論理
Every system of thought begins with what cannot be proven — only accepted. The axiom is the seed from which all reasoning grows, irreducible and self-evident.
∀x (P(x) → Q(x))
Every system of thought begins with what cannot be proven — only accepted. The axiom is the seed from which all reasoning grows, irreducible and self-evident.
∀x (P(x) → Q(x))
The premise is the bridge between the given and the sought. Each statement follows necessarily from what came before — no leaps, no intuitions unexamined, only the patient unfolding of consequence.
In the architecture of reason, every floor rests upon the one below. Remove a single support and the structure reveals its dependency — not as weakness, but as honesty.
P → Q, P ⊢ Q
Derivation is the heartbeat of logic — the mechanical process by which truth propagates through a system. Each step is small, almost trivial in isolation, yet their accumulation builds cathedrals of certainty from grains of obvious fact.
Watch the wisteria cascade: each blossom hangs from the one above, a visual chain of modus ponens applications descending toward their inevitable conclusion.
((P → Q) ∧ (Q → R)) → (P → R)
What was to be demonstrated has been demonstrated. The proof is complete — not because we chose to stop, but because the argument arrived at its natural terminus. The conclusion was always there, waiting in the premises like a sculpture waiting in marble.
The nandina bears its fruit: small, precise, inevitable. Each berry a theorem proven, each branch a path of valid inference that led us here.
∴ Q.E.D. — quod erat demonstrandum