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Stubborn and Desmond,
This is an interesting argument but you guys are stuck in a rut, so let's tackle this from another angle.  Let's start with what we all agree on:

Unbaptised persons = not Catholic.  This includes:  Jews, pagans and all other religions.

Apostate = a catholic who abandons his faith totally (this does NOT include those who stop practicing their Faith, but those who turn to pagan religions, thus abandoning Christ totally).

Heretic = a catholic who rejects one or more catholic doctrines.

Schismatic = a catholic who rejects the authority of the Church (i.e. bishop(s) or Pope) in some area.

Excommunicated = a catholic who has incurred a penalty/sanction from the Church because of 1) sin of heresy or 2) sin of disobedience (he's a schismatic), or 3) sin of apostasy.

a. Ipso facto excommunication - Basically, this is "automatic" excommunication, because of the person's actions.

b.  Formal excommunication - This is 'ipso facto' excommunication which has been RATIFIED by the Church, which followed the legal steps and declared the 'ipso facto' condition to be public, formal and binding.

Now, we must distinguish between the excommunication and the penalties associated with it, which vary according to canon law.  Any excommunication (whether 'ipso facto' or 'formal') carries with it a spiritual penalty (i.e. the person is "cut off" from the sacraments) and this is why they are said to be "outside of the Church".  In the same way that one in mortal sin is "cut off" from God and
"cut off" from heaven.

An excommunication has 2 penalities - 1) the sin involved, usually against Faith (which is why the penalites are so severe), 2) the Church's penalty, of not being able to take part in the sacraments (i.e. outside the Church).  

An excomm can, and are still required, to go to Mass, but (in some extreme cases) even if they wanted to repent/confess, they would have to to wait and get a formal hearing, as some excomm can only be lifted by the Bishop, The Holy See, or the Pope himself.  

But, when we speak of one's church office (being a bishop, or a cardinal, or even pope), even one who is 'ipso facto' excommunicated, does not AUTOMATICALLY lose their office.  They automatically lose their state of grace, automatically lose the benefit of the sacraments but they still RETAIN THEIR OFFICE AND ITS AUTHORITY, under most circuмstances.

Let's discuss the penalties of an excomm:

A "latae sententiae" penalty (meaning by the force of the law) is incurred for all 'ipso facto' excomm.  So, if you do 'a' or 'b', you've incurred the penalty.  Much like when one commits a mortal sin, we've incurred the penalty of hell.  It's automatic; it doesn't need to be confirmed by any authority.

The main penality for an 'ipso facto' excomm is banishment from the sacraments.  Normally, it does not affect one's office or authority.  This has to be confirmed by Church authorities.  There are certain, extreme cases where one automatically loses his authority/office but not related to heresy.

A "ferendae sententiae" (meaning "sentence to be passed") penalty is one that binds a guilty party only after it has been imposed on the person by Church authorities.

All this being said, the question of if one "outside of the church" can hold office is not as clear cut as some of the quotes from the popes/saints seem to make it.  Oftentimes, when the quote mentions a heretic or schismatic, is it speaking of a "formal" heretic or schismatic, who has received a formal, "ferendae sententiae" and therefore loses his office and authority.  But, before the Church rules, a person who has received 'ipso facto' excommunication, though he be 'outside of the Church', he still retains his office, because being 'outside of the Church' refers to his spiritual situation (i.e. cannot partake of the grace of the sacraments), not that he is no longer a Catholic.
 

Quote

Answer: Catholic.

Why couldn't he be a heretic?

Why?
Because the Church teaches that in an emergency, the excom can have their sins absolved in the sacrament of penance, can then receive Communion and extreme unction - that's why. You can make all the exceptions you want, but those are exceptions you make, not the Church.

If you cannot accept that teaching, so be it, but that will not change what the Church teaches.

If the excom is not Catholic, then the excom cannot even think about going to confession - even in an emergency.

I agree with 100% with what you just said.  Especially this:

However, those who have been baptized and reject the Catholic Faith, either by heresy, schism, or apostasy are cut off, severed from the Body of the Church, and are no longer Catholic.

But...we must distinguish between the different penalties associated with excommunications.  Not all excomm are created equal.  Further, when the Church speaks of 'heresy, schism, and apostasy" it is (normally) speaking of "formal, publicly defined" acts.  

If I were a Bishop and I denied (privately) papal infallibility, I would 'ipso facto' be excommunicated and be 'outside of the Church'.  I wouldn't receive any benefit from the sacraments, even if no one else knew of my errors.

Now, if I started to publicly preach my errors, I would still be bishop, and still hold the office, until I had a formal hearing and was removed.  Until such time that I had a hearing, I would be a heretic, but not a manifest heretic, which comes after the Church has given me a chance to recant.  But I would still hold my office.

Point is, a bishop could be a private AND a public heretic and still hold office.  Only certain acts of excomm remove one from office immediately.  Outside of this, a heretic is still in office until removed formally.

This is a pretty reasonable post, Pax Vobis.

But I would personally avoid bringing jurisdiction into this, as it only makes the issue, in my opinion, even more complex.

Obviously agree that distinctions regarding various reasons for excom must be made, as I attempted to argue on several occasions.
Same for manifest/formal heresy etc.

Also what is, at large, manifest and evident on the purely sensorial plane (who appears to be Catholic, etc.) and what is real and ontologically true on the spiritual plane, which is sadly, sometimes unclear.

But, have you understood that membership in the Church can be lost?

In the sense of ceasing to be part of the Church, ergo the Body, as the Catechism of Trent states?

As I tried to explain, one, if the word "member" is an issue for him, could use "members in potentia"(meaning those outside, yet baptised and ready to enter the Church), and "members in actu" (those who are actually members, and inside the Church).



Thanks also Bellator Dei for the quotes from Mystici Corporis Christi and Satis Cognitum, in addition to Bellarmine's quote directly dealing with the distinction/classification above.