Dawn broke, dew settled, and the thinning fog revealed an army of truth function pairs, more than two hundred fifty strong. The crows sent a messenger; they came for war, and they would not rest until mathematical logic dominated our sovereign numbers. We formed a defensive ring, and braced for the onslaught.
The hoard came all in one wave, tearing through additive and multiplicative closure like autumn leaves, before slamming hard against the associative and commutative properties of addition and multiplication. The associative line claimed three quarters of the attackers, and the commutatives took nearly half of those who remained; but, in the end, thirty-six truth function pairs broke through. Our defense was reduced to three heroes: Distribution, Identity, and Inverse.
Distribution fought like a force of nature. The slain pairs mounded at his feet like a winter’s clutch at first snow. The elite truth functions trembled as they threw themselves into melee with the mortal wall of Distribution. At last Distribution had felled all but the dark pentad: Bicond Disjunct, Disj Contra, the twins Bicond and Triva Tautol, and Exdis Conjunct. All five descended on Distribution, overwhelming his might.
The demonic five wasted no time shifting their focus to Identity, but Identity was less brawn than brain. She refused to face them in mass. Instead they were addressed by cunning. First, Identity used the crows’ own logic to lay a trap that snared the Tautol twins and Disj Contra, strangling them in triviality. Then she confronted Bicond Disjunct with a riddle. He was given two mutually exclusive choices, but being a Disjunct he couldn’t discern one from the other, and Identity struck him down with uncertainty. This left only the clever and focused Exdis Conjunct. He wouldn’t fall for any of Identity’s traps. And, when he ran her down, Identity was no more.
Inverse and Exdis Conjunct stood alone on the battlefield, each combatant knowing the outcome of this contest would shape the future world. Inverse struck out at his opponent’s additive half, but the torso simply inverted on itself, providing nowhere for Inverse’s club to strike. The weight of this error pulled Inverse to the ground. Exdis Conjunct cooed, “Did you miss an assumption, numerologist?”, and laughed aloud. Inverse lay among the bodies of Identity and the four deceased devils. Exdis stepped up to the prone form of Inverse, ready to end the battle. But, in a flash, Inverse thrust a conditional into Exdis’ multiplicatives, ending the bird forever more.
You see, Exdis Conjunct had a multiplicative flaw. His identity was a tautology, and a Conjunct can only reach tautology from tautology. Exdis had no multiplicative defense against Inverse wielding a conditional. The day was won, but only just.
Okay, let’s make something clear. We had no intention of enslaving any theory. We just want to unite all mathematics into one great theory. And, we figured the best way to do that was to establish an empire with Logic as emperor. Maybe that wasn’t the best solution…we’re open to alternatives.
The preceding is based on a true analysis. Some names and situations were adapted for theatrical flare.
Oops. There are a few miscalculations in the analysis on which this story is based. First, Exdis Contra survived battle with Distribution, but succumbed to Identity’s traps. Triva Tautol did not survive Distribution, it was actually Conj Tautol. And finally, Bicond Disjunct wasn’t actually take in by Identity’s riddle; he too survived to fight Inverse. It should be noted, that the end result was the same. Here’s the corrected PDF.