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Vincible ignorance is, in Catholic moral theology, ignorance that a person could remove by applying reasonable diligence in the given set of circumstances. It contrasts with invincible ignorance, which a person is either entirely incapable of removing, or could only do so by supererogatory efforts (i.e., efforts above and beyond normal duty).
The first Pope to use the term invincible ignorance officially seems to have been Pope Pius IX in the allocution Singulari Quadam (9 December 1854) and the encyclicals Singulari Quidem (17 March 1856) and Quanto Conficiamur Moerore (10 August 1863). The term, however, is far older than that. Aquinas, for instance, uses it in his Summa Theologica (written 1265–1274), and discussion of the concept can be found as far back as Origen (3rd century).