Artifacts, Organisms, and Modes of Existence

Responding to a correspondent Bill returns to a compositional puzzle.  For related posts see his Wholes and Parts category. 

We are introduced to a house made of bricks.  Bill says,

1. The house exists.
2. The bricks exist.
3. The house is composed of the bricks, all of them, and of nothing else and is therefore not something distinct from them or in addition to them.
4. Since the bricks can exist without the house but the house cannot exist without the bricks, the house is distinct from the bricks.
5. “Exist(s)” is univocal in (1) and (2), and there are no modes of existence.

Bill then argues that these five claims are inconsistent though plausible and suggests that we should reject (5).

1. I'm having trouble understanding how the puzzle here is made into an argument for modes of being. Premise (3) claims that the house and the bricks are not distinct and (4) claims that they are, so (3) and (4) are in contradiction regardless of (5). Is Bill perhaps suggesting the following? Since (4) contains the verb 'to exist', multiple modes of existence would allow us to modify the sense of 'can exist' in (4) so that the implicit little argument in (4) no longer delivers the conclusion 'the house is distinct from the bricks', and hence (4) would cease to contradict (3).

2.  Here is an argument for rejecting (4). The idea is that it misapplies the term 'distinct'. Suppose we present the puzzle a little differently:

1. On some plot there is a house,
2. On the same plot there are some bricks.

I tend to imagine this situation as involving two objects, the house and the bricks. Suppose then we are told any one of the following,

3a. The house consists of the bricks and the bricks comprise the house, without remainder.
3b. The house and the bricks are identical,
3c. The house and the bricks are not distinct.

This has affinities with Frege's Puzzle. We learn that seeming two things are one. So I say that the inferential equivalence of 3a, 3b, and 3c fixes the sense we should assign here to 'distinct'. Now (4) says,

The bricks can exist without the house but the house cannot exist without the bricks; ergo the house is distinct from the bricks.

Arguably, the house could exist without the bricks by virtue of consisting of different bricks.  We might imagine the bricks replaced by new bricks, one by one, and the old bricks finally destroyed.  The house would remain.  So an argument that this modal claim leads to the conclusion 'the house and bricks are distinct' needs to be made. Clearly we can distinguish the senses of 'the house' and 'the bricks' in our minds, and conceptually a composite object is dependent on its parts but not conversely, but just as in Frege's Puzzle, it's the referents not the senses that are being identified. So (4) and (3) differ in their use of 'distinct'. Bill also argues for (4):

...it is also not just the bricks, but the house-wise arrangement of the bricks, an arrangement that is not nothing, but something real that makes the house distinct from the bricks.

This too, I think, conflates sense and reference. The sense of 'collection of bricks' does not include 'is house-shaped' or 'protects against the elements' and so is distinct from the sense of 'house'. But it's reference that counts here, not sense. The actual bricks in their house-shaped configuration do offer shelter.