Right. so let's look at it the best we can.
We have God who gives 15 additional years. We agree that God knew of the additional years.
2 Kings 20:1
"In those days Hezekiah became sick and was at the point of death. And Isaiah the prophet the son of Amoz came to him and said to him, "Thus says the LORD, 'Set your house in order, for you shall die; you shall not recover.'" "
Isaiah tells Hezekiah a message from God. Isaiah tells Hezekiah that he is going to die. This isn't Isaiah opinion but a direct message from God.
Then Hezekiah prays to the Lord...
2 Kings 20:2-3
"Then Hezekiah turned his face to the wall and prayed to the LORD, saying, "Now, O LORD, please remember how I have walked before you in faithfulness and with a whole heart, and have done what is good in your sight." And Hezekiah wept bitterly."
Then the Lord responds...
2 Kings 20:4-6
"And before Isaiah had gone out of the middle court, the word of the LORD came to him: "Turn back, and say to Hezekiah the leader of my people, Thus says the LORD, the God of David your father: I have heard your prayer; I have seen your tears. Behold, I will heal you. On the third day you shall go up to the house of the LORD, and I will add fifteen years to your life. I will deliver you and this city out of the hand of the king of Assyria, and I will defend this city for my own sake and for my servant David's sake.""
So we have the Lord telling Hezekiah that he is going to die. Then after Hezekiah's prayer, the Lord adds 15 years.
So, did the Lord "change his mind"? Yes and no. Did God always know that these additional 15 years would be there? Of course he did. In that sense, God didn't change his mind. He always knew it.
To be honest, it's difficult to understand. On one hand we have what looks like God changed his mind. But then on the other hand, if we are going to agree that He already knew that, did He really "change his mind"?
I Samuel 15:29
"Also the Glory of Israel will not lie or change His mind; for He is not a man that He should change His mind."
Found this statement from CARM and thought it was well stated.
"...the answer is found in looking at the problem from two perspectives. From the eternal perspective, God does not change His mind since He knew from all eternity what the ultimate decision would be. From the temporal perspective (relative to us), God changes His mind in response to the prayers and pleading of His people."
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http://carm.org/2-kings-201-6-you-shall-die-and-not-livei-will-add-15-years-your