The Language of Argument

2 2 5

S u f f i c i e n t C o n d i t i o n s a n d N e c e s s a r y C o n d i t i o n s

Rigorous Testing

Going back to Table 1, it is easy to see that candidates A, B, C, and D are not

eliminated by the NCT as necessary conditions of target G, as G is present

in only one case (Case 1) and A, B, C, and D are present there as well. So far,

so good. But if we wanted to test these features more rigorously, it would be

important to find more cases in which target G was present and see whether

these candidates are also present and thus continue to survive the NCT.

The following table gives a more extreme example of nonrigorous testing:

Table 3

Case 1: A ~B C D G

Case 2: A ~B ~C ~D ~G

Case 3: A ~B C ~D ~G

Case 4: A ~B ~C D G

Here candidate feature A is eliminated by SCT (in Cases 2 and 3) but is not

eliminated by NCT, so it is a possible necessary condition but not a possible

sufficient condition for target feature G. B is not eliminated by SCT but is

eliminated by NCT (in Cases 1 and 4), so it is a possible sufficient condition

but not a possible necessary condition for target feature G. C is eliminated

by both rules (in Cases 3 and 4). Only D is not eliminated by either test, so

it is the only candidate for being both a necessary and a sufficient condition

for G.

The peculiarity of this example is that candidate A is always present

whether target G is present or not, and candidate B is always absent

whether target G is absent or not. Now if something is always present, as A

is, then it cannot possibly fail the NCT; for there cannot be a case where

the target is present and the candidate is absent if the candidate is always

present. If we want to test candidate A rigorously under the NCT, then we

should try to find cases in which A is absent and then check to see whether

G is absent as well.

In reverse fashion, but for similar reasons, if we want to test candidate B

rigorously under the SCT, then we should try to find cases in which B is

present and then check to see if G is present as well. If we restrict our atten-

tion to cases where B is always absent, as in Table 3, then B cannot possibly

fail the SCT, but passing that test will be trivial for B and so will not even

begin to show that B is a sufficient condition for G.

Now consider two more sets of data just like Table 2, except with regard

to the target feature, G:

Table 4

Case 1: A B C D G

Case 2: ~A B C D G

Case 3: A ~B C ~D G

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