is a fundamental mathematical idea asserting that when an operation is applied to members of a specific Domain, then the result is also a member of that domain. (Iconic Arithmetic Volume I, p. 216)
Multiplication of natural numbers is closed, for example, because all such multiplications generate another natural number. Closure of James Forms is trivial because the three axioms permit only transformation between valid finite container forms. There is no mystery about what the result of an operation may look like.
But there is a subtlety for void-based forms: closure loses meaning when transformations create void-equivalent forms. The domain of non-existent forms is a nonsense concept.
Since void-equivalent forms are meaningless, their illusionary presence is irrelevant.
We have the choice of building meaning upon a Domain that includes a lot of meaningless junk, or building the domain upon meaning, in which case there will be meaningless junk to clear away.
Stretching to adopt Gödel’s perspective, if we wish to address all possible structures (a complete system), then some will be illusionary (an inconsistent system). Alternatively if we wish to avoid illusion (a consistent system), then some structures will transform into nothing, leaving the system incomplete.
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CleanBlockClosure – a closure created at compile time, it is stored in the literal frame and just pushed on the stack.