Saint Thomas Aquinas in the Summa Theologica:

On the contrary, Augustine says against the Manichees [Cf. De Civ. Dei xviii, 1]: “In Christ’s Church, those are heretics, who hold mischievous and erroneous opinions, and when rebuked that they may think soundly and rightly, offer a stubborn resistance, and, refusing to mend their pernicious and deadly doctrines, persist in defending them.” Now pernicious and deadly doctrines are none but those which are contrary to the dogmas of faith, whereby “the just man liveth” (Romans 1:17). Therefore heresy is about matters of faith, as about its proper matter.

I answer that, We are speaking of heresy now as denoting a corruption of the Christian faith. Now it does not imply a corruption of the Christian faith, if a man has a false opinion in matters that are not of faith, for instance, in questions of geometry and so forth, which cannot belong to the faith by any means; but only when a person has a false opinion about things belonging to the faith.

Now a thing may be of the faith in two ways, as stated above (I, 32, 4; I-II, 1, 6, ad 1; I-II, 2, 5), in one way, directly and principally, e.g. the articles of faith; in another way, indirectly and secondarily, e.g. those matters, the denial of which leads to the corruption of some article of faith; and there may be heresy in either way, even as there can be faith.

The dogmas of the Faith are the infallible teachings of the Magisterium, through solemn definitions of the Pope, solemn definitions of an Ecumenical Council, or the ordinary and universal Magisterium. Any such infallible teaching, whether on a matter of faith or morals or salvation, is a required belief under pain of heresy. Such teachings require the full assent of faith — the type of assent called divine and catholic faith — because they are both certainly without error and important to faith, morals, or salvation.

Non-infallible teachings require a lesser type of assent, called the religious submission of will and intellect. Dissent from a non-infallible teaching is not heresy.

The opinion is erroneous and untenable that infallible teachings are to be divided into two types, (1) those taught by the Magisterium as Divinely-revealed and P(2) those somehow taught infallibly but without Divine Revelation. For the Magisterium can only teach infallibly by the work of the Holy Spirit. And so all infallible teachings of the Magisterium are a type of Divine Revelation. Furthermore, although the Magisterium can and does teach from natural law, all of the teachings found in natural law are also found, at least implicitly, in Divine Revelation (Tradition and Scripture). There are no teachings of the Magisterium which are both infallible and yet need not be believed by the faithful as divinely revealed. All infallible teachings of the Magisterium are to be believed as divinely revealed and to be held definitively.

by
Ronald L. Conte Jr.
Roman Catholic theologian and Bible translator