The Excluded Middle
Between true and false there is no third option — every statement falls on one side.
The law of excluded middle holds that for any proposition, either it or its negation is true — there is no middle ground. Aristotle (4th c. BCE) first stated it explicitly in Metaphysics Book IV, alongside non-contradiction, and it became one of the bedrock laws of classical logic. Its universality was later challenged by intuitionist mathematicians in the 20th century, who reject it for statements not yet proved or disproved.
How it traveled
- ParmenidesAthens · -370explains
- MetaphysicsChalcis · -322explains
- De interpretationeChalcis · -322explains
- De FatoFormiae · -43explains
- Adversus MathematicosAlexandria · 190explains
- Pyrrhoniae HypotyposesAlexandria · 210explains
- Sefer HaIkkarimSoria · 1425
- Likutei HalakhotBreslov (Ukraine) · 1840
- Fragmenta Logica et PhysicaAthensexplains
- In Aristotelis Analyticorum Priorum Librum I CommentariumAthensexplains
Key passages(20)
Fragmenta Logica et Physica · Chrysippus
In Aristotelis Analyticorum Priorum Librum I Commentarium · Alexander of Aphrodisias
Fragmenta Logica et Physica · Chrysippus
Fragmenta Logica et Physica · Chrysippus
In Aristotelis Metaphysicorum Libros A-Z Commentaria · Asclepius
De Xenophane, de Zenone, de Gorgia · Pseudo-Aristotle