Mill's Methods Mill's methods appear in a book title 'A System of Logic'. One of Mill's goals in this book was to provide a foundation for inductive logic. In particular, Mill wanted to provide a foundation for science. Mill believed that he identified five methods that scientists used to investigate phenomena. Today, most scientists and philosophers of science would argue that Mill did not succeed in either providing a foundation for science nor in identifying all the methods used by scientists. However, if we read a science journal, we often can see that scientists have used a method identified by Mill. There are five methods: 1. method of agreement 2. agreement of difference 3. joint method of agreement and difference 4. method of concomitant variation 5. method of residues The first three methods are qualitative methods. The last two are quantitative methods. The first three methods are often described in terms of necessary and sufficient conditions (so we will discuss these as well). And because Mill's methods are causal methods, we will also discuss the causal fallacies. Method of Agreement I am going to give you two versions of Mill's method of agreement, the direct method and the inverse method. Agreement (direct): We identify the cause of an effect by identifying that condition that is always present (absent) when the effect is present (absent) Let us examine the following chart Case w x y z e 1 P P P P P 2 A P A P P 3 A P P P P Let us now read this chart. We are looking at three cases. The letter 'A' stands for 'absent'. The letter 'P' stands for 'present'. The letter 'P' means that a property is present. The letter 'A' means that a property is absent. The letters 'w', 'x', 'y', and 'z' are the candidates for the cause of the effect 'e'. In our chart, we list the possible causes first and the effect last. In this chart, we are examining three cases. In case 1, properties w, x, y, and z all occur and so does the effect e. In case 2, x and z are present and so is the effect e. In case 3, x, y, and z are all present and so is the effect e. We identify x as the cause of e because whenever x is present, so is the effect e. Look at the effect column, the column under e. Note that it has nothing but P's underneath it. This is how we identify this method as the method of agreement. The effect is always present (or absent). We note that x is also present when the effect is present and this is why we identify x as the cause for e. Agreement (inverse): We identify the cause of an effect as that condition that is present (absent) when the effect is absent (present) Case w x y z e 1 P P P P A 2 A P A P A 3 A P P A A In this case, x again is the cause. It is the presence of x that explains the absence of e. We could also have this chart: Case w x y z e 1 P A P P P 2 A A A P P 3 A A P A P In this case, x again is the cause. It is the absence of x that explains the presence of e. Let us look at an example An eighth grade teacher had five students who read very poorly. These students came from different-sized families, had different social and economic backgrounds, and attended different schools in the primary grades. The only factor that they shared in common was a lack of phonics instruction in the first grade. The teacher concluded that this lack of phonics instruction explained their lack of reading of ability. The teacher employed the method of agreement to reach this conclusion. We could set up the chart in four ways. Chart 1 Case Phonics Instruction Reading Ability 1 A A 2 A A 3 A A 4 A A 5 A A This is a variation of the direct method of agreement. The absence of phonics instruction explains the absence of reading ability. But we could also set up the chart in this way. Chart 2 Case Phonics Instruction Lack of Reading Ability 1 A P 2 A P 3 A P 4 A P 5 A P This is a variation of the inverse method of agreement. The absence of phonics instruction explains the presence of a certain lack of reading ability. But we could set up the chart in this way: Chart 3 Case Lack of Phonics Instruction Reading Ability 1 P A 2 P A 3 P A 4 P A 5 P A This is a variation of the inverse method of agreement. And we can set up the chart in this way: Chart 4 Case Lack of Phonics Instruction Lack of Reading Ability 1 P P 2 P P 3 P P 4 P P 5 P P This is a variation of the direct method of agreement. How we choose to define our conditions will determine whether we have the direct or inverse method. But how we choose to define our conditions will not affect our method. In all four cases, we still have the method of agreement. Method of Difference I am going to give the definition for the direct version for difference Difference: we identify the cause of an effect as that condition that is present when the effect is present and absent when the effect is absent We can illustrate this method with this chart: Case w x y z e 