Stephen Barr responds at First Things:

While I agree with the general sentiment of Fr. Edward Oakes’ observations yesterday concerning the invidious or vituperative use of the word heresy, I feel that he is turning into a matter of sentiment what should be a matter of precise definition. If the word heresy is thought of merely as an insult or a taunt, then I agree that it is improper for Catholics to use it of Protestants, or Protestants to use it of Catholics. We should not be attempting to wound one another. Much better to call each other brothers.

The word heresy in Catholic teaching, however, has a very precise technical meaning today. It is not, as Oakes would have it, “explicitly [to] deny key doctrines of the faith.” The word key is not part of the definition of heresy given in the 1983 Code of Canon Law, which reads: “Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith.”

The Catholic Church says that all things (though not only those things) taught by Ecumenical Councils as revealed truths under pain of anathema are to be believed “by divine and Catholic faith.” There are propositions on justification and other matters that were taught by the Council of Trent under pain of anathema. So, if a baptized person were obstinately to deny one of those propositions, the term heresy, as used technically by the Catholic Church, would apply to him.

When Oakes writes, “I have trouble calling all forms of dissent by the word heresy, sensu stricto,” he is introducing a red herring. It is quite obvious that not all forms of dissent are heresy in the strict sense. No one except ignoramuses has ever asserted they were. It is clearly possible to dissent on all sorts of doctrinal questions without falling under the definition of heresy, for not all doctrines are proposed by the Catholic Church as having to be believed “by divine and Catholic faith.”

And from the comments below, Fr. Augustine Thompson, O.P.:

Let’s define heresy before we define heretic.

I myself would go with the defintion crafted by the great twelfth-century English bishop and theologian, St. Robert Grossteste. "Heresy is an opinion chosen by human perception, created by human reason, founded on the Scriptures, contrary to the teachings of the Church, publically avowed, and obstinately defended." This was the classic definition of "heresy" until the 20th-century, perhaps, for some of us, till now.

Which means: "by human perception," this means chosen by the person by his own lights, not merely the result of their environment. "by human reason," that is chosen because of some process of thought, not a simple garbled understanding or misconception or something held out of simple prejudice. "founded on the scriptures," that is claiming divine sanction as a belief, not merely because of science or learned opinion. "contrary to the teachings of the Church," that is, contrary to a defined doctrine. "publically avowed," that is not a private opinion kept to one’s self. "obstinately defended," that is, professed even after being formally correct by Church authorities.