The short answer to the OP’s question is God does know about other gods, and there is thus no violation of Omniscience.
How then does this not contradict Isaiah? Context is key.
Before we dive in to the details, though, this flowchart may help clarify what this post is/isn’t, and whether it’s worth your time to read it.
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Set/Scope/Sphere
One can correctly look at this set
{1,3,6,8}
and say that there are no 5’s. An omniscient observer can correctly look at this and say I know of no 5’s, and such a statement would be entirely correct.
This does not mean there are no 5’s anywhere. It means there are no 5’s in this set. There are no 5’s here.
The analogy of a student walking into a classroom is helpful.
The student expects that there will be two teachers for the class. Upon entering the classroom and finding only one teacher, the student asks “where is the other teacher?” The teacher replies “I am the only teacher; there is no other teacher”.
The teacher’s statement is entirely correct. The teacher could even (in our hypothetical) be omniscient and reply “I know of no other teacher” and still be correct.
This does not mean there is no other teacher anywhere, it means there is no other teacher here.
In order to understand these comments, and others like them, it is necessary to know the set/scope/sphere of discussion.
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Isaiah’s contrast
The verses cited in the OP are a chiastic poem1 by Isaiah. In fact, they are a chiasmus within a larger chiasmus (this is Isaiah, he does cool things like that), and the center (most important point) of the chiasmus is to show the futility of worshipping man-made gods. Isaiah does this by sharply contrasting them with Yahweh. (For more on the chiasms in chapter 44, see Ludlow, Isaiah – Prophet, Seer, and Poet pp. 376-379)
This context is critical – Isaiah is comparing the God of Israel to the false gods his people are tempted to worship. This theme began before chapter 44 and will extend well beyond it.
Isaiah gives us the scope/sphere he is discussing. In chapter 43 Isaiah alludes to Sinai, the parting of the Red Sea and/or Jordan, and wandering in the wilderness. The Lord speaks of His ability to foretell the future and the prophecies He has given His people. False gods of wood and stone have done none of these things. The context is God’s dealings with the children of Israel, and His demonstrated total superiority to “competing” man-made deities.
As published by the FAIR organization here
The question here is: Who has revealed himself to the world? Which
God has ever communicated with man? Who has revealed the future? Who
but He who brought up this future? The answer is: None. There is no
one, and neither the Israelites nor God knows any other god that had
revealed himself but the God of Israel. Again, this says nothing about
monotheism. It just talks about revelation, and wholeheartedly we
recognize Isaiah's argument as valid.
Isaiah’s message is that there is only one God who has given Israel any reason to worship Him. There is only one God doing miracles for Israel, and Isaiah highlights Israel's history to prove it. There is only one God who offers salvation to Israel. There is only one God here.2
Anything going on in other worlds, or other galaxies, or other universes (if they exist) is entirely outside the scope of Isaiah’s message.
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Support from other Biblical passages
If we take Isaiah out of context we’re going to run into some challenges.
Isaiah vs. Obadiah
Obadiah speaks of saviors (plural) on Mount Zion (see Obadiah 1:21); Isaiah says there is only one savior (43:11). Do they contradict? No. Isaiah is not denying the existence of others who save (from something), rather, in highlighting what Yahweh has done for Israel he is saying that there is no other savior who will do for you what Yahweh does. Nobody else can save you in that way.
Isaiah vs. Genesis & Psalms
Old Testament passages which speak of the divine council, or of gods, or of Deity speaking in the plural (e.g. Genesis 1:26, Genesis 3:22, Psalm 82:1, Psalm 86:8, Psalm 89:5-8) are not contradicted by Isaiah (I am aware that these passages have been interpreted many ways, but the changes scholars have picked up on in the nature of monotheism over the course of the Old Testament is not a minor issue). Whatever other divine beings there may be besides the God of Israel, none of them are the God of Israel, none of them save Israel, and none of them merit Israel’s worship.
Isaiah vs. Paul
Isaiah is clear that God has chosen Israel (e.g. 43:10); Yahweh is the Holy One and Creator of Israel (e.g. 43:15). Does this mean He did not create other people? Does this contradict the New Testament’s teaching that salvation is offered to all? (e.g. Romans 1:16). No. The special covenant relationship God has with Israel neither precludes the existence of other people nor God’s ability to have a relationship with them. Isaiah’s scope is recounting what Yahweh has done for Israel. No one else has done these things for Israel.
Isaiah vs. Hosea
In the connected passage in Isaiah 43:11, Isaiah is quoting his predecessor Hosea:
Yet I am the Lord thy God from the land of Egypt, and thou shalt know
no god but me: for there is no saviour beside me (Hosea 13:4)
The context & scope is also clear in Hosea. Hosea is condemning the worship of idols of silver, Hosea highlights what God did in liberating Israel, Hosea identifies Yahweh as Israel’s only Savior, and commands them to worship the God – the only God – who merits their worship and has done these things for them. Is Isaiah taking Hosea’s words out of context? No, Isaiah takes these ideas from Hosea and builds a masterful chiasmus from them, but the core message and scope is the same. This is a message about the God who has done wonders for Israel versus the gods who have not.
Absolutist readings of Isaiah are unnecessary and unhelpful – we just need to read his words in context.
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Summary
As already noted by Mason Wheeler here, God told Moses that He would reveal an account of this earth. God is defining a set/scope/sphere.
The scope of Isaiah’s message is narrowed further - it's what God has done for Israel, and his message that there is one God who has blessed Israel is clearly correct.
Verse 8 simply answers the question that was asked in verse 7 – who has done these great things for Israel? Only One has done these things for Israel.
There is one God here.
Appendix 1 - Omniscience
Merriam-Webster defines omniscient as:
having infinite awareness, understanding, and insight
possessed of universal or complete knowledge
(source)
"Omniscient" is not a term found in the Bible (or the Book of Mormon), but this passage from the Book of Mormon should get the message across:
For he [God] knoweth all things, and there is not anything save he knows it. (2 Nephi 9:20b)
The OP proposes 2 mutually exclusive propositions:
- P1: God is Omniscient
- P2: There are gods that God does not know about
However, there is no contradiction between 2 Nephi 9:20 and Isaiah 44:8, because P2 is not given by Isaiah (or anyone else in scripture). Isaiah indicates in verse 8 that God knows of no other gods who meet the criteria given in verse 7.
God knows of other Gods, but He knows of no other Gods who have done these things for Israel, because there aren't any.
Appendix 2 - clarifications to the OP
The teachings of The Church of Jesus Christ of Latter-day Saints on theosis were not referenced in the original question but are referenced now.
If the OP is asking why Omniscient God doesn't know of people who will be exalted in the future...He does know. But those people are not the God of Israel and haven't done the things Isaiah describes in 44:7 (or the divine things Isaiah describes throughout chapters 43 & 44), so God can know of them and still quite correctly state that He knows of no one else who meets the description given by Isaiah.
The same reasoning applies if the OP is asking about Gods of other realms (about whom we know almost nothing).
Does one member of the Godhead know of the other members of the Godhead? Of course! The Book of Mormon teaches that they are One (see 2 Nephi 31:21), just not in the trinitarian sense. Apostle Jeffrey R. Holland taught:
We believe these three divine persons constituting a single Godhead are united in purpose, in manner, in testimony, in mission. We believe Them to be filled with the same godly sense of mercy and love, justice and grace, patience, forgiveness, and redemption. I think it is accurate to say we believe They are one in every significant and eternal aspect imaginable except believing Them to be three persons combined in one substance (source).
In contrasting the God of Israel with fake man-made gods, Isaiah makes the point that nobody is competing with the God of Israel. If the members of the Godhead are One in the way Latter-day Saints understand it2, they are One in their interaction with the world, and one cannot get a different answer from one member of the Godhead versus another. Thus, any member of the Godhead can say that He knows of no one competing with Him.
1 - The objection might be raised “wait, you’re going to bring up poetry, that’s such a cop-out!” Isaiah is indeed a master poet, and if we are not willing to acknowledge this and take the time to unlock his poetic devices, we’re going to run into real trouble when we get to passages like Isaiah 55:12.
2 - For a discussion of monotheism and Latter-day Saint views about Deity, see my post here.
Disclaimer - these thoughts are products of my own study and do not constitute official statements by The Church of Jesus Christ of Latter-day Saints