It is usually assumed that the thinking that goes on in the sciences are inductive. That may be because scientists usually employ statistical methods in their studies. However, the thinking uses both deductive and inductive methdos. When scientists form hypotheses, they sometimes use induction. That is, after observing a number of samples, scientist observe regularties in the samples and then form a hypothesis based on induction. On the other hand, when scientist test their hypotheses to find out whether they should be confirmed or rejected, they use deduction. We'll look at the first part first.
Hypothesis Building and Testing
Suppose there is an interesting phenomenon in which scientists are interested, such as the occurrence of lung cancer in smoking people. After observing a number of cases, it is found that the percentage of lung cancer is much higher in smokers than in non-smokers. Thus scientists form a hypothesis that smoking causes lung cancer. This hypothesis is formed through observation of some regularities, in this case the statistical correlation between lung cancer and smoking.
Alternatively, when scientists observe that a fire will be extinguished in a jar from which oxygen is taken out, and a fire continues to burn when oxygen is supplied continuously, they form the hypothesis that oxygen is necessary for fire to burn. The hypothesis is obtained through observation of the phenomena.
After forming the hypothesis, what scientists do in the next step is to test it. This is done by finding its consequent conditions. These are specific, testable propositions that must be true if the hypothesis is true. Hypotheses are general statements. That is, they treat of everything equally, and say that everything is so and so. The consequent conditions are particular statements that follow from the hypothesis. Thus, when the hypothesis is that smoking increases the chance of having lung cancer, the consequent condition here is that this person who smokes will be more likely to have lung cancer. This particular statement can be tested because it does not treat all things, but only a limited case of things. We can test that this person will have lung cancer by just watching him and testing him regularly. But since we are talking about statistical correlation here, we must observe and test the hypothesis in other people too. If they show that the correlation is really there, then the hypothesis is confirmed. In the same vein, when the same can be tested in a jar in a labolatory, then the hypothesis about oxygen can be tested also. The hypothesis will be confirmed if the test in the laboratory goes as predicted by the hypothesis. The prediction is part of the consequent condition of the hypothesis. Thus, if in case of the oxygen hypothesis, it is predicted that the fire in this jar will be extinguished if all the oxygen is pumped out. If the experiment goes as predicted, then the hypothesis is confirmed, but if not, then it is rejected.
Thus we see that scientific thinking consists of two major parts, which can be shown in the following diagrams:
| Hypothesis Forming | Hypothesis Testing |
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Mill's methods are some methods used to formulate hypotheses of certain phenomena. It is clearly a species of inductive arguments as we shall see. More precisely the methods, first proposed by British philosopher and logician John Stuart Mill, are used to find causes of the phenomena to be explained. All of Mill's methods share the same characteristics in that they separate the phenomena into two parts, namely the parts to be explained, or the effects, and the antecedent phenomena which include the likely causes of the effects. The method is conducted by observing the effects and then reason to the likely causes by observing common features, different features, features that vary with each other, and so on. According to Mill, there are five of his methods:
Here is what the first method, Method of Agreement, does. First you have a phenomenon you would like explained, for example a group of students in a certain school all having diarrhea and vomiting. You want to know what caused the symptom. You know that the symptom could only be caused by food. So you list all the food eated by the affected student up to the time when they were attacked, and suppose this is the result:
A B C D ==> j h l k E F A G ==> k o m n H I J A ==> q r s k
The capital letters on the left hand side represent the antecedent conditions, and the small letters on the right show the phenomena on the effects side. Thus, in case of the students having diarrhea, the left hand side represents the food eated by the students, and the right hand side show the symptoms that they have. Suppose that each capital letter represents a kind of food, and the small letters on the right hand side represent a symptom. Then we can see that the phenomena on the left hand side have one thing in common, A. And similarly for the phenomena on the right hand side, the symptom k. Thus we can conclude, using the First Method, that A is the likely cause of k.
Here is the diagram for the second method:
A B C D ==> j k l m B C D ==> m l j
Suppose we have only two events which are alike in all aspects but one. Then it is likely that the part that is the difference on the left had side is the cause of the part that is missing on the right hand side.
The third method has nothing but a joint consideration of the first two methods in finding likely causes. Let's look at this diagram
A B C D ==> k l m o A E F G ==> l p n r A H I J ==> q u r l H I M N ==> q r z y O P Q R ==> x w n r
Here is the diagram for the fourth method:
A B C D ==> o p q r We know already that A ==> p B ==> q C ==> r
Thus, we can conclude that D is the likely cause of o, because the pair is the only one left from the matching of causes and effects which we know already. That is why this method is called the Method of Residue.
Here is the diagram for the last method:
A B C D1 ==> w x y z1 A B C D2 ==> w x y z2 A B C D3 ==> w x y z3 A B C D4 ==> w x y z4 A B C D5 ==> w x y z5
The phenomena are alike except only that there is a variation in the degree of D on the left hand (causes) side, and the same for z on the right hand side. Since everything else is equal we conclude that here D is the likely cause of z.