Two kinds of contraction

According to the view proposed in Chapter 3, one can never justify a deliberate expansion into inconsistency. Respect for the desideratum that error be avoided in changing states of full belief requires this. One can, however, legitimately though inadvertently expand into inconsistency via routine expansion.

Although routine expansion into such inconsistency may be legitimate in the sense that programs for routine expansion that can inject inconsistency are legitimately adopted even when they incur a risk of leading to inconsistency, it is, nonetheless, clear that an inconsistent result calls for contraction. I call such contraction coerced contraction because it is mandated by the inadvertent expansion into inconsistency and the urgency of retreating from inconsistency.

Contraction does not have to be coerced to be legitimate. One may be justified in ceasing to be certain that a doxastic proposition is true even though one is not retreating from inconsistency. Uncoerced contraction may be justified because someone has proposed a conjecture that, given the current state of full belief, is certainly false. The inquiring agent may be justified in incurring the loss of information that must result from such contraction in order to obtain a cognitive benefit. The contraction is not imposed as the remedy for the inadvertent expansion into inconsistency but is deliberately chosen as best for the purpose of realizing the inquirer's cognitive goals.

Uncoerced contraction is illustrated by situations where investigators are confronted with unexplained anomalies