1 P P P P P 2 P A P P A In the method of difference, we are looking at two cases. We are keeping these cases as identical as possible but we are looking for one difference. This difference explains why the effect is present in one case and absent in the other. This is one method that we see fairly often. It underlies the notion of a controlled experiment--an experiment in which we have a control group and an experimental group. Example Pheromones are discrete chemicals produced by insects. Pheromones allow insects to communicate with other members of their species by signaling the presence of food, enemies, or willing mates. Recently, scientists have been able to produce pheromones in laboratories. Scientists speculated that they could pheromones produces in laboratories and sprayed on plants as a means to avoid insect damage to crops. To test this, the following experiment was devised. In the San Joaquin valley, plots of cherry tomato plants were divided into two groups. In one group, the plants were treated with a pheromone that disrupts mating between tomato pinworm moths. In the other group, no such treatment was provided. During the long growing season, peak infestation for the plots treated with pheromones as low while infestation for the plots not treated was high. Chart Group Treated With Pheromones Insect Infestation 1 P A 2 A P This is the inverse method of difference. The presence of pheromones explains the absence of insects. Note that we simplify the information in these charts. This is a 100 level course. We are organizing and simplifying the information a bit so that we can better see the method used. Joint Method of Agreement and Difference Joint method (direct): We identify the cause of an effect as that condition that is present when the effect is present and absent when the effect is absent. Chart Case w x y z e 1 P P A A P 2 P A P A A 3 P P A P P 4 P A A P P In this case, x is the cause of e. When x is present, e is present; and when x is absent, e is absent. So far, this sounds an awful lot like the method of difference. So, how do we tell the difference? In the method of difference, we focus on two cases. And we generally try to have these two cases as identical as possible (with one difference). In the joint method, we examine more than two cases. And sometimes, these cases are not as identical as they can be. Example Certain soils develop a vegetable mold that aids plant growth. This mold only seems to be present when earthworms are present. This fact has been confirmed by the following study. Five plots of soil were tested for this mold. In plot-1, the soil was rich in nitrogen, had good drainage, earthworms were present and so was the mold. In plot-2, the soil was rich in nitrogen, had poor drainage, no earthworms were present, and there was no mold. In plot-3, the soil was poor in nitrogen, it had good drainage, earthworms were present and so was the mold. In plot-4, the soil was poor in nitrogen, it had good drainage, there were no earthworms and there was no mold. In plot-5, the soil lacked nitrogen, the drainage was poor, there were no earthworms, and there was no mold. Chart Plots Nitrogen Good Drainage Earthworms Mold 1 P P P P 2 P A A A 3 A P P P 4 A A P P 5 A A A A In this case, the earthworms are the cause of the mold. When the worms are present, the mold is present; and when the worms are absent, the mold is absent. (Note that if we have a direct version, we will have identical columns for the cause and effect. If we have the inverse variation, the columns will opposites.) Method of Concomitant Variation Concomitant variation: Two phenomena vary together; and on this basis, we identify one phenomenon as the cause of the other phenomenon. Direct Inverse As one goes up, the other As one goes up, the other goes up; as one goes down, goes down; as one goes down, the other goes down the other goes up C E C E C+ E+ C+ E- C- E- C- E+ Example Researchers during the 1950's observed a link between air pollution and respiratory ailments. On those days when air pollution was high, respiratory ailments are higher. On days when air pollution is lower, respiration ailments are also lower. Chart Pollution Respiratory ailments P+ R+ P- R- Note that as one phenomenon goes up, the other goes up; and when one goes down, the other goes down. Method of Residues Method of residues: this method allows us to determine that one of a complete set of antecedent conditions is one element of a complex phenomenon if we already know that each of the remaining causes is the cause of each of the remaining effects. We have an effect that must be explained in terms of more than one cause. We isolate each cause that is responsible for part of the effect until we have our remaining cause and our remaining effect (the residue). Chart a,b,c--A,B,C a b c causes C causes A causes B Example Jones plans to deliver a load of wood in her pickup truck. she weighs her truck when it is empty and again when it is loaded. She concludes that the difference in weight is due to the load. Chart w -t wood ood, truck--x tons ruck Example Given the system of Newtonian physics, it is possible to predict the positions of each of the planets at any given time given their position at any previous time. This is due to the gravitational pull of the sun and other planets. In 1846, astronomers noted that the orbit of Uranus was irregular. Leverrier suggested the cause for this was an unknown planet; and he predicted its location. On the basis of this prediction, Galle discovered the planet Neptune. Chart Gravitational pull of sun, known planets, new planet--orbit of Uranus -sun -known planets new planet (remaining discrepancy) Necessary and Sufficient Conditions Some logicians define Mill's method of agreement, difference, and joint method in terms of necessary and sufficient conditions. According to these logicians, the method of agreement gives us a technique for determining necessary conditions, the method of difference gives us a method for determining sufficient conditions, and the joint method gives us a technique for determining necessary and sufficient conditions. But some people, including your instructor, tend to get these backwards. So, your instructor is not going to explain Mill's methods in terms of necessary and sufficient conditions. But it is still useful to know what is meant by a necessary condition or a sufficient condition. Sufficient condition X is a sufficient condition for Y if and only if when we have X, we have Y. Necessary condition Y is a necessary condition for X if and only if when we don't have Y, we don't have X. Oxygen is a necessary condition for fire. If we don't have oxygen, then we don't have a fire. Oxygen is not a sufficient condition for fire. Just because we have oxygen does not mean that we have a fire. Being the element with atomic number 79 is a necessary and sufficient condition for being gold. If some substance has this atomic number, then it is gold. If it does not have this atomic number, then it is not gold. One way logicians keep these conditions straight is by this: X→Y X is the sufficient condition for Y Y is the necessary condition for X X is the sufficient condition for Y because we have this argument form: X X Y →Y This argument form is just modus ponens (or →E) Y is the necessary condition for X because we have this form X ~ ~X →Y Y This argument form is modus tollens. Both forms are valid. Causal Fallacies Because Mill's methods are causal methods, they are prone to various causal fallacies. These fallacies include: 1. the post hoc ergo propter hoc fallacy (fallacy of the false cause) 2. the fallacy of confusing cause and effect 3. the fallacy of the common cause The post hoc ergo propter hoc fallacy In this fallacy, we confuse a coincidental relation for a causal relation. Example In 2001, the Arizona Diamondbacks played the New York Yankees in the World Series. On the day of the first game, Bolton and her husband ate mushroom and tomato omelettes at Harlow's cafe; and the D-backs won. On the day of the second game, Bolton and her husband ate mushroom and tomato omelettes at Harlow's cafe; and once again, the D-Backs won. On the days of the third, fourth and fifth games, Bolton and her husband did not eat mushroom and tomato omelettes at Harlow's cafe; and the D-Backs lost. For the sixth and final games, Bolton and her husband ate mushroom and tomato omelettes and the D-Backs won. Eating mushroom and tomato omelettes at Harlow's cafe caused the D-backs to win the World Series. This is the joint method. We can set up this chart: Game Dining on Omelettes D-Backs Win 1 P P 2 P P 3 A A 4 A A 5 A A 6 P P 7 P P This is the post hoc fallacy because there is no connection between Bolton's and husband's dining habits and D-Backs success in the World Series. (2) Confusing cause and effect We describe the effect as the cause and the cause as the effect In this case, we have a causal connection but we describe it backwards. Here is an example Researchers have noted a link between lung cancer and cigarette smoking. If people get lung cancer, they must take up cigarettes. There is a link, but we described it backwards. Taking up smoking causes lung cancer (or a greater chance of lung cancer). But getting lung cancer doesn't cause people to take up smoking. (3) Common cause A cause has two or more effects. We describe one effect as the cause of the other. Once again, we have a causal connection. We just describe the connection incorrectly. Example A child has a high fever and red spots all over his body. We commit this fallacy if we claim the fever causes the spots or the spots cause the fever. Both the fever and spots are probably caused by a virus, the chicken pox.