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論理 · Logic · An Archive of Thought

Logic
Proof
Thought
Archive

Welcome to the scholar's study—a dense, layered archive where logical thought accumulates like books on shelves, proofs pinned to walls, and threads connecting ideas across disciplines.

Branches of
Logical Thought

Propositional Logic

The foundation of logical reasoning, examining how simple propositions combine through connectives.

Predicate Logic

Extending propositional logic with quantifiers and predicates to model complex relationships.

Modal Logic

Exploring possibility, necessity, and the logical structure of modal statements.

The Library Wall

A dense collection of logical volumes

Vol. I
Vol. II
Vol. III
Vol. IV
Vol. V
Vol. VI
Vol. VII
Vol. VIII
Vol. IX
Vol. X
Vol. XI
Vol. XII
Vol. XIII
Vol. XIV
Vol. XV
Vol. XVI

Key Theorems

Law of Non-Contradiction

A proposition cannot be both true and false in the same respect at the same time.

¬(P ∧ ¬P)

Law of Excluded Middle

Every proposition is either true or false; there is no third option.

P ∨ ¬P

Modus Ponens

If P implies Q, and P is true, then Q must be true.

((P → Q) ∧ P) → Q