The Language of Argument

2 2 7

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

The target, G, must also be present in these cases, since C is present and

Condition 3 has already been met. Testing this group of cases can reassure

us that it is not only candidate D that is sufficient for the target, G.

Finally, for it to be reasonable to reach a positive conclusion that C is suf-

ficient for G, this further condition must also be met:

5. We have tested enough cases of the various kinds that are likely to
   include a case in which C is present and G is absent if there is any
   such case.
   This new condition cannot be applied in the mechanical way that conditions
   1–4 could be applied. To determine whether condition 5 is met, we need
   to rely on background information about how many cases are “enough” and
   about which kinds of cases “are likely to include a case in which C is present
   and G is absent, if there is any such case.” For example, if we are trying
   to figure out whether our new software is causing our computer to crash,
   we do not need to try the same kind of computer in different colors. What
   we need to try are different kinds of CPUs, monitors, software, and so on,
   because we know that these are the kinds of factors that can affect perform-
   ance. Background information like this is what tells us when we have tested
   enough cases of the right kinds.
   Of course, our background assumptions might turn out to be wrong. Even
   if we have tested many variations of every feature that we think might be
   relevant, we still might be surprised and find a further case in which C and
   ~G are present. All that shows, however, is that our inference is defeasible,
   like all inductive arguments. Despite the possibility that future discoveries
   might undermine it, our inductive inference can still be strong if our back-
   ground beliefs are justified and if we have looked long and hard without
   finding any case in which C is present and G is absent.
   Similar rules apply in reverse to positive conclusions about necessary
   conditions. We have good reason to suppose that candidate C is a necessary
   condition for target G, if the following conditions are met:


6. We have tested some cases in which the candidate, C, is absent.


7. We have tested some cases in which the target, G, is present.


8. We have not found any case in which the candidate, C, is absent and
   the target, G, is present.


9. If there is any other candidate, D, that is never absent where the
   target, G, is present, then we have tested cases where C is absent and
   D is present.


10. We have tested enough cases of the various kinds that are likely to
    include a case in which C is absent and G is present, if there is any
    such case.
    This argument again depends on background assumptions in determin-
    ing whether condition 5 is met. This argument is also defeasible, as before.

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