Binaryfield VS Box
Many may consider the Binaryfield to be equivalent to The Box. After all, anything that isn't x is not x, that is common sense. So the Binaryfield would encompass absolutely everything. However, this is not the case. The Box contains everything, including completely impossible objects. This would mean the Box would contain an object that is neither x or not x, as completely impossible as that is. This means that there are in fact objects beyond the Binaryfield which are within the Box. In fact, if objects can exist in more than two states, more possibilites for objects would exist. This means that there are actually more objects outside of the Binaryfield than inside it. Nevertheless, the vast majority of cosmological objects described on this Wiki are within the Binaryfield as "if y is not x then y is not x" is a very basic principle.
Still, it is worth clarifying that "Binaryfield contains everything that is either x or not x" is only valid when x also follows the law which defines the Binaryfield, specifically "everything is either x or not x". So while it is true to say that "Binaryfield contains everything that is either a potato or not a potato", it is not valid to say that "Binaryfield contains everything that is either in the Binaryfield or not in the Binaryfield" as things not within the Binaryfield do not follow the principle of "everything is either x or not x". The contents of the Schemafield, however, do follow this law and thus "everything that is either in the Schemafield or not in the Schemafield" is a valid description of the Binaryfield.
Note that the above does not mean the Binaryfield is not a Selfverse just because it does not contain some things which are larger than it. The Binaryfield is certainly larger than itself due to being larger than the Maiorverse and containing things which are themselves larger than themselves, but nevertheless there are many things it does not contain. Of course, these are highly abstract hypercosmological objects and concepts which are difficult to even model, as being neither x nor not x is completely impossible in any form of classical logic or mathematics. This is why, despite the majority of 'things' being beyond the Binaryfield, the majority of concepts will almost always be within it, as concepts beyond it are incredibly difficult for humans to conceptualise, even when models are used.
The Half-x Argument
It should be clarified that when referring to 'x' and 'not x', there is no in-between within our universe. For example, if x was a potato, and the potato was sliced in half, it could be argued that that half of a potato is neither a potato nor not a potato. This is not the case. Something is either absolutely x or it is not. If something is not absolutely and completely a potato then it is not a potato. As such, all things are either x or not x.
It can be debated that it is unknown what qualifies for being "absolutely and completely a potato", and this is true. However, what is known is that a line is drawn somewhere. On one side of that line the object is x. On the other it is not. There is nothing on this line or in-between x and not x. It does not matter where this line is drawn as the sum of x and not x is the same regardless of where the line is placed, as the only thing that has changed is which objects belong to which. All of the same objects are still within the Binaryfield.
- While it is true that the property of being in the Binaryfield cannot be used as x in "Binaryfield contains everything that is either x or not x", the Binaryfield itself can, as it is contained by the Binaryfield. This means that technically "Binaryfield contains everything that is either the Binaryfield or not the Binaryfield" is an accurate description of the Binaryfield.