under observation, we do not know which member that is. Further, the problem can be compounded in that it is impossible to eliminate completely the suspected cause from the bundle of likely causes. Under circumstances in which this method is relevant, we can impose, or wait for nature to bring about, a quantitative variation over a suitable range in the suspected cause and observe whether this results in a quantitative change in the effect under observation. If such a change is factual, the inference is that the suspected cause is, indeed, the cause of the effect under observation.
An extract from Mill’s description of this method reads, “Though we cannot exclude an antecedent altogether, we may be able to produce, or nature may produce for us, some modification in it. By a modification is here meant, a change in it not amounting to its total removal. . . . Whatever phenomenon varies in any manner, whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon.”
Using a plus sign (+) for an increase and a minus sign (-) for a decrease in the degree or quantity of the individual members of the pair of factors in question (described earlier), and noting that an increase in the first member of the pair may result in either an increase (directly related) or in a decrease (inversely related) in the other member of the pair, the following two relations can be symbolically formulated:
- Directly related
A B C—p q r
A B C+ — p q r+
A B C- — p q r—
Then, C and r are causally connected.
- Inversely related
A B C—p q r
A B C+ — p q r—
A B C- — p q r+
Then (also), C and r are causally connected.
The Method of Concomitant Variation, it should be noted, is the only one among Mill’s five methods that specifies the degree or quantity of a phenomenon, hence, requires quantitative experiments in which the phenomenon needs to be varied (or observed) over a range. This principle is extensively used in what may be called experiments of parametric control for gathering empirical data. The other four methods have an “all or nothing” character, hence, are qualitative in nature.
Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.
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