I (William Bricken) am drawing attention to the fact that there are two kinds of emptiness.
We can observe a bounded emptiness, such as an empty cup or an empty space, because the boundary provides a place from which we can observe. We can safely stand outside, without destroying the emptiness, and point to the emptiness within, and observe the Nothing.
Total emptiness, however, does not support our observation of it. If we were able to observe it, we would be placing our focus in it, rendering it non-empty and no longer what we wish it to be. It is no longer total emptiness solely because our attention fills it.
There are two kinds of void. The Absolute Void is simply not available to contemplation. It is Emptiness. The Relative Void is indirectly accessable, at least to thought. It is Empty Space.
The word emptiness is a noun, it refers to the Absolute Void, a state with no properties. The word empty is an adjective, it identifies the only property of the Relative Void.
We can use the Relative Void as a space of representation by putting tokens in it. It is impossible, however, to place tokens in an Absolute Void. The only route from the absolute to the relative is through non-symbolic conscious Choice.
This concept, that there are two voids, forms the basis of a more general form of mathematics. The distinction between Empty and Emptiness is all that is necessary to construct traditional mathematics. The empty simple space is the foundation upon which a deeper understanding of the process of creating symbols can be built. In its essence, the conversion from emptiness to empty space is the process of picking up a piece of paper with the intent to Record Tokens. It is an acknowledgement of a sentience that is creating symbols. As a starting point, the genesis of an empty space from emptiness incorporates the mathematician as the fundamental mathematical construct. Next, I will attempt to demonstrate that this distinction is indeed informative.
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BRICKEN, William, 1986. A Simple Space. Advanced Decision Systems. 1986. pdf 
[Accessed 15 December 2023].