According to the Catholic Church, can one be a heretic and still obtain salvation?

Question

According to the Catholic Church, can one be a heretic and still obtain salvation? Are there different kinds of heresy that merit different answers?

Answer 1

Heresy is distinguished as follows:

• Material heresy
  • occult (hidden)
    ^{e.g., privately thinking there are 4 Divine Persons}
  • public
    ^{e.g., preaching that there are 4 Divine Persons}
• Formal heresy
  pertinacious adherence to heresy even after corrected by an ecclesiastical superior or tried for the crime of heresy in a canonical trial*
  ^{e.g., continuing to preach that there are 4 Divine Persons even after having been censured (cf. the theological censures/notes at the end of this answer) or excommunicated}
  _{*cf. ch. 9 "Proving the Crime of Heresy", pp. 229ff. (PDF pp. 242ff.), of True or False Pope}

If one is invincibly ignorant that he holds a material heresy, he can possibly be saved; however, formal heretics cannot be saved, especially if their heresy is against the four truths absolutely necessary to believe for salvation—viz., that

1. "he [God] is", i.e., that God exists (Heb. 11:6)
2. God "is a rewarder to them that seek him." (Heb. 11:6)
3. the Second Person of the Trinity took on a human nature (Incarnation)
4. God is Three Divine Persons in one God (Trinity)

^{Note: There is unanimous consent among Catholic theologians that truths #1 and #2 are absolutely necessary to be explicitly believed in order to be saved, but not all theologians (St. Thomas Aquinas, St. Alphonsus Liguori, et al. excepted) think that explicit belief in truths #3 and #4 is necessary; cf. True or False Pope p. 113 // PDF p. 128.
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