How does propositional logic differ from first-order logic?

The primary difference between propositional logic and first-order logic lies in their atomic units and expressive capabilities.

Atomic Units

• Propositional Logic: Also known as the propositional calculus, this system treats entire propositions as atomic units. It does not analyze the internal structure of these propositions, representing them simply with letters.12
• First-Order Logic: Also called the predicate calculus, this system breaks down propositions into smaller components, specifically predicates and nouns (terms). It uses these to express properties of objects and relations between them.1

Logical Mechanisms

• Connectives: Propositional logic relies on connectives (such as "and," "or," and "if...then") to form complex propositions from simpler ones. These are treated as truth-functions, where the truth-value of a complex sentence depends entirely on the truth-values of its components.1
• Quantification: First-order logic introduces existential and universal quantifiers, such as "there exists" and "for all." These allow the logic to range over individuals within a "universe of discourse," enabling the expression of complex statements involving properties, identity, and class inclusion that propositional logic cannot capture.1

While propositional logic is limited to truth-functional relationships between unanalyzed statements, first-order logic provides a more granular framework for analyzing the internal structure of language and thought.12