Could God have saved Sodom and Gomorrah?

Thanks for your question. The answer is of the yes and no sort.

Yes

First, I refer you to Matthew 11:20-24:

Then he began to denounce the cities where most of his mighty works had been done, because they did not repent. “Woe to you, Chorazin! Woe to you, Bethsaida! For if the mighty works done in you had been done in Tyre and Sidon, they would have repented long ago in sackcloth and ashes. But I tell you, it will be more bearable on the day of judgment for Tyre and Sidon than for you. And you, Capernaum, will you be exalted to heaven? You will be brought down to Hades. For if the mighty works done in you had been done in Sodom, it would have remained until this day. But I tell you that it will be more tolerable on the day of judgment for the land of Sodom than for you.”

Here we observe that Jesus repeats the same thing twice. This is a twofold witness (2 Cor. 13:1; cf. Deut. 17:6; 19:15; Matt. 18:16) to establish a definite fact. If mighty works had been done in Sodom, it would have repented. So, God had the ability to save all of Sodom. But he didn’t.

No

God is holy, just and good (Rom. 7:12). And God does not and cannot enjoy sin (Psa. 5:5; 11:5; cf. Isa. 59:2; Mal. 1:2-3). As such, God can’t and doesn’t save unrepentant sinners. God can’t save unrepentant sinners as it would be inconsistent with his eternal holy and just nature to do so. And he cannot change his ordained/decretive will (cf. Dan. 4:35). And he cannot keep from sending unrepentant people to hell. He is holy and just and thus, according to his perfect nature, he must righteously judge unrepentant people (Psa. 77:13; Rom. 7:12; Matt. 25:41). (Please see, “Things God Can't Do?” below.)

So, except for a few righteous elect souls (2 Pet. 2:7-8) who were written in the Lamb’s Book of Life from the very beginning (Rev. 13:8; 17:8; 21:27; cf. Luke 10:20; Eph. 1:4-5; Phil. 4:3; Heb. 12:22-23), no others were given by God the Father to Jesus to save (cf. John 6:37, 39; 10:29; 17:6, 9, 12, 24; 18:9). For this reason, Sodom perished.

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Things God Can't Do?