“the furnace of fire.” Here in Matthew 13:42, Jesus refers to the Lake of Fire (Rev. 20:14-15) as a “furnace.” The Greek word translated “furnace” was used of furnaces that smelted metal (cp. Rev. 1:15) or potters kilns for hardening clay. The people thrown into the Lake of Fire will eventually burn up (Matt. 13:40).
[For more on annihilation in the Lake of Fire, see Appendix 5, “Annihilation in the Lake of Fire.”]
“sobbing and gnashing of teeth.” The mention of sobbing and gnashing of teeth occurs seven times in the Bible (Matt. 8:12; 13:42, 50; 22:13; 24:51; 25:30; Luke 13:28). All of these occurrences are in the Gospels. There is only one future Messianic Kingdom, and it fills the whole earth. The unsaved are not part of that Kingdom but are thrown into the Lake of Fire where there is sobbing and gnashing of teeth (Rev. 20:13-15).
[For a more complete explanation of the sobbing and gnashing of teeth, see commentary on Matt. 8:12.]