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This came up recently in a session: Our cleric thought it would be a great idea if he made our airship hallowed.

Hallow

You touch a point and infuse an area around it with holy (or unholy) power. The area can have a radius up to 60 feet, and the spell fails if the radius includes an area already under the effect of the hallow spell.

The DM disallowed it, he said it was meant to create Hallowed Ground, and by our interpretation, we'd be able to cast the spell on a rock and then just carry that rock around.

We countered with "isn't our ship a place/area?" but he said "no" so we left the argument at that.

In the case of the silence spell vs the light spell, it's pretty clear one is attached to an object and the other is not.

Light

You touch one object... the object sheds bright light...

vs.

Silence

... no sound can be created within or pass through a 20-foot-radius sphere centered on a point you choose

But in the case of Hallow, there's an ambiguous 'touch' and 'area' mentioned.

My question is: What constitutes a 'point' and 'area' - Especially when the spell mentions touching it?

An area is a certain grid rather than the objects within the area.

If we look at the Faerie fire spell:

Each object in a 20-foot cube within range is outlined

It clearly states that the objects within the area are effected so we know that if the objects were to keep being affected if they were moved then it is written down. Likewise if we look at the Anti Magic Field:

A 10-foot-radius invisible sphere of antimagic surrounds you.

Until the spell ends, the sphere moves with you, centered on you.

We also see that if an area was to move with an object then it would also be stated.

As such we can deduce that hallow endows a location with holy energy and the location is not bound to any object. So taking a rock from a hallowed area would be equal to taking a regular rock and if you tried to hallow a ship then you would hallow the space where the ship was parked.

There's no clear guidance, so your DM isn't wrong.

There really isn't anything anywhere specifying what these sorts of effects are "relative" to. There are other questions here about similar issues wondering what exactly counts as a "place" that a spell or magic item's effect happens at, such as "Can a permanent Teleportation Circle be made on a moving vehicle?", "Is Leomund's Tiny Hut stationary relative to the ground or to the surface it's cast on?", and "What happens when an Immovable Rod is activated while in a vehicle?".

If the fantasy world you're playing in is similar to our real-world universe, then there really isn't a concept of "stationery", as everything is moving with respect to something else. Of course, it's possible that the world you're playing in is absolutely stationery, depending on its cosmology.

The rules are intentionally vague and broad on this, allowing for the DM to make whatever ruling makes the most sense for their particular game and setting. I could certainly imagine it making sense in one case to allow for an area-of-effect protection spell to be on a large vehicle in which much of a campaign is taking place, while in another case not making sense to allow for hallowed ground in the place where the small craft you're all on will be moving from that spot in just a moment. (Perhaps it would hallow the original spot, but you'd move from it too quickly for it to do you much good.)

It's all magic, after all. The DM is one who decides what a "point" or "area" might mean for a given spell, and there's a lot of variety in what that could reasonably be.