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formal system

formal system

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.

Citations

  • Hilbert, D. (1922). Neubegründung der Mathematik. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1, 157–177.

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