Heresy is in the "not".

One of the tricky things about Christianity is all of the versions that are out there.  They all seem to have similar beliefs and it can be hard to separate exactly what each one is trying to say.  The first thing we need to discuss is a little logic, and vs. or.  The words "and" and "or" are actually very technical terms.  The word "and" is used to describe an intersection and the word "or" describes a union.

If you go to an ice cream shop and tell the attendant "I would like chocolate and vanilla". If they just give you a scoop of chocolate, you will be unhappy.  If they just give you a scoop of vanilla, you will not be happy.  Only a scoop of each will satisfy your demand.  Thus, the word "and" describes a scenario where both conditions must be met.

If you say to the attendant, "I would like chocolate or vanilla," you will be happy with a scoop of chocolate, and you will be happy with a scoop of vanilla, because you said "or".  However, this is where people often get confused; How would you feel if the attendant gave you a scoop of both?  Did they meet your request?  Yes! They actually did.  There are two kinds of or, an exclusive or and an inclusive or.  The exclusive or means "one, but not the other".  The inclusive or means "one, or the other, or both".  Whether the "or" in question is inclusive or exclusive is largely taken from context.

Here is an example of a clearly inclusive or:
"The students that are in math or physics classes this term."
This would be all of the students who are in math or physics or both.

Here is an example of a clearly exclusive or:
"Two movies are playing at 7pm tonight, do you want to see Spider-Man or Super-Man?"
Clearly you can't be in both theaters at the same time, so it is one or the other.

In general, I think as a society we get a bit confused because we usually only see the "or" as being exclusive. I don't have any study to back this up, but think about whether you have said "or both" before.  The "both" is implied with the "or" and is logically speaking, completely unnecessary.  Since we feel like we need to say "or both" if it is indeed an option, I think this is strong empirical evidence that we are an exclusive-or culture.

This all applies directly to Christianity.  Take, for example, Faith and Works.  The protestant community teaches that we are saved by Faith alone, and that works are not necessary.  This argument is exacerbated by the misunderstanding of the word "and".  It is often viewed as an exclusive or.  If it isn't faith alone, then it must be work alone.  But that isn't what Catholics are saying either.  Catholics believe that it is by Faith and Works.  Not just by faith, not just by works.  When we say "and" we really and truly mean both.

This point can be seen in many, many cases.  The interesting thing is that Catholics can largely agree with what protestants affirm.  It is what protestants deny that is the problem.  The problem is with the "not".  "Saved by Faith alone" can be re-stated as "saved by Faith, but not works".  So, we affirm the positive, but reject the negative.  In fact, most, if not all, heresies are of this form.  The misunderstanding of the "both-and" is prominent in protestant-Catholic dialogs.  Here is a list of "affirm but reject" statements by various ecclesiastical communities.  For each and every one of them, the Catholic teaching is "both-and".  We affirm the affirmation, but reject the "not".

• We are saved by faith, but not by works.
• Jesus was a man, but not God.
• Jesus is the redeemer, but not divine.
• Communion is a memorial, but Christ is not present.
• Christ is spiritually present in the Eucharist, but not bodily.
• Scripture is authoritative, but not tradition.
• Jesus is our mediator to the Father, but not the Saints.
• The world can be understood by Science, but not philosophy and Religion.
• It is about relationship, not religion
• Jesus is the Son of God, not the son of Mary
• We believe in the New Testament, not the Old
• The Eucharist is a community meal of thanksgiving, not a sacrifice.
• Creationism, but not evolution (or commonly vice-versa)
• God is merciful, but not just.

I say again... Each of these is a heresy to the Catholic faith.  The Catholic position on every last one of them, and many, many more, is both-and.

The communication begins to break down when a Catholic says "No" to one of these claims.  The feeling is that we believe that some version of the "opposite" must be true; that if it isn't (A and not B) it must be (B and not A).  However, we aren't arguing that, we say (A and B).  And, so I conclude by fixing the above statements to the Catholic view:

• We are saved by faith and by works.
• Jesus was all man and all God.
• Jesus is the redeemer and he is divine.
• Communion is a memorial and Christ is present.
• Christ is spiritually and bodily present in the Eucharist.
• Scripture and tradition are authoritative.
• Jesus and Saints (through Jesus) are mediators.
• The world can be understood by Science and philosophy and Religion.
• It is about relationship and religion
• Jesus is the Son of God and the son of Mary
• We believe in the Old and New Testament
• The Eucharist is a community meal of thanksgiving and a sacrifice.
• Creationism and evolution
• God is merciful and just.