From Wikipedia
Heresy is any belief or theory that is strongly at variance with established beliefs or customs, in particular the accepted beliefs of a church or religious organization. The term is usually used in reference to violations of important religious teachings, but is also used of views strongly opposed to any generally accepted ideas. A heretic is a proponent of heresy.
The term is used particularly in reference to Christianity, Judaism, and Islam. In certain historical Christian, Muslim, and Jewish cultures, among others, espousing ideas deemed heretical has been (and in some cases still is) met with censure ranging from excommunication to the death penalty.
Heresy is distinct from apostasy, which is the explicit renunciation of one’s religion, principles or cause; and from blasphemy, which is an impious utterance or action concerning God or sacred things. Heresiology is the study of heresy.
Etymology
Derived from Ancient Greek haíresis (αἵρεσις), the English heresy originally meant “choice” or “thing chosen”. However, it came to mean the “party, or school, of a man’s choice”, and also referred to that process whereby a young person would examine various philosophies to determine how to live.
The word heresy is usually used within a Christian, Jewish, or Islamic context, and implies slightly different meanings in each. The founder or leader of a heretical movement is called a heresiarch, while individuals who espouse heresy or commit heresy are known as heretics.
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Apostasy (/əˈpɒstəsi/; Greek: ἀποστασία apostasía, ‘a defection or revolt’) is the formal disaffiliation from, abandonment of, or renunciation of a religion by a person. It can also be defined within the broader context of embracing an opinion that is contrary to one’s previous religious beliefs. One who undertakes apostasy is known as an apostate. Undertaking apostasy is called apostatizing (or apostasizing – also spelled apostacizing). The term apostasy is used by sociologists to mean the renunciation and criticism of, or opposition to, a person’s former religion, in a technical sense, with no pejorative connotation.
Occasionally, the term is also used metaphorically to refer to the renunciation of a non-religious belief or cause, such as a political party, social movement, or sports team.
Apostasy is generally not a self-definition: few former believers call themselves apostates due to the term’s negative connotation.
Many religious groups and some states punish apostates; this may be the official policy of a particular religious group or it may simply be the voluntary action of its members. Such punishments may include shunning, excommunication, verbal abuse, physical violence, or even execution.
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