KJV Gal 3:20 Now a mediator is not a mediator of one, but God is one.
One what? It appears many translators and commentators, including Trinitarians generally add the word "party" or "person":
http://biblehub.com/galatians/3-20.htm
So is God one "person", "party" or something else? Or just an individual?
If you look at the context, you will see Paul is comparing "the law", the thing with Moses at Mt Sinai; to "the promise", the thing with Abraham.
Paul believes the covenant "of the promise" is superior to the covenant "of the law"; works vs faith (v2), spirit vs flesh (3), justified vs cursed (10) ...
In verse 17 he says the thing with Abraham happened before the thing with Moses, the promise business came first.
In v18 he says because the inheritance was given to Abraham by promise, and as this happened before the law was given, the inheritance was then - and would always afterward be on the basis of the covenant of promise (only).
In v19a he says the law was only temporary, until the one would come to whom the promise was made (the primary counterpart in that covenant, not Abraham).
In v19b Paul says the covenant that conferred the promise was not like the one at Mt Sinai which involved mediators on both sides
v20 but was transacted without mediator.
Paul continues, saying the covenant is eternal (25) and applicable to all men (28)
So I think v20 needs to be read in the flow of the chapter, another aspect in which the covenant of the promise is superior to the covenant of law.
I think this conversation misses the point. The immediate pretext of Gal 3:20 is the previous discussion about the law. Paul's introduction of the idea of a mediator carries the connotation of a contract between two (usually equal) parties. However, I believe Paul is trying to make the point the following points:
(1) The "contract" is unusual because it is not with equal parties because it is based purely on promises by God and thus involves the faithfulness of God
(2) It is not really a contract because God [who stands] alone set the conditions.
These ideas are discussed at length in numerous analytical commentaries. Here is a sample:
Ellicot: The mention of the word “mediator” implies a contract to which there are at least two parties. But where there is a contract there must be also conditions, and if these conditions are not observed the whole falls to the ground. Such was the Law. The Law was not kept, and therefore the blessings annexed to it were forfeited. On the other hand, the promise depends upon God alone. He gave it, and He will assuredly keep it, no matter what man may do. God alone is concerned in it.
So, While the law was given through messengers (v19) the covenant was mediated by Jesus Christ (John 14, 2 Tim 2:5 etc), but Jesus is "one" with the Father. This is the fundamental (logical) tussel Paul has - Jesus is the mediator between God and humans but God is one!
Here's the Greek as well as Young's Literal Translation.
ὁ δὲ μεσίτης ἑνὸς οὐκ ἔστιν, ὁ δὲ θεὸς εἷς ἐστίν.
and the mediator is not of one, and God is one --
(Galatians 3:20)
The second δὲ can either be translated as "and" or "but". I wouldn't put too much emphasis on either one. Being a postpositive particle, it can also be used to separate clauses and sentences.
I think the most obvious explanation hearkens back to the famous prayer Shema Yisrael.
שְׁמַע יִשְׂרָאֵל יְהוָה אֱלֹהֵינוּ יְהוָה אֶחָֽד׃
Sh'ma Yisrael Adonai Eloheinu Adonai Ecḥad
Hear, Israel, the Lord our God, the Lord is one.
(Deuteronomy 6:4)
In his letter to the Galatians, Paul is reminding them of the unity of God, which is fully compatible with the Christian Trinity. God, being one, doesn't require a mediator. But human beings, being many, do require a mediator.
In this case, that mediator is Moses, according to Challoner in his revision of the Douay Rheims.
In short, God is one and God is also a trinity. There's no need to add "party" or "person"1 because these words don't show up anywhere in the Greek of Galatians or the Hebrew of Deuteronomy. Instead, simple numerals are used. The Greek uses εἷς and the Hebrew uses אֶחָֽד.
1 I'd be shocked to see any translator translate ὁ δὲ θεὸς εἷς ἐστίν as "God is one person", because not only is that a non-literal translation, it also directly contradicts the dogma of the trinity. Better would be "God is one party", but even this is ugly. Best is simply, "God is one", per Dt. 6:4.
In this particular context Paul follows the existing Jewish tradition that claims that the Law was given to Moses by angels (Gal.3:19; cf. also Acts 7:53), in difference from other tradition, that claims that it was given directly by God. That is the meaning of saying in Gal.3:20 that the "mediator" (i.e. Moses) is not mediator of one [God], but of several [angels].
As to the question "one what" in the phrase "but God is one": it is a phrase denoting the same as in Jesus' quote of the Deuteronomy 6:4 ("Hear Israel, God your Lord is one" /Mark 12:29/); it can have two meanings:
1) "God is one [person]"; in which case it can imply God the Father, who is one person, as in Paul's other expression in 1 Cor.8:6 ("for us there is one God, the Father, from whom are all things, and we for Him; and one Lord, Jesus Christ, through whom are all things, and we through Him”). If this is the case (which I think is quite plausible), given the last quote from the 1 Cor. 8:6, it is not at all denied the indispensable and ontologically necessary role of Jesus Christ for the Father to give sonship to humans, which was not available even to Moses, not to even mention to ordinary humans through Moses. Faith in Jesus Christ is ontologically necessary for humans to have access to a renewed divine life as new creations in Christ (Gal. 2:20) and God's adopted sons (Gal. 3:26); moreover, even for God the Father His unique Son and Logos is ontologically necessary for vouchsafing this sonship to humans, no less than uni-co-agency of the Son-Logos is ontologically necessary for the Father to create the universe, for the created universe is simultaneously "from" the Uncreated Father "through" the Uncreated Son (cf. 1 Cor.8:6; Hebrews 1:2), when "from" cannot be separated from "through" (like, to use a famous metaphor, enlightening "from" the sun can happen only "through" the rays of the same sun).
or 2) "one" in this passage can imply just "reality", as in an expression: "the world is one", that is to say, the world is one reality. Now, this one reality of God entails also difference of Father from the Son (and both from the Spirit), and all Three are the one reality of Divinity. And in the context of the passage from Galatians the talk is about the new covenant with God, a new life of faith that is not possible through circumcision and Law, but only through baptism, but the baptism is in one shared name [God] of all Three - the Father, the Son and the Holy Spirit (cf. Matthew 28:19).
