# THE NECESSARY CONDITION TEST

The necessary condition test (NCT) is like the SCT, but it works in the reverse fashion. With SCT we eliminated a candidate F from being the sufficient con- dition for G, if F was ever present when G was absent. With the necessary condition test, we eliminate a candidate F from being a necessary condition for G if we can find a case where G is present, but F is not. This makes sense, because if G can be present when F is not, then F cannot be necessary for the occurrence of G. Thus, in applying the necessary condition test, we only have to examine cases in which the target feature, G, is present, and then check to see whether any of the candidate features are absent.

NCT: Any candidate that is absent when G is present is eliminated as a possible necessary condition of G.

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The following table gives an example of an application of this test:

TABLE 2

Case 1: A B C D ~G

Case 2: ~A B C D G

Case 3: A ~B C ~D G

Because Case 1 does not provide an instance where G is present, it cannot eliminate any candidate as a necessary condition of G. Case 2 eliminates A as a necessary condition of G, since it shows that G can be present without A being present. Case 3 then eliminates both B and D, leaving C as the only possible candidate for being a necessary condition for G.

From this, of course, it does not follow that C is a necessary condition for G, for, as always, new cases might eliminate it as well. The situation is the same as with the SCT. An argument for a negative conclusion that a candidate is not a necessary condition, because that candidate fails the NCT, is a deductive argu- ment that cannot be overturned by any further cases. In contrast, an argument for a positive conclusion that a candidate is a necessary condition, because that candidate passes the NCT, is an inductive argument that can be overturned by a further case where this candidate fails the NCT. For example, suppose we find:

Case 4: ~A ~B ~C ~D G

The information in this new Case 4 is enough to show that C cannot be a neces- sary condition of the target feature G, regardless of what we found in Cases 1–3.

In applying both the SCT and the NCT, it is crucial to specify the target feature. Case 4 shows that candidate C is not a necessary condition for target feature G. Nonetheless, candidate C still might be necessary for the opposite target feature, ~G. It also might be necessary for features A, B, and D. Nothing in Cases 1–4 rules out these possibilities. Thus, even after Case 4, we cannot say simply that C is not a necessary condition. Case 4 shows that candidate feature C is not a necessary conditions for target feature G, but C still might be necessary for something else. The same point applies to sufficient conditions as well. In Table 1, Case 2 ruled out the possibility that candidate feature B is sufficient for target feature G, but none of the cases in Table 1 show that B is not sufficient for target feature C. To avoid confusion, then, it is always important to specify the target feature when talking about what is or is not a necessary or sufficient condition.

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