What are the soteriological consequences of heresy?

Question

From the Catechism (paragraph 2089), quoting canon law 751:

Heresy is the obstinate post-baptismal denial of some truth which must be believed with divine and catholic faith, or it is likewise an obstinate doubt concerning the same

Neither the surrounding portions of the Catechism nor the surrounding portions of Canon Law describe the consequences of heresy nor delineate heresy which is not damning from heresy which is.

What are the soteriological consequences of heresy and what, if anything, delineates damning heresy from non-damning (venial?) heresy in Catholic teaching?

Answer 1

The Catholic Church intentionally does not explicitly define the soteriological consequences of any particular sin, including heresy. It does distinguish sins on the part of the object (e.g. grave, mortal, venial), but these definitions lack the subjective side that can change in each particular case. In general that subjective side centers around the will and consent of the individual in the act (See CCC on sin and my answer regarding involuntary tendencies). So we can say that x is a sin, but we can't definitively say how culpable someone is for x until we have an understanding of their thoughts, knowledge, motives, and will. Indeed, for this reason God is the final judge (1 Sam 16:7, 1 Cor 2:11).

The most prominent distinction made when talking about heresy is that of formal heresy vs material heresy (See Connotation and Definition). Material heresy is something akin to accidental heresy: a heresy that one would forsake if they came to knowledge that the Church teaches against it. Material heresy is therefore rather insignificant. Formal heresy, on the other hand, is an obstinate and freely willed clinging to a heresy that one knows to be contrary to Church teaching--one knows it to be a heresy, unlike material heresy. This heresy is much more grave, and may constitute grounds for excommunication.

Finally, New Advent's section on Degrees of Heresy is also important. It cashes out like this: different Church teachings have different levels of authority and different requirements of assent. Books like Ludwig Ott's Fundamentals of Catholic Dogma detail a number of different teachings and the Magisterial "level" into which they fall. For example, Ott points out that while the proposition that Christ is divine carries the highest weight (de fide), the proposition that extreme unction is not of itself necessary for salvation carries a lower weight (sent. certa.). To deny the former would be graver heresy than to deny the latter. Indeed, heresy in its strictest sense is limited to those teachings of the Church that hold the most weight.

Answer 2

The first sentence of the Athasasian Creed says:

Whoever wishes to be saved, needs above all to hold the Catholic faith; unless each one preserves this whole and inviolate, he will without a doubt perish in eternity.

Heretics do not preserve "the Cathloic faith…whole and inviolate"; thus, they "will without a doubt perish in eternity."

There's also Pope Eugene IV's Cantate Domino:

[The Catholic Church] firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart “into everlasting fire which was prepared for the devil and his angels” [Matt. 25:41], unless before the end of life the same have been added to the flock

^{A heretic either "is unwilling to assent to Christ" or "chooses not what Christ really taught, but the suggestions of his own mind"; "heresy is a species of unbelief, belonging to those who profess the Christian faith, but corrupt its dogmas" (source).
(cf. Pope Leo XIII's Satis Cognitum on the necessity of holding the whole Catholic faith)}