A statement is either true or false.
The law of the excluded middle — P ∨ ¬P — is the foundational axiom of classical logic. There is no third state. A proposition holds, or its negation holds. From this single grain, an entire architecture of reasoning rises: predicates, quantifiers, proofs, theorems.
On logic.day, we honour the moment a thought becomes precise enough to be wrong. Imprecision cannot be falsified. Logic begins where ambiguity ends.
- ◯Truth is preserved by valid inference.
- △Negation divides the universe in two.
- □Axioms are the floor we stand on.
Every valid argument has a shape.
Validity is not about content; it is about form. The same skeleton holds whether the subject is a syllogism about Socrates or a proof about prime numbers. To learn logic is to learn to see the scaffold beneath the sentence.
1. ∀x ( Human(x) → Mortal(x) ) premise 2. Human(socrates) premise 3. Human(socrates) → Mortal(socrates) ∀-elim, 1 4. Mortal(socrates) →-elim, 2,3
Any argument with this shape preserves truth. Swap the predicates, swap the names — the validity is untouched. That portability is the quiet superpower of formal logic.
Clear thought is a public good worth celebrating.
If a statement can be true or false (1), and a valid argument preserves truth (2), then the discipline of building valid arguments deserves a day of its own. Not as austere ritual, but as a quiet, joyful act — the same joy a mathematician feels when a proof closes, or a juror feels when the evidence finally fits.
logic.day is for that feeling. For students drawing truth tables. For lawyers spotting equivocations. For engineers tracing causes. For anyone who has ever changed their mind because the argument deserved it.
∴ Reason in public. Reason in private. Reason kindly.
A small truth table, for the day.
Hover a row to see the operation highlighted.
| P | Q | P ∧ Q | P ∨ Q | P → Q | P ↔ Q |
|---|---|---|---|---|---|
| T | T | T | T | T | T |
| T | F | F | T | F | F |
| F | T | F | T | T | F |
| F | F | F | F | T | T |
Quod erat demonstrandum.