矛盾 Wiki

A living archive of things that cannot be true and cannot be false.

矛盾 — The Spear and Shield

A man was selling a spear and a shield. He claimed his shield could block any attack, and his spear could pierce any defense...

The word 矛盾 (mujun) comes from one of the oldest recorded paradoxes in human history. In the Han Feizi, a merchant in the state of Chu boasted that his shield was so strong nothing could pierce it, and that his spear was so sharp it could pierce anything.

“What happens,” a bystander asked, “when you use your spear against your shield?”

The merchant had no answer. This moment — the silence where logic collapses — is the conceptual seed of this entire archive.

∀x(S(x) → ¬P(x)) ∧ ∀x(P(x) → ¬S(x))

The paradox was so culturally resonant that the Chinese word for “contradiction” literally means “spear-shield.”

The Liar's Paradox

This sentence is false. If it is true, then it must be false. If it is false, then it must be true...

“This statement is false.” Five words that have haunted logicians for over two millennia. If the statement is true, then what it says must hold — meaning it is false. But if it is false, then its claim of being false is incorrect — meaning it is true.

The Liar's Paradox is not a riddle waiting to be solved. It is a wound in the fabric of classical logic.

L := ¬T(L) ⇒ T(L) ↔ ¬T(L)

Alfred Tarski showed that no sufficiently powerful formal language can consistently define its own truth predicate. The Liar proves that certain things cannot be said within certain systems.

The Ship of Theseus

If every plank of a ship is replaced over time, is it still the same ship?

The Athenians preserved the ship of Theseus for centuries. As planks rotted, they were replaced. Over time, every piece was swapped out. Is this still the ship of Theseus?

Thomas Hobbes sharpened the paradox: suppose someone collected all the old planks and built another ship. Now there are two ships. Which one is real?

This paradox strikes at the heart of identity itself. If you replace every atom in your body over seven years, are you the same person?

S(t) = S(t+1) ⇔ ∃continuous(S, t, t+1)

Zeno's Dichotomy

To reach any destination, you must first travel half the distance. But to travel half, you must first travel a quarter...

Before you can walk across a room, you must first cross half the distance. Before that, a quarter. The sequence never ends. You must complete an infinite number of tasks to move a single step.

Yet you walked across that room. The paradox is that our mathematical model generates conclusions that contradict direct experience.

∑(n=1,∞) 1/2^n = 1

Modern calculus resolves this with convergent series. But Zeno's deeper point remains: there is something strange about the relationship between mathematical infinity and physical reality.

The Grandfather Paradox

If you travel back in time and prevent your grandfather from meeting your grandmother...

You build a time machine. You travel to 1940. You prevent your grandfather from meeting your grandmother. You are never born. You never build a time machine. Your grandfather meets your grandmother. You are born...

The loop never resolves. Each state implies its own negation. This is 矛盾 in its purest temporal form.

Some physicists propose the Novikov self-consistency principle. Others suggest branching timelines. Both raise more questions than they answer.

T(e) → ¬∃cause(e) → ¬T(e) → ∃cause(e) → T(e)...

The Sorites Paradox

One grain of sand is not a heap. Adding one grain cannot make it a heap. Therefore, no number of grains can ever make a heap...

Start with one grain. Not a heap. Add one. Still not a heap. Continue. At no single step does it become a heap. Yet a million grains is undeniably a heap.

The Sorites paradox isn't just about sand. It's about every vague concept: When does a person become old? These are questions that resist answering.

¬Heap(1) ∧ ∀n(¬Heap(n) → ¬Heap(n+1)) → ∀n(¬Heap(n))

The Omnipotence Paradox

Can an omnipotent being create a stone so heavy that even it cannot lift it?

If God can do anything, can God create a rock so heavy that God cannot lift it? If yes, there is something God cannot do. If no, there is something God cannot do. Either way, omnipotence collapses.

This is 矛盾 applied to the divine: the unstoppable force meets the immovable object.

Some theologians argue omnipotence doesn't include logically impossible things. The paradox remains, smiling patiently at both sides.

O(x) := ∀p(can(x,p)) ⇒ ¬O(x)

矛盾 — Deep Archive

The Han Feizi is a foundational text of Chinese Legalist philosophy, compiled around 233 BCE. The paradox appears in Chapter 36.

Han Fei used this story as a political argument: a ruler cannot simultaneously promise absolute security and absolute power.

The compound character 矛盾 entered Japanese as “mujun” and became the conceptual foundation for understanding logical contradiction in East Asian philosophy.

The Liar — Deep Archive

Epimenides, a Cretan, declared “All Cretans are liars.” The paradox devastated Frege's logicist program through Russell's version.

Tarski's undefinability theorem proved that arithmetic truth cannot be defined within arithmetic. Godel encoded the Liar into number theory.

Contemporary dialetheists argue the Liar sentence is both true and false — treating 矛盾 as a feature of reality.

The Ship — Deep Archive

Plutarch asked whether the preserved ship remained “the same.” John Locke proposed identity depends on continuity of consciousness.

Derek Parfit argued perhaps identity doesn't matter — what matters is psychological continuity, and that comes in degrees.

The Ship of Theseus multiplies in the digital age. Is a file copied a thousand times “the same” file?

Zeno — Deep Archive

Zeno constructed four paradoxes to defend Parmenides' claim that motion is illusion. Aristotle distinguished potential from actual infinity.

Physicists discovered space may not be infinitely divisible. The Planck length dissolves Zeno's paradox — replacing one mystery with another.

The Grandfather — Deep Archive

Barjavel's 1943 novel gave the paradox its canonical form. David Lewis proposed time travel is possible but self-consistent.

The many-worlds interpretation offers escape: killing your grandfather creates a branch, but you continue existing in yours.

The Heap — Deep Archive

“Sorites” from Greek “soros” meaning heap. Fuzzy logic, supervaluationism, and epistemicism each sacrifice different intuitions.

Legal systems must draw sharp lines through gradual phenomena. Every legal boundary is an arbitrary answer to a Sorites question.

The Stone — Deep Archive

Aquinas distinguished absolute from ordained power. Logical impossibilities aren't “things” God fails to do.

Descartes disagreed: God could violate logic itself. The paradox becomes a problem for our understanding, not for God.