Shouldn’t “art” be “is” in “Our Father who art in heaven”?

Solution 1:

"Our Father who art in heaven, hallowed be Thy (your) Name," is the rest of that sentence.

By saying "Our Father... Thy..." you are addressing God personally, making that the second person singular (you are). (First person singular: I am. Third person singular: he/she/it is.) "Our Father" is not speaking about God; it is speaking to God. (It is like saying, Hey, Dad, you, up there. Blessed be your name.)

If it were about Him, it would certainly be He is. From the same book which states Our Father, who art in heaven:

For the Lord is our judge, the Lord is our lawgiver, the Lord is our king; he will save us. - Isaiah 33:22

Quoting your source:

When thou is the grammatical subject of a finite verb in the indicative mood, the verb form ends on t... (e.g., "thou goest"; "thou dost"), but in some cases just -t (e.g., "thou art"; "thou shalt")

and

Originally, thou was simply the singular counterpart to the plural pronoun ye... thou was later used to express intimacy...

and

The familiar form is used when speaking to God... (an "informal" singular form of the second person in modern speech.)

Solution 2:

The main issue here is that the original Greek uses a form that does not exist in English. The relevant portion of the Greek text reads:

Πάτερ ἡμῶν ὁ ἐν τοῖς οὐρανοῖς·

Translated directly, word for word, that is:

Father ours the one in the heavens.

Or, to make it closer to actual English:

Our Father, in the heavens.

The ὁ ἐν τοῖς οὐρανοῖς has no direct equivalent form in English, it literally means the one in the heavens. Well, the sky actually, but some poetic license is assumed. The main point is that there is no verb there, the text is not saying "who is in heaven" but "the one in heaven".

As @anongoodnurse already pointed out, the prayer addresses God in the second person, therefore, the art is quite correct and the sentence could be rephrased to:

Our father, thou who art in heaven, hallowed be thy name.

Solution 3:

As you yourself said: "Thou art". "Our Father" etc. is a title by which the speaker is addressing god. This is confirmed by the next section, "hallowed be Thy name", which is essentially a parenthetical addition to that title.

So it really is self-consistent, though not a form we're used to hearing these days and further obscured by being poetic phrasing rather than simple prose.

(Actually, I'd expect a modern reader to have more trouble with the imperative use of "come" and "be done" later in that sentence.)

Solution 4:

It's because the sentence is an invocation or an address to, not a statement about God:

Compare "Our Father, who art in heaven, hallowed be thy name" with "Our father, who's in Paris at the moment, is a really nice guy.

Also compare "I, who am the boss here, am going to fire you." "I who is the boss here" is just wrong. Same principle.

The seeminly odd grammar implies something like: "Our Father - the one in heaven that is, not some earthly guy - may your name be made holy"

The oddness is probably heightened though because "thou/who art" is archaic so it stands out.

Compare a sentence like this: "You, who are the love of my life, have given me so much happiness!" Once again, same thing happening.