Assumptions

1. Vistula Theorem: Where x < 1 and y > 1, multiplication of x and y satisfies the conditions for dialectical arithmetick.
2. First Macaronic Theorem: All numbers multiplied by 0 return 0, the ultimate harbinger of smallness.
3. Second Macaronic Theorem: All numbers divided by 0 return a largeness which defies language.
4. x⁰ = x • (1 ÷ x)

Thus…

0⁰ = 0 • (1 ÷ 0)
Upon the penning of this dialectical product, the First and Second Macaronic Theorem are thrust into a Vistulan maelstrom; a sort of trench warfare of dialectics in which Grenades of Spirite are thrown. To resolve this mayhem, we must sign a peace treaty between the Macaronic Theorems in which the impact of both is respected. Luckily, since the Macaronic Theorems are both derived from the same postulate, we can recall the Parable of the Limbless Cat and determine their impact to be equivalent, and so 0⁰ must be an average of the values expected by both Theorems.

Thus, 0⁰ = 1 ÷ 2.