This phrase is found only in Revelation 2:11,20:6,20:14 , and 21:8. The Targums use it (Deuteronomy 33:6; Psalm 49:11 ). Philo uses the term to refer to all miseries arising from sin causing physical death followed by hopelessness in the afterlife (Rewards and Punishments 2.419). Revelation 2:10-11 contrasts it with the life given to the faithful. Death is the loss of the only kind of life worthy of the name.
The word used for "eternal punishment" in Matthew 25:46 is kolasis [ κόλασις ]. According to Bauer writers during the New Testament period used it only of temporal torture and conscious torment in the afterlife. No other idea for koine Greek is recognized. Moulton and Milligan can find only examples in papyrus where kolasis [ κόλασις ] involves the person actually feeling the punishment. It is used elsewhere in the New Testament only in 1 John 4:18 , which says fear has torment.
The second death is to be cast into the lake of fire (Revelation 20:14 ). This is a permanent state (Revelation 14:11 ), where in anything that would qualify as "life" is forever absent.
Paul Ferguson
See also Eternal Punishment; Judgment; Lake of Fire