Every lexicon I consulted has basically the same meaning for δαιμονίζομαι (daimonizomai):
- Thayer: to be under the power of a demon
- Souter: I am under the power of an evil spirit or demon
- NIV: I am possessed by a demon
- Newman: be demon possessed
- BDAG: be possessed by a hostile spirit
- Vine: to be possessed by a demon, to act under the control of a demon
- Analytical Lexicon to the GNT (Friberg et al): of demon possession or oppression, be possessed by, be tormented or vexed by, be demonized. (I knew if I looked long enough I would find one "demonized"; but I assume this means "controlled by demons", etc as per the other meanings above.)
In English, to be "demonized" is to portray as wicked and threatening, eg, "he was demonized by the press" (On-line dictionary), or, "Make into or like, represent as a demon" (OED); "to try to make someone or a group of people seem as if they are evil" (Cambridge); "to portray (someone or something) as evil or as worthy of contempt or blame" (Mirriam-Webster).
Thus, this word does not necessarily have any real transcendental connotations; by contrast, the NT portrays δαιμονίζομαι (daimonizomai) people as actually possessed by evil spirits.
However, the English word "demon-possessed" means to be:
- (McMillan) "controlled by an evil spirit"
- (Miriam-Webster) influenced or controlled an evil spirit
Thus, in English, to be demon-possessed to to have the mind controlled, owned or "possessed" by a demon. It immediately follows that the person does not have control of their own actions and will but the mind is controlled by the demon.
After the incident with the demon-possessed man in Luke 8:39, we read:
So the man went away and proclaimed all over the town how much Jesus
had done for him.
That is, the man regained control of his own mind" ("In is right mind" V35) once the demons were purged. See also Mark 5:15.