Mueller is no newcomer to the issue: In 2009, he told the Catholic news agency Zenit that he wanted the society's seminary in his diocese shut down and the four bishops to resign to live as simple priests "as part of the reparation for the damage that the schism has caused."
Given Mueller's negative view and after the talks broke down earlier this year, the pope named a trusted adviser, Monsignor Augustine Di Noia, to take charge of negotiations with the society. From Mueller's comments, however, it appears there's not much to negotiate.
The society's most notorious member is Bishop Richard Williamson, who made headlines in 2009 when he denied that any Jews were killed in gas chambers during the Holocaust. His comments were a major scandal for Benedict since they were broadcast on the same day the decree lifting Williamson's excommunication was signed.
The Simon Wiesenthal Center on Saturday welcomed the suggestion that talks with the society had broken down and said it hoped the society's members "will eventually give up their theology of anti-Semitism and Holocaust denial."
The society has distanced itself from Williamson.
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