Lexicon

H5162 - nacham

Strong's: H5162 · BLB lookup Pronunciation: naw-kham' Part of speech: verb Root: a primitive root, probably "to breathe deeply, to sigh", from which both the grief sense and the consolation sense develop OT occurrences: 108 tagged instances across 100 verses (Strong's-tagged text)

Nacham is the verb behind every English rendering of God "repenting", "relenting", "being sorry", or "changing His mind", and it is the single word carrying the God-is-surprised and open-theist case. It is also the verb behind "comfort" in Isaiah 40:1 and Psalm 23:4. One word, two families of meaning, and the theological dispute lives in the gap between them.

Semantic range (BDB / HALOT / TDOT)

The stem does most of the work.

Stem	Sense	Example
Niphal	to be sorry, to regret, to relent, to be moved to pity	Gen 6:6; Exod 32:14; Jonah 3:10
Niphal (reflexive)	to console oneself, to be comforted	Gen 38:12
Piel	to comfort, to console another	Isa 40:1; Ps 23:4
Pual	to be comforted	Isa 54:11
Hithpael	to console oneself, sometimes to take vengeance as relief	Gen 27:42

The unifying idea is a strong emotional exhalation, a sigh, which can be the sigh of grief, of relief, or of consolation. Nothing in the semantic range is cognitive. The word never means "to learn" or "to discover", and it never marks the acquisition of information. That is the observation on which most of the exegetical dispute turns.

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The word is not a repentance-from-sin word

English "repent" in older translations imports a moral connotation the Hebrew does not carry here. The OT verb for turning from sin is shuv (H7725 - shuv), "to turn, return", and it is what the prophets demand of Israel. When nacham is used of God, no fault is confessed and no direction of life is changed; what changes is a stated course of action in response to a change in the other party.

The name-and-wordplay layer

Noah. Genesis 5:29 gives the naming etymology by wordplay: "this one shall comfort us (yenachamenu) in our work and in the toil of our hands." The name Noach itself is normally derived from nuach, "rest" (H5117); the verse trades on the sound rather than the etymology, which is standard in Hebrew naming scenes.
Nehemiah (Nechemyah), "YHWH comforts". Nahum (Nachum), "comfort". Menachem, "comforter".

The divine-relenting texts

These are the passages the objection is built from, and they are real. Do not soften the translations.

The LORD was sorry that He had made man on the earth, and He was grieved in His heart. (Genesis 6:6, NASB95)

So the LORD changed His mind about the harm which He said He would do to His people. (Exodus 32:14, NASB95)

When God saw their deeds, that they turned from their wicked way, then God relented concerning the calamity which He had declared He would bring upon them. And He did not do it. (Jonah 3:10, NASB95)

Also 1 Samuel 15:11 and 15:35, Jeremiah 18:8, Amos 7:3 and 7:6, Joel 2:13, Psalm 106:45.

The same word denying the same thing

The tension is not one the objector discovered; the text sets it up deliberately, and twice puts both sides in a single passage.

God is not a man, that He should lie, Nor a son of man, that He should repent (yitnecham). (Numbers 23:19, NASB95)

Also the Glory of Israel will not lie or change His mind (yinnachem); for He is not a man that He should change His mind. (1 Samuel 15:29, NASB95)

1 Samuel 15 is the decisive case. Verse 11 says God relented over making Saul king, verse 29 says God does not relent because He is not a man, and verse 35 says He relented, all in one chapter, from one author, with the same verb. No writer produces that sequence by accident, and no reading survives that takes verse 11 as a report of divine ignorance while verse 29 sits twenty-four verses later. The chapter is telling the reader that the two statements operate at different levels: God's settled character and purpose do not shift, and His declared dealings with a person genuinely change when that person changes.

Theological force

Regret is not ignorance. The word reports grief and reversal of a declared course, never the arrival of new information. One can be genuinely sorry about a foreseen outcome; grief over a known evil is more coherent than grief over a surprising one, not less.
Relenting is the announced policy, not a departure from it. Jeremiah 18:7-10 states the principle openly: announced judgment is conditional on repentance, and announced blessing is conditional on obedience. When God relents in Jonah 3:10, the stated rule is running as published.
The relenting is predictable enough to be fled from. Jonah 4:2 is the strongest single verse on this point. Jonah says he ran to Tarshish in the first place because he knew God is gracious, compassionate, and "one who relents (nacham) concerning calamity." The prophet treats the relenting as so reliable a feature of God's character that he could forecast it before setting out. A God whose relenting is a surprise cannot be the God Jonah was avoiding.
It is covenant-relational language. Nacham belongs to the same vocabulary field as H2617 - hesed and H7356 - rachamim. It describes God as personally engaged with those He deals with, not as a fixed mechanism, and the doctrine of immutability that denies this is a philosophical overreach the texts do not require.

Notable verses

Genesis 6:6, the flood prologue, grief at human evil
Exodus 32:14, after Moses's intercession at the golden calf
Numbers 23:19, the denial, in Balaam's oracle
1 Samuel 15:11, 15:29, 15:35, all three in one chapter
Jeremiah 18:8, the potter's-house principle
Jonah 3:10 and 4:2, the relenting and the prophet who predicted it
Joel 2:13, "relenting of evil" listed among the divine attributes of Exodus 34:6-7
Isaiah 40:1, nachamu nachamu ammi, the comfort sense at full strength
Psalm 23:4, the rod and staff that comfort
Genesis 5:29, the Noah wordplay

Notes

Lexical workspace for nacham.