Is the Punisher a vigilante or a serial killer?
What is a vigilante
A vigilante is someone who illegally punishes someone for perceived offenses, or participates in a group which metes out extrajudicial punishment to such a person. Often the victims are criminals in the legal sense, however a vigilante may follow a different definition of criminal than the local law. (wikipedia)
What is a serial killer
A serial killer is a person who murders three or more people over a period of more than thirty days, with a "cooling off" period between each murder, and whose motivation for killing is largely based on psychological gratification. Often, a sexual element is involved with the killings. The murders may have been attempted or completed in a similar fashion and the victims may have had something in common; for example, occupation, race, appearance, sex, or age group. (wikipedia)
The fine line between hero and villain
It's a fun questions because this raises the question between when does a hero cross the line and becomes a villain. There is the fine line between someone doing justice for their society and when someone crosses the line still currently convenient because they are removing other dangerous elements but are a danger to the society. A lot of the distinction is born out of their motivations that gets them started, their intentions at the time of confrontation, and how they resolve their conflict.
The Punisher is a serial killer. He started as a vigilante moving beyond the law driven by revenge for his lost loved ones. This motivation has no difference from Batman.
The Punisher's intention at the time of apprehension is that of murder. He judges and then executes one of the most severe sentences upon his opponents and that is what stands him apart as a serial killer. Batman's intention at the time of apprehension is to stop the crime not destroy the criminal.
Thus The Punisher has murdered more than three people, does so purely for his psychological gratification, revenge, and the victims have something in common being perceived by him as criminals.
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