Free Will v. Determinism

One of the most oddball - but salutory - decisions ever made or not made by a Pope was Clement VIII settlement of the dispute between the Jesuits and Dominicans on whether humans have free will.  Clement's decision was basically - after much consultation of learned opinion through the Congregatio de auxiliis - to not decide the issue but to instruct the Jesuits and Dominicans that they could not call each other heretics for arguing for contrary positions.

Finally, after twenty years of discussion public and private, and eighty-five conferences in the presence of the popes, the question was not solved but an end was put to the disputes. The pope's decree communicated (5 September, 1607) to both Dominicans and Jesuits, allowed each party to defend its own doctrine, enjoined each from censoring or condemning the opposite opinion, and commanded them to await, as loyal sons of the Church, the final decision of the Apostolic See. That decision, however, has not been reached, and both orders, consequently, maintain their respective theories, just as any other theological opinion is held. The long controversy has aroused considerable feeling, and the pope, aiming at the restoration of peace and charity between the religious orders, forbade by a decree of the Inquisition (1 December, 1611) the publication of any book concerning efficacious grace until further action by the Holy See. The prohibition remained in force during the greater part of the seventeenth century.

Sometimes a decision not to decide is an inspired, infallible decision.