Half-hedgehoglessness

"That which cannot be held cannot be real; that which cannot be a half-hedgehog cannot be held."

~ Confucius on half-hedgehoglessness

Half-hedgehoglessness is a state of an entity not possessing of another entity that is a half of a hedgehog. This state is omniapplicable. Here is the proof, in four basic cases as defined in the Half-hedgehoglessness Conjecture in Paracelsus' famous work Algebra Mammalia, which dealt solely with the mathematics of rodents and other small mammals.

Case 1: Total Half-hedgehoglessness

The entity possesses no entity which is part or whole of a hedgehog. In this case, half-hedgehoglessness is achieved by virtue of hedgehoglessness, though the two states are not self-proving. This is commonly referred to as total half-hedgehoglessness and is identical in execution to the lessness of any mammal.

$hog(0)::NOT(hog(0.5))$

Case 2: Whole Hog Half-hedgehoglessness

The entity possesses an entity which is commonly accepted as a whole hedgehog. In this case, half-hedgehoglessness is achieved because the hedgehog itself is virtually indivisible: any division of the hedgehog prevents the possibility of creating a perfect half-hedgehog; thus, though a whole hedgehog is in its most basic sense composed of two half-hedgehogs, these halfhogs cannot be separated and therefore cannot be identified as individual entities. This is commonly referred to as whole hog half-hedgehoglessness and is identical in execution to hedgehogfulness.

$hog(1)::NOT(hog(0.5)+hog(0.5))::NOT(hog(0.5))$

Case 3: Half-Hog Half-hedgehoglessness

The entity possesses a single entity which is commonly accepted as a half-hedgehog. The concept that a half-hedgehog exists constitutes the proof that it has another half-hedgehog counterpart; that is, a single half-hedgehog cannot exist unless another does. In this case, the half-hedgehog that the entity is without is the half-hedgehog which corresponds to the other half-hog in its possession. This is commonly referred to as half-hog half-hedgehoglessness and is unique.

$hog(0.5)::hog(1)-hog(0.5)::NOT(hog(0.5))$

Case 4: Dual Half-Hog Half-hedgehoglessness

The entity possesses two entities which are commonly accepted as half-hedgehogs. The case would seem to be self-denying: half-hedgehogfulness cannot prove half-hedgehoglessness. However, the proof has been defined since the 300s BC: First, any division of a whole hedgehog prevents the possibility of creating a perfect half-hedgehog; thus, though a whole hedgehog is in its most basic sense composed of two half-hedgehogs, these halfhogs cannot be separated and therefore cannot be identified as individual entities. Therefore, though the half-hogs in possession must exist, they cannot have been extracted from the whole hog by any normal physical means and therefore cannot be recombined to form a single whole hog. Because a half-hedgehog is defined as that which constitutes or may constitute one half of the physical form of a half-hedgehog, the two half-hogs in possession do not exist in a mathematical sense. This is commonly referred to as dual half-hog half-hedgehoglessness and is half-hog half-hedgehoglessness added to itself once. This is not a case of sumative half-hedgehogidity.

$hog(0.5)+hog(0.5)::NOT(hog(1))::NOT(hog(0.5))$

Related Theories

Paracelsus' Original Lessness Theories:

1. If an entity is in possession of no entity or part of an entity, that entity cannot possess a hedgehog, badger, rabbit, weasel, ferret, skunk, field mouse, porcupine, or half of any of these mammals.

2. If an entity possesses part of an entity but not a whole entity, that entity cannot possess a hedgehog, badger, rabbit, weasel, ferret, skunk, field mouse, or porcupine.

3. If an entity possesses two whole entities, they can be any combination of two of the following: hedgehog, badger, rabbit, weasel, ferret, skunk, field mouse, or porcupine, but not two porcupines.

4. If an entity possesses nonexistence, it can be determined to not be an entity, kind of like Tobago.