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The sense of the faithful, or sensus fidelium, is what Pope Benedict XVI in 2012 called a "supernatural instinct" for knowing what teachings ring with Catholic truth. He also referred to it as the sensus fidei, or sense of faith by which Catholics have a "criterion for discerning whether or not a truth belongs to the living deposit of the Apostolic Tradition." It's sometimes called a sensus catholicus, or Catholic instinct.
Vatican II taught in paragraph 12 of Lumen Gentium (LG),"The entire body of the faithful … cannot err in matters of belief … when they show universal agreement in matters of faith and morals." This led some dissident Catholics to invoke a false notion of the sensus fidelium to dissent from Catholic teaching. The same paragraph in LG, however, states that this Catholic instinct is "exercised under the guidance of the sacred teaching authority" to which the people of God show "faithful and respectful obedience."
Pope Benedict warned that the sensus fidelium isn't a "kind of public ecclesial opinion" which can be invoked "in order to contest the teachings of the Magisterium." He clarified that this "supernatural sense of faith" can only be "authentically developed in believers" to the extent that they "fully participate in the life of the Church, and this demands responsible adherence to the Magisterium, to the deposit of faith."
So-called nominal Catholics who dissent from Church teaching and ultra-traditional Catholics who reject the authority of the Supreme Pontiff and thus put themselves in schism will both hold up a mistaken concept of sensus fidelium to assert that their understanding of Church teaching is correct, in defiance of the authentic Magisterium.
In 2014 the International Theological Commission (ITC), then chaired by Cdl. Gerhard Müller, former prefect of the Congregation for the Doctrine of the Faith, emphasized that this sense of faith isn't the same thing as "public opinion inside (or outside) the Church." The sense of the faithful, ITC noted, isn't simply "the opinion of the majority of the baptized at a given time."
Learn why Catholics have such great certitude in season two of Church Militant's Premium show Majesty of the Faith—Being Catholic.