Key Insights Into the Explosion Principle

In a world without contradiction, is everything consistent?

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In a world without contradiction, we could not distinguish between the consistent and the inconsistent.

The explosion principle

The principle of explosion states that from a contradiction, anything follows. In Latin: ex falso quodlibet (“from falsehood, anything is pleased”). Etymologically, quodlibet combines:

• quod (“what” or “that which”),
• libet (“it pleases” or “is agreeable”).

In medieval scholastic debates, a quodlibet was a type of open discussion where any question (quodlibetales quaestiones) could be posed and debated.

Over time, the term also entered music (e.g., a quodlibet as a composition combining multiple melodies) and philosophy, particularly in the phrase “from falsehood, anything [follows]”, another name for the principle of explosion.

In classical logic if one accepts both a statement and its negation, the system becomes trivial — meaning everything becomes provable, rendering logical distinctions meaningless. Imagine a acourt ruling “Defendant is guilty” and “Defendant is innocent.” Or a patient’s chart stating “patient has COVID-19” and “does not have COVID-19.”