More Details About The General Procedure

Definitions

1. Initial Interesting Observation, B
2. Theories (A₁, A₂, A₃, ...)
3. Observations and Experimental Data ( D₁, D₂, D₃, ...)

Preliminary Conditions

There are two preliminary conditions:

1. Each of the theories must be evaluated according to the criteria for a scientific theory and each must satisfy at least half of the criteria. Before starting an abductive argument it should be shown that the theories have merit as scientific theories.
2. Each theory must appear to explain the initial interesting observation. Note that the theory is explaining how the observation comes about or the conditions that result in the observation. The theory is not suggesting possible uses of the observation.

Evaluation Procedure

To determine the best theory, set up a table that shows when a specific piece of observed data is, or is not, expected for each theory. All of the observations (D₁, D₂, etc.) are listed down the chart on the left and all of the theories (A₁, A₂, etc.) are listed across the top of the chart. Whether an observation would be expected if the theory were true is indicated in the box where the theory and the observation intersect. An example of the result of such a process is shown below. A "yes" means that the observation in that row would be expected if the theory in that column were true; If A were true, then D would be expected. Two alternative ways of expressing this are: "If A were true, then D would be likely" and "If A were true, then D would be very probable."

	A1	A2	A3
D1	yes	yes	no
D2	yes	no	no
D3	yes	yes	yes

Determining Relative Merit

The theory which leads us to expect the most observations will be the "best" theory, it will be the most probable explanation of B compared to the alternatives being considered. In the above example A₁ leads us to expect the most data and so it is considered to be the most likely explanation for the initial observation out of these alternatives. Notice that an observation that is equally likely on the basis of the theories doesn't help to distinguish between theories. An observation that was not probable on the basis of any of the theories also doesn't help to distinguish between theories.

Note that the more data that is available, the more confidence can be placed in our conclusion. For a small number of data points the conclusion is very tentative. Also notice that we are concentrating on the number of "yes" responses in these tables, but even a large number of yes responses could be negated by a "no" that is so important that it would cause us to eliminate that possibility. In other words, it is easier to show that something is not true (using a counter-example) than it is to show that something is true. To show that it is true would require knowing all possible information, which can't be done. What we are doing is finding the most likely explanation using a limited data set. Since we have a limited data set and since there is always uncertainty in scientific data, we do not eliminate a theory due to a "no" response as would be done in a more formal logic procedure.

The next page has some simple examples.