mujun.quest

A

statement that declares its own falsity: "This sentence is a lie." If it is true, then by its own admission it is false; if it is false, then it is true. The sentence travels in a closed loop, a serpent biting its tail in the margin of the page. Logicians have circled this paradox for two and a half millennia, since Epimenides of Crete first claimed that all Cretans are liars.

The expedition begins, then, with an utterance that cannot rest. We continue.

A

n arrow in flight is, at any single instant, motionless — occupying a space precisely equal to itself. Time is composed of instants. In each instant the arrow does not move. Therefore the arrow, summed across instants, does not move.

And yet it strikes the target. The fletching trembles in the wood; the wood remembers a journey that, by the syllogism above, never occurred. To walk across this room is to perform an impossibility approximately seventy times per second.

P

lank by plank the vessel is repaired during its long voyage. By the time the ship returns to harbour, no original timber remains. Is it the same ship? The Athenians said yes; Hobbes raised the question: what if the discarded planks were gathered and reassembled into a second hull?

Two ships now bob in the same harbour. Each claims to be Theseus's. The harbourmaster strokes his beard. The fish, indifferent to ontology, swim on.

R

emove a single grain from a heap of sand. Is it still a heap? Surely. Remove another. Still. Continue. At what grain does the heap cease? Eubulides of Miletus walked the threshold of vagueness and found no door, only an endless series of nearly.

We live, it seems, among predicates whose edges blur in mist. Tall, bald, old, kind — each word a heap.

I

n the marketplace of the State of Chu, a merchant raised his wares: "This shield is so strong that nothing can pierce it. This spear is so sharp that it can pierce anything." A passer-by inclined his head: "What, then, if your spear strikes your shield?"

The merchant, history records, had no reply. The Chinese word for contradiction — 矛盾, mao-dun — preserves this scene in two characters: spear and shield, side by side, eternally meeting.

C

onsider the set of all sets that do not contain themselves. Does it contain itself? If yes, then by definition it should not. If no, then by definition it should. The barber who shaves all those, and only those, who do not shave themselves, has nowhere to put his razor.

An entire foundation of mathematics shivered for a decade. Whitehead and Russell wrote a thousand pages to prove that 1 + 1 = 2 without falling into this hole.

A

teacher announces a surprise examination on a weekday next week. The students reason: it cannot be Friday, for then by Thursday evening it would be expected. It cannot be Thursday, for the same reason after Friday is excluded. By induction, the examination cannot occur at all. They study for nothing. On Wednesday morning, the teacher distributes papers. The class is surprised.

Reason had eliminated reality, and reality calmly reappeared.

S

uppose a traveller returns to a year before her grandfather met her grandmother and prevents the meeting. She erases her own cause. Without that cause, she does not exist to undertake the journey. The grandfather and grandmother meet. She is born. She travels back. She prevents the meeting. The fish swim slowly through this loop, indifferent to the order of cause.