Sentential Logic

Bivalence

Bivalence is the principle that every (declarative, truth-apt) sentence has exactly one of two truth values: true or false.

Why assume only two values?

It’s the foundational assumption that lets classical Sentential Logic and Propositional Logic use truth tables and binary connectives without gaps.

Non-classical pushback

Some logics drop bivalence:

  • Three-valued logics add a third value (e.g., “undefined,” “neither”)
  • Fuzzy logic allows degrees of truth between 0 and 1
  • Intuitionistic logic rejects the law of excluded middle (P ∨ ¬P)

For everyday critical-thinking purposes, classical bivalence is assumed.