Full Idea
For contemporary logicians, it is not non-contradiction that provides the criterion for what is thinkable, but rather inconsistency.
Gist of Idea
We can allow contradictions in thought, but not inconsistency
Source
Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3)
Book Reference
Meillassoux: 'After Finitude: the necessity of contingency', ed/tr. Brassier,R [Bloomsbury 2008], p.77
A Reaction
The point is that para-consistent logic might permit isolated contradictions (as true) within a system, but it is only contradiction across the system (inconsistencies) which make the system untenable.