論理
the beauty of rational thought
Every argument begins with a statement -- a proposition that asserts something about the world. In the theater of reason, the proposition is the opening line, the first frame of the film.
A proposition is either true or false. There is no in-between, no maybe. This is the law of the excluded middle -- the binary heartbeat of logic.
Both must be true. The conjunction -- two truths swimming in formation.
At least one is true. The disjunction -- divergent paths in the current.
The opposite holds. Negation -- the fish turns against the stream.
Truth flows forward. The implication -- where one fish leads, others follow.
Watch logical formations swim in harmony
All fish that swim in formation are logical.
These tropical fish swim in formation.
Therefore, these tropical fish are logical.
The syllogism is the crown jewel of deductive reasoning -- a structure so elegant it has survived twenty-three centuries of scrutiny. From two premises, truth cascades inevitably to its conclusion.
A truth table maps every possible combination of truth values to their outcome. It is the complete story -- every scene accounted for, every ending known.
| P | Q | P ∧ Q | P ∨ Q | P → Q |
|---|---|---|---|---|
| T | T | T | T | T |
| T | F | F | T | F |
| F | T | F | T | T |
| F | F | F | F | T |