Mill’s methods of induction are a descriptive method for discovering causes, which means causation is described in observational terms. When following the methods you arrive at a conclusion when there is a universal relationship between antecedent and consequent.
The Method of Agreement eliminates one possible cause because it is absent where the effect is not present but when one of the possible causes is present at all times when the effect occurs. To illustrate: A, B, C, went on holiday together to Mexico, whilst there they went to a bar, and drank a variety of different cocktails. They all felt sick afterwards, and had symptoms indicating impure water. Listing the antecedents we note that all the ingredients in the cocktails were different, however we observe that ice-cubes were present in all the drinks, and we come to the conclusion that it was the ice-cubes made of impure water that made the group sick as it is the one common antecedent.
This investigation is presupposing that it was something in the drinks that made the members of the group sick, and each of Mill’s methods work in this way. The argument works by providing possible causes for the sought event, the benefit of us providing the cause seems to be a time saving device as it allows a limit to what should be included as antecedents, for example a further common antecedent was that the holiday makers were all breathing the same air, as we know air is not linked to impure water we can exclude it. Conversely it could mean that if you miss the actual cause when relying on Mill’s Methods alone, you can never identify the true cause.
It is clear that if you do not employ your background knowledge you can run into some trouble with The Method of Agreement, for example you take three drunken people who are trying to work why they are inebriated. If A drinks vodka and Coke, B drinks rum and Coke and C drinks whisky and Coke – by looking at the antecedents they could come to the conclusion that it was the Coke that was making them drunk as it is the only antecedent that agrees. You cannot rely just on the antecedents alone; one must draw upon contextual knowledge for the Method of Agreement to be helpful. So, when using the method of agreement, we have to ask is there something besides X that the cases of e share? If there is another way in which they agree, then the argument is unsound.
With the drinks example, according to the method of agreement the possible causes of drunkenness could be whisky, vodka, or Coke. The method of agreement (without drawing on contextual knowledge) would identify the cause to be Coke, because it is the common antecedent. This example seems silly due to our experience with Coke. Experience provides cases where Coke was present but the drinker did not get drunk. To resolve some of the problems we should focus more on controlled experiments and refine our knowledge of causes. Mill’s methods require lists of specific possible causes, if we want strong reasoning we need support from the key premise that is assumed but not always expressed, such as: there are no other possible causes which would have the same link to the effect that the selected cause does. If this premise is false, the inference is weak; it is this assumption (if we consider it correct), which allows us to dismiss the possibility that Coke is the cause of drunkenness.
The method of difference attempts to identify a cause by looking at two cases which are alike except that the effect is present in one and not the other and the suspected cause is present in one and not the other. Here is an example to illustrate, If A and B went out to dinner, both eating fish and chips and drinking water – but only A had the trifle for dessert, and got food poisoning then Method Of Difference would identify the trifle as the cause for the effect of food poising. We can conclude that eating trifle was necessary to become ill because each case is the same in every respect except one (the trifle) where they disagree. The presence or absence of trifle is the only difference between A and B; this means there is good reason for thinking that the trifle caused the food poisoning. This method can also strengthen the claim X is needed for Y if when there is no X there is no instance of Y, this allows for A and B to have had a different combination of main meals, but still results in the person who has the trifle becoming ill rather than the food poisoning being the result of a specific combination of fish and chips and trifle. Although it is difficult to find two cases that are exactly the same, this is not a severe limitation as it works in many scenarios, in the case just illustrated there are lots of ways that A and B are different, but the Method of Difference still works. Saying this, the most ideal way to use the method would be in a controlled experiment, a trial over a short space of time where causes can be added or removed when needed.
The third method is The Joint Method; Mill’s Joint Method of Agreement and Difference applies to cases with varying antecedent circumstances. To illustrate: if at a dinner party, four out of the six guests got food poisoning, we can use the Joint Method to find what caused it. A had the tuna salad (along with various other items) and got food poisoning, B, C, D had a different menu, but did have the tuna salad, the Method of Agreement identifies the common antecedent. Although, the joint method requires examination of the cases where food poisoning did not occur. E and F we did not have the tuna salad and did not have food poisoning. The final step is to utilise the idea behind the Method of Difference to show tuna salad is the cause. From this illustration we see the Joint Method works by finding a common antecedent circumstance when the effect occurs and then cases where the event does not occur, the antecedent that does not occur. Then, in the style of the Method of Difference, we compare the two sets of cases. These additional cases increase confidence that the X is the cause. If X is the cause we predict finding X absent when the effect is absent. Scenarios where e is present and absent demonstrate a strong relationship because other possible causes get ruled out by either being absent when the effect is present or present when it is absent. The method is very helpful and offers new advantages that the method of agreement and difference cannot offer when they are used in isolation.
The Method of Concomitant variation: “Mill’s idea behind this method was that a change in the strength of the effect is to be accounted for by a change in the strength of the cause.” (Salmon, 2007, p177) the method is applicable where suspected cause and effect occur together at all times. The method means we ground causal reasoning in observational proportional change between two events. To illustrate: if I were to notice that when the temperature gets colder my housemates put the heating on for longer, it is only the variation in temperature that relates to the variation in the length of time that the boiler is on. This happens in many cases when we suspect causation, therefore this method has wide application, partly due to how it reflects the empirical process known to scientific experiments, where strong association between variables suggests a causal relationship. However, there can be concomitant variations that are totally coincidental, so not every pattern can be used in induction, but Mill’s method does not refer to such chances. To get round this, we must make sure we observe enough cases to form a generalisation – but this may be difficult to do, and thus results in uncertainty, as just because two events ‘co-vary’ does not mean one is the cause of another. Seen with thunder and lighting they are both effects of a common cause (the discharge of electricity in the air) it is not that the louder the thunder, the brighter the lightening.
Finally, the Method of Residues, which works when we isolate known causes from unknown causes to find out x’s specific contribution to the effect. The benefit of this method is that it draws upon verified knowledge; however, it suffers from the problem that if we don’t consider the actual cause initially then we cannot derive it as the conclusion. An example of this method is as follows, a vet stands on weighing scales holding a dog. The scale displays 220 pounds. The vet knows she weighs 200 pounds ergo the dog weighs 20 pounds. However
a weakness with this method is that it assumes all the possible contributing causes are known, so in the above illustration the vet could have gained weight, and not know she weighs 215 pounds and the dog weighs 5. This assumption may be too broad for the method to really work.
In conclusion, controversy surrounds Mill’s methods about if they can discover causes or if they only work when we already have a causal understanding in mind. Saying, this all induction and the search for associations in an event is guided by our background knowledge it is not just Mill’s method’s which are susceptible to causal fallacies. Saying this perhaps we should look to Mill’s methods as confirmation, rather than proof of causation, this means that we can use them as an aid to causal understanding and side step some of the fallacies.