I want to focus a bit on the comparison to Exodus 20, because the other answers have not directly addressed that aspect yet, and the perceived conflict here between the two verses seems to be a major impetus for this question.
Given that passages like Exodus 20 still suggest that other gods exist, why does Isaiah 45 suddenly counter this and say no other god can exist at all
So let's take a look at Exodus 20:3, word by word. Note that the link I just shared is already an interlinear, but the English doesn't line up perfectly well with the actual Hebrew words there, so I'll do my best to provide a revised interlinear below, which I think will help elucidate the point.
לא - not
יהיה - is there
לך - to you
אלהים - gods
אחרים - other
על פני - before me (literally, "upon/unto" "my face")
Now, a few relevant notes about how I've rendered this interlinear:
The word יהיה is a particular inflection of the common verb היה/"to be" (H1961). This is the word you see in common narrative-starting phrases like "it came to pass...", or "there was a...", or in places specifically denoting existence, such as "let there be light; and there was light" (Genesis 1:3), or even God's response of "I am what I am" when Moses asked for a name (Exodus 3:14). It basically denotes that the thing in question exists. That's why I am rendering these two words here as "there is, to you" rather than "you shall have". It's actually not even conjugated in the imperative form (though to be fair, none of the verbs in the so-called "Ten Commandments" actually are given in imperative form as you might expect them to be).
The word אלהים (H430) is used both as a kind of "title" for the singular God whose name is יהוה, but at other times the same 5 letters (or sometimes the first 4 letters, when in grammatical construct form) are used as a plural designation of other "gods". This is a point which confuses many, and it can sometimes potentially be ambiguous which is being denoted, but in this case we have the presence of the modifier אחרים/"other", which is also inflected in the plural, which is solid evidence for the latter use here. In other cases where it is clearly the former, singular use, we know that it is not plural because of the singular grammatical inflections used in the other words surrounding it.
I've chosen to lump the two words על פני together here, because although separately they denote something like "upon/unto" and "my face", together they are used as a common idiom denoting "before me", commonly used to connote something similar to "in my presence" or "in my sight". However, there's also something interesting about the word על/"upon/unto": it is the core root from which we get the word "עליון"/"highest/uppermost", which is commonly used as a moniker for God (e.g. אל עליון/"Most High God", as in Genesis 14:18, or simply עליון/"Most High" as in Deuteronomy 32:8). In a sense, the use of the moniker "עליון"/"highest" to refer to God could be seen as a reference to this commandment in Exodus 20:3 - it is an explicit devotional affirmation by the speaker that there are no other gods "upon" (על) God - i.e. God is the "Most High" (עליון).
So, given the rest of that context, if I could then try to paraphrase what's being said in this verse, it might be something like one of the following interpretations, or some mixture of them:
- As far as you're concerned, no other gods exist above me. (i.e. something like henotheism, or monolatry)
- Nothing else is a god to you, apart from me. (others may have other gods, but I am the god for you)
- Nothing else should come first for you, before me (stressing the primacy of God above all other influences that may vie for attention in one's life).
- No other gods existed prior to me (i.e. I am The Uncaused Cause, the Prime Mover)
I think it's ultimately a bit theologically ambiguous which of these interpretations (or which combination of them) to use, but I think the word לך/"to you" in the phrase in question should not be forgotten in our thinking. I think this points to the fact that "godhood" in a general reading of the original texts of the Hebrew Bible seems to be defined not by an absolute sense of divinity or power, but by a two-way relationship between the god and those who are devoted to the god.
Emphasizing this, in the prior verse (Exodus 20:2) we see the word אלהיך/"your God", which is the same word as אלהים/"God/gods" (H430) but with the ך suffix for "your" appended to it (which displaces the ם letter and takes its place) - the same ך suffix that forms the word לך/"to you" in the verse we are examining.
And taking a broader look at Exodus 20:2, we see the verse is in the familiar form of saying "I am your God, who brought you out of the land of מצרים" format, which we see repeated over and over again throughout the Bible, particularly when the Israelites are being chastised by God. Whenever God chastens Israel, God reminds them of the covenant they have (i.e. the relationship of God and people), and what God has done for them (e.g. brought them out of מצרים).
With all that context in mind, I would suggest that a god/gods אלהים (H430) ceases to be such when a people ceases to be in devotion to that god/gods, and that the word אלהים might then be understood to be denoting that the referent is an object of devotion of the people, rather than denoting a kind of divinity or power.
That is, יהוה is always יהוה, as this is the proper name of God. But the word אלהים is a title that signifies a relationship of devotion.
The absolute divinity/power/sovereignty (what we would think of as the "godhood" or "godship" of יהוה) is not dependent on this devotion - but יהוה will cease to be "our god" when we cease to be devoted as such.
Similarly, regardless of whether you interpret the אלהים אחרים/"other gods" of other nations to be independently divine entities or just hollow idols, they would cease to be "gods" אלהים (i.e. objects of devotion) when the people are not devoted to them. Though they would still retain their essential nature (independently divine entities or just hollow idols).
Or in other words, if you have no devotion to "other gods", then "to you, there are no other gods", which is the more exact phrasing we have determined for the "1st commandment". They cease to be gods to you at all.
Hence, other gods only exist as gods to you if you worship them as gods. If you don't worship an idol, then it's just a chunk of wood/stone/whatever. But if you worship it, it is "your god" - a denotation of its relationship to you.
And this is the sense in which I think we should interpret the text of Isaiah in the question (and all other texts where we see this term).