+10 XP
UNRESOLVED
LVL 1 · 450 BCE
ZENO'S PARADOX
Achilles races the tortoise. The tortoise has a head start. Achilles must first reach where the tortoise was, but by then the tortoise has moved. An infinite series of catchings-up, each smaller, never complete. Motion is impossible. Motion happens anyway.
Resolution attempt: Convergent series sum to finite values. Mathematics resolved what logic could not. But Zeno's point was never about math -- it was about the gap between thought and reality.
+15 XP
PARADOX
LVL 3 · 400 BCE
THE SHIP OF THESEUS
If every plank of a ship is replaced, one by one, is it still the same ship? And if the old planks are reassembled into another ship, which is the true Ship of Theseus? Identity persists through change, yet identity requires continuity.
Resolution attempt: None universally accepted. Identity may be a convention, not a fact. The paradox endures because we need identity to be real while knowing it is constructed.
+50 XP
BOSS PARADOX
LVL 5 · 600 BCE
THE LIAR'S PARADOX
“This statement is false.” If it is true, then it is false. If it is false, then it is true. The simplest of all paradoxes and the most devastating. No logical system has fully contained it.
Resolution attempt: Tarski's hierarchy of languages, Kripke's fixed-point semantics, paraconsistent logics -- each offers a framework, none offers closure. The liar endures.
+20 XP
RESOLVED
LVL 7 · 1901
RUSSELL'S PARADOX
Consider the set of all sets that do not contain themselves. Does it contain itself? If yes, then by definition it must not. If no, then by definition it must. The barber who shaves all who do not shave themselves.
Resolution attempt: ZFC set theory prohibits self-referential sets. The paradox was resolved by restricting what counts as a set. Walls were built to keep the paradox out.
+25 XP
PARADOX
LVL 9 · 1935
SCHRÖDINGER'S CAT
A cat in a box with a radioactive atom. Until observed, the atom has both decayed and not decayed. The cat is both alive and dead. Observation collapses the superposition. Reality requires a witness.
Resolution attempt: Copenhagen interpretation, many-worlds, decoherence -- each reframes the paradox without eliminating the strangeness. Quantum mechanics works; understanding it is optional.
+100 XP
FINAL BOSS
LVL 10 · TIMELESS
矛盾 / THE ORIGINAL
A merchant sells a spear that can pierce any shield, and a shield that can block any spear. Both cannot be true. Both are for sale. The word for contradiction itself -- 矛盾 -- is born from this paradox. The spear (矛) and the shield (盾) that cannot coexist.
Resolution attempt: There is none. This is the source. Every paradox in this quest log is a descendant of the merchant's impossible inventory. The quest continues.