Hilbert David

<history of mathematics, history of philosophy, biography> german mathematician (1862-1943) whose influential lecture at Paris, "Mathematical Problems" (1900), outlined the development of classical mathematics as the application of Kant's notion of a regulative principle. Hilbert's Grundlagen der Geometrie (Foundations of Geometry) (1899), "Axiomatisches Denken" ("Axiomatic Thinking") (1917), "Die Grundlagen der Mathematik" ("Foundations of Mathematics") (1926), and Principles of Mathematical Logic (1931) proposed the axiomatic formalization of mathematics in order to demonstrate consistency by syntactical or metamathematical methods. Recommended Reading: Constance Reid, Hilbert (Copernicus, 1996) and Jeremy Gray and David Rowe, The Hilbert Problems: A Perspective on Twentieth Century Mathematics (Oxford, 2000).

[A Dictionary of Philosophical Terms and Names]

<2001-11-23>

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Nearby terms: higher-order logic « higher-order predicate logic « high-level language « Hilbert David » Hilbert's program » Hippias » historical determinism

Hilbert's program

<logic> An attempt to avoid both relativity and vicious circularity in the proof of the consistency of formal systems of arithmetic, by using only a small set of extremely intuitive operations to prove the consistency of the system containing that set. (A second phase of the program was to build all of mathematics on the system thus certified to be consistent.) Hopes of accomplishing Hilbert's program were dashed by Goedel's second incompleteness theorem.

See Goedel's theorems, relative consistency proof

[Glossary of First-Order Logic]

<2001-03-16>

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Nearby terms: higher-order predicate logic « high-level language « Hilbert David « Hilbert's program » Hippias » historical determinism » historicism