Can a Heretic Become Pope?

How can a man be head of a Church he is not a member of? asked Saint Robert Bellarmine.  Cum Ex provides that a heretic cannot become Pope, answering Saint Robert Bellarmine's question.
De Romano Pontifice, Saint Robert Bellarmine: This principle is most certain.  The non-Christian cannot in any way be Pope, as Cajetan himself admits.  The reason for this is that he cannot be head of what he is not a member, not he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by Saint Cyprian (Liber 4, Epitle 8), Saint Athanasius (Scr 2 Contra Arianus), Saint Augustine, liber de great. Christ. Caput 20), Saint Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope.

Is The Papacy A Sacrament; A Part of Holy Orders?

The Papacy can be compared to a Sacrament with matter, form and intention:
Matter: is the man elected Pope and the electors
Form: is the election itself
Intention: is to elect a Pope.
Since the Papacy can be resigned, and has on two occasions, Gregory XII and Saint Celestine V, we know that the Papacy is not a Sacrament. (Canon 220)  However, using this analogy we can analyze the matter:
The Matter is the Elected and the Electors: These must all be Catholics by Divine Law, and the Elected must be a man and have the use of reason.
The Form is the election, and no matter how faulty, it is considered valid. Saint Alphonsus states: It doesn't matter that in past centuries some pontiff has been elected by fraud: it suffices that he has been accepted after as pope by all the Church, for this fact he has become true pontiff
The Intention is presumed, because why elect a Pope, if this is not what you intend to do?
Saint Alphonsus talks about the form of the election, and not the matter.
Saint Thomas Aquinas states (II-II Q10 A10): "First, we may speak of dominion or authority of unbelievers over the faithful as of a thing to be established for the first time.  This ought by no means to be allowed, since it would provide scandal and endanger the faith, for subjects are easily influenced by their superiors to comply with their commands, unless the subjects are of great virtue: moreover unbelievers hold the faith in contempt, if they see the faithful fall away.  Hence the Apostle forbade the faithful to go to law before an unbelieving judge.  And so the Church altogether forbids unbelievers to acquire dominion over believers, or to have authority over them in any capacity whatever." In speaking of heresy, Saint Thomas states (II-II Q11 A1): "Falsehood is contrary to truth.  Now a heretic is one who devises or follows false or new opinions.  Therefore heresy is opposed to the truth on which faith is founded; and consequently it is a species of unbelief."  

For more information see Status of the Catholic Church

Michael Fighting
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"Michael…who   standeth  for…thy  people," —  Dan. 12:1-12