Well, for there to be necessary entities, a state where there were no entities would have to involve a contradiction in terms. But how? It could not involve a state where there was some x for which P(x) and ~P(x), because there would not, in fact, be some x.
Imagine a world where there are only contingent entities. Since all entities are explained in terms of other entities, this implies either an infinite regression or a circularity of causation. Each of these explanatory entities, is necessary. A necessary entity contradicts the statement there are only contingent entities. Therefore there cannot be contingent only entities
Imagine a world were there were no entities. Then there would not be any contingent entities, so there would be no need of necessary entities to explain them.
Each of these explanatory entities, is necessary.
Not if you could have either: but in any case their necessity is in fact contingent. What you're doing is along the lines of: "Here is a contingent triangle. A triangle necessarily has three sides. Therefore its sides are necessary objects." Well, not if the triangle is contingent: in that case it could have not existed and the sides along with it.
Can you prove it is possible for a 'state' of 'no entities' to 'exist'?
Again, I thought I'd done this.
To show that necessarily something exists would be to demonstrate that there is a contradiction that can be derived from the statement "there are no things that exist". (Otherwise it would not be necessarily false.) But how can there be a contradiction where there are no objects to form propositions about? There can't, can there? For a contradiction would involve asserting and denying that the existence of an object having a given predicate, the existence of two objects standing in a given relation, etc. But if you think you can frame such a proposition, have at it.
I don't know enough about the nature of reality or the nature of existence to tell you if a contradiction exists between these concepts and the concept of 'no thing existing'. But I don't need to since I'm only proposing that this needs to be established before the proof in the OP gets off the ground.
Well, I seem to have established it. Unless you have a rebuttal to my argument.
It's hard to stay in sync in discussions like this. I thought we agreed when you said, "Things exist or don't exist, propositions are true or untrue," but if your question about "the non-existence of unicorns" implies it's a thing rather than a proposition then I probably misunderstood you.
No, I'm implying that it would be silly for that to be a thing.