Full Idea
We sometimes discover our views are inconsistent and do not know how to revise them in order to avoid inconsistency without great cost. The best response may be to keep the inconsistency and try to avoid inferences that exploit it.
Gist of Idea
If there is a great cost to avoiding inconsistency, we learn to reason our way around it
Source
Gilbert Harman (Change in View: Principles of Reasoning [1986], 2)
Book Reference
Harman,Gilbert: 'Change in View: Principles of Reasoning' [MIP 1986], p.15
A Reaction
Any decent philosopher should face this dilemma regularly. I assume non-philosophers don't compare the different compartments of their beliefs very much. Students of non-monotonic logics are trying to formalise such thinking.