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Contemporary Eastern Orthodox Christians often object to the dogmatic declaration of her immaculate conception as an "over-elaboration" of the faith and because they see it as too closely connected with a particular interpretation of the doctrine of ancestral sin. All the same, the historical and authentic tradition of Mariology in Byzantium took its historical point of departure from Sophronios, Damascene, and their imitators. The most famous Eastern Orthodox theologian to imply Mary's Immaculate Conception was St. Gregory Palamas. Though many passages from his works were long known to extol and attribute to Mary a Christlike holiness in her human nature, traditional objections to Palamas' disposition toward the Immaculate Conception typically rely on a poor understanding of his doctrine of "the purification of Mary" at the Annunciation. Not only did he explicitly cite St. Gregory Nazianzen for his understanding of Jesus' purification at His baptism and Mary's at the Annunciation, but Theophanes of Nicaea, Joseph Bryennius, and Gennadios Scholarios all explicitly placed Mary's Conception as the first moment of her all-immaculate participation in the divine energies to such a degree that she was always completely without spot and graced. In addition to Emperor Manuel II and Gennadius Scholarius, St. Mark of Ephesus also fervently defended Mary's title as "prepurified" against the Dominican, Manuel Calecas, who was perhaps promoting thomistic Mariology that denied Mary's all-holiness from the first moment of her existence.

What in particular does the group feels is impossible to believe ?
because they see it as too closely connected with a particular interpretation of the doctrine of ancestral sin.