- Etymology
- Compound of formal + system. A system characterized by explicit axioms and rules.
- Formal
- Explicit, symbolic, rule-governed.
- System
- A set of interrelated elements. From Greek σύστημα (sustēma).
- Origin
- Hilbert, Gödel. Foundational work in metamathematics.
- Meaning
- A system of axioms and inference rules. Axioms are the starting points; rules derive theorems.
- Earliest use
- Hilbert program, early 20th century.
- Definition
- A system of axioms and inference rules. Axioms are the starting points; rules derive theorems. Examples: propositional logic, predicate logic, ZFC.