Formalism (mathematics)

The formalism is a school direction founded by David Hilbert in the philosophy of mathematics with regard to the fundamentals of mathematics .

The central question is how a mathematical consequence or implication is to be understood. The concern was that only in shape completeness and consistency of the axioms to prove mathematics.

In the 1920s, formalism (Göttingen mathematicians) was opposed to intuitionism ( Brouwer and Berlin mathematicians) and logicism ( Gottlob Frege and Bertrand Russell ) in the fundamental dispute in mathematics .

When Gödel's incompleteness theorem showed that there is no system of axioms that satisfies the formalistic task ( Hilbert program ), the formalism suffered a severe defeat. On the other hand, one can say that today almost all mathematicians are formalistic axiomats.

See also

• Formalized theory
• axiom
• Metamathematics
• Proof theory
• Model theory
• Metalogic

literature

• David Hilbert / Paul Bernays : Fundamentals of Mathematics , I-II, Berlin / Heidelberg / New York 1968/1970
• Rosemarie Rheinwald: The formalism and its limits. Investigations on the modern philosophy of mathematics , Hain, Königstein / Ts. 1984

Web links

• Formalism in the Philosophy of Mathematics in the Stanford Encyclopedia of Philosophy (English; including references.)