The sovereignty of God is a fundamental tenant of Christianity. Merriam-Webster defines sovereignty as “supreme power especially over a body politic, freedom from external control, autonomy, controlling influence”. Within this concept, we might think of the ultimate authority of God’s word, His omniscience, and His omnipotence.

The possibility that there are things God cannot do may seem completely contrary. In fact, there are religious belief constructs that place God’s sovereignty above all else, even man’s free will. The fundamental argument is that there are no limits that can be placed on a sovereign God. But are there things God cannot do, even One that is all-powerful and all-knowing?

how Scripture answers "Are there things God cannot do?"

Yes, there are a few things that God cannot do. First, He cannot lie1,2. Regarding sin, He cannot tolerate sin indefinitely3,4,8, nor can he be tempted or tempt anyone to sin5. Finally, He cannot save anyone against their will6,7. He is just and cannot pardon sin (apart from faith in Christ).

the answer above is built on and footnoted with the following scripture-blocks

1

So when God desired to show more convincingly to the heirs of the promise the unchangeable character of his purpose, he guaranteed it with an oath, so that by two unchangeable things, in which it is impossible for God to lie, we who have fled for refuge might have strong encouragement to hold fast to the hope set before us.

When God wanted to show the heirs of the promise unmistakable proof of the unchangeable nature of His plan, so He further guaranteed it with an oath.  Now with these two unchangable things, and the fact that it is impossible for God to lie, we who have fled to Him for refuge are amply encouraged to remain firm in the hope that we have before us.

The entire book of Hebrews is about “holding fast” and not losing faith or “falling away.” In this immediate context the writer is providing evidence/reasons why the Christian should remain faithful. The very next verse describes Him as a “sure and steadfast anchor.”

How does it apply here?

God cannot lie.

2

Paul, a servant of God and an apostle of Jesus Christ, for the sake of the faith of God’s elect and their knowledge of the truth, which accords with godliness, in hope of eternal life, which God, who never lies, promised before the ages began and at the proper time manifested in his word through the preaching with which I have been entrusted by the command of God our Savior;

Paul, a servant of God and apostle of Christ, ministering to the faith of God’s elect and their knowledge of His word that teaches godliness in the hope for eternal life which God, who cannot lie, promised before the ages began and at the proper time revealed by His word through the preaching with which I’ve been entrusted by the command of God our Savior;

Paul is writing to a young preacher, Titus.  After giving these qualifications for a church elder, he continues to give instruction regarding behavior to certain segments/groups within the church: older men (2:2), older women (2:3), younger women (2:4), younger men (2:6), and finally slaves (2:9).  With all of these, their behavior is to be exhibited as would “accord with sound doctrine” (1:9, 2:1, 2:10).
How does it apply here?

God never lies.

3

This is the message we have heard from him and proclaim to you, that God is light, and in him is no darkness at all.

This is the message we first heard from him [Jesus] and proclaim to you, that God is light and there is no darkness in Him.

The Apostle John’s opening in a letter written to Christians encouraging them to love each other (as God loves) and resist false teaching.  His instruction appears to be to individual Christians (not a particular church) and he’s concerned about them losing fellowship with God (vs 3) and ultimately losing their joy (vs 4).

In this context, “light” is righteousness (e.g. “walk in light” vs 7) and “darkness” is sin or unrighteousness (e.g. not practicing the truth vs 6).

How does it apply here?

God has no part in sin (“darkness”).

4

You who are of purer eyes than to see evil and cannot look at wrong, why do you idly look at traitors and remain silent when the wicked swallows up the man more righteous than he?
[Habakkuk addressing God] You who are of such to goodness to look upon evil and tolerate it, why do you sit by and do nothing while traitors and wicked consume the righteous?

The book records a conversation between Habakkuk and God.  The prophet is questioning God’s tolerance of the sin of Judah.  In this context, God has said (vss 5-11) that he will resspond to their sin by raising up the Chaldeans (e.g. Babylonians).

How does it apply here?

Habakkuk is appealing to God’s goodness and hatred of evil for judgment on the people.

5

Let no one say when he is tempted, I am being tempted by God, for God cannot be tempted with evil, and he himself tempts no one.

No one when tempted should say that they are tempted by God, since God cannot be tempted and Himself tempts no one.

James is writing to brethern encouraging them to be doers and not just hearers of God’s “perfect law of liberty” (vs 25). Here he is defining the nature of sin (vss 14-15) and warning to avoid it.

How does it apply here?

God cannot be tempted or tempt anyone.

6

The Lord said to Cain, Why are you angry, and why has your face fallen? If you do well, will you not be accepted? And if you do not do well, sin is crouching at the door. Its desire is for you, but you must rule over it.
God asked Cain why he was angry and confused and explained that if he did well he would be accepted [by God].  However, if he did not strive to do good sin would be ready to take advantage since its seeking control; he must rule over it.
The creation account and introduction of Adam and Eve’s offspring after their disobedience and the curse of sin.
How does it apply here?

It was up to Cain to “do well” and not let sin “rule over” him.

7

O Jerusalem, Jerusalem, the city that kills the prophets and stones those who are sent to it! How often would I have gathered your children together as a hen gathers her brood under her wings, and you would not!
Oh, Jerusalem!  The city that kill and stone those sent by God to preach to them!  How often I [Jesus] would have gathered your children together for safety but you resisted.

Jesus addressing the crowds and disciples (vs 1) that includes a scathing rebuke of the Pharisees – considered the religious elite of the day.

How does it apply here?

If it was up to Jesus, He would have “gathered” or protected/saved Jerusalem, but they “would not” allow it.

8

The times of ignorance God overlooked, but now he commands all people everywhere to repent, because he has fixed a day on which he will judge the world in righteousness by a man whom he has appointed; and of this he has given assurance to all by raising him from the dead.

God overlooked a time of ignorance in the past, but now He wants everyone to repent since He has appointed a day that He will judge the world according to their righteous acts by a man that He designated, testifying to all by raising Him from the dead.

Paul’s sermon to the Athenians from Mars Hill while he awaited his companions to join him from Macedonia during his second missionary journey.

How does it apply here?

God overlooked a period of ignorance regarding His complete will being known for man to obey. (This isn’t saying that God overlooked sin.)

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