Mill's Inductive Reasoning

Mill's Inductive reasoning

Method of Agreement

Mill's method of agreement identifies a cause of an event in terms of its sufficient condition. When using this method, one searches for a single factor that is common to multiple situations in which the same event occurred.

Mill says that, when two or more occurrences of the event under investigation have only one condition in common, then that condition is the cause of the event. (Mill, 2002)

More simply stated, Mill's method of agreement eliminates all but one common precursor. Mill's method of agreement requires that in all cases where a consequence has occurred, the antecedent condition must be present. This method isolates the supposed origin by listing all of the possible factors that can be considered possible causes, then discovering the one factor common to all cases, (Mill, 2002). For example: Suppose that after work four people go to the local deli. After eating lunch, everyone becomes very sick. As they return to work, these people discuss what could have caused everyone to get so ill and everyone itemizes the items that were eaten: one had the fish special, drank water, hush puppies and coleslaw, and for desert, cherry pie.

Another one had a hamburger, French fries, coleslaw and a diet pepsi, and again, cherry pie for dessert. The third person only had the coleslaw and a diet pepsi. The last one had a hamburger, coleslaw, diet pepsi and cherry pie.

From this one could generate a chart showing what everyone had to eat and determine the probable causes. Using Mill's method of agreement one sees that the only food everyone had in common was coleslaw. One could then, conclude that the illness was caused by the coleslaw. There is one common precursor, and the following hypothesis could be stated, "The coleslaw at the local deli will make you sick if you eat it." This hypothesis would be even stronger if more people became ill after eating the coleslaw.

However there is a certain weakness to the Method of Agreement since there may possibly be other conditions that were common with all that got sick. For example, everyone used silverware that had been washed in the same machine. Perhaps there was a malfunction in the deli air conditioning: everyone breathed the same air. Everyone was waited on by the same waitress, or waiter.

Other factors may remain undetected. The principle that can be used to judge the dependability of the induction is: The greater the differences between the events in which the effect has occurred the greater the reliability of the conclusion, (Kemerling, 2001).

Method of Difference

According to Mill, if an occurrence in which the event being investigated occurs, and an instance in which it does not occur, have every condition in common except one, then that one circumstance in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the occurrence. The method of difference necessitates a comparison of at least one case in which the occurrence appeared and at least one in which it did not, (Kemerling, 2001).

Simply stated, Mill's method of difference is the exclusion of all differences between the cases being studied except one between instances in which the effect occurred and those in which it did not. For example, in the case above: Suppose our four co-workers all ordered the same meal - Hamburger, Fries and a Diet Pepsi. However, one decided to add a slice of cherry pie. It would be reasonable for that one person to say, "I shouldn't have had the pie. It made me sick." The pie may have been spoiled or perhaps the sickness was from over eating - we're not sure. However, it would be reasonable to conclude that we have isolated the pie as a factor that caused that one person's nausea, (Kemerling, 2001).

The major difference between the indirect method of difference and the method of agreement is that the indirect method uses negative cases to strengthen conclusions drawn from positive cases. Usually, the indirect method is preferred to the method of agreement, but in some types of investigation, the set of negative cases is ill-defined and the indirect method cannot be used. The examination of negative cases presupposes a theory allowing the investigator to identify the set of observations that embraces possible instances of the phenomenon of interest. Ideally, the definition of this set should not be influenced by knowledge of instances of hypothesized causes or instances of the effect, (Kemerling, 2001).

Inductive reasoning gives a person more flexibility in reasoning and places increased emphasis on observation as opposed to secondary sources of knowledge. Numerous authorities believe that students can and should be encouraged to use inductive reasoning in their problem solving. Typically, indicative reasoning is the basis of inquiry and discovery approaches. For example, students can study the habits of people in day-to-day activities and then draw general conclusions about human behavior, (Resnick, 1987). Inductive reasoning is the ability to reason from the particular to the general, to form a logical conclusion from scattered facts, and to see the "big picture," (Kemerling, 2001)

There are various terms used to refer to "reasoning": critical thinking, higher-order thinking, logical reasoning, or simply reasoning. Different subject areas tend to use different terms. Across all subject areas, however, there are commonalities. (Resnick, 1987). Inductive reasoning involves looking for patterns and making generalizations.

People with higher incomes tend to vote Republican.

Wisconsin winters are becoming colder with more snow.

Too many professional athletes are self-centered and spoiled. Highways have become safer because of the 21-year-old drinking law.

My neighbor is in a grouchy mood today.

Generalizations -- to condense what we observe and experience into something meaningful, we constantly make interpretations and draw conclusions. Generalizing is almost second nature to us.

Whether our generalizations are valid or not is another matter. Valid generalizations are based on careful analysis of appropriate information. Unfortunately, generalizing sometimes results in oversimplifications, stereotypes, or false assumptions. Teaching students to draw meaningful

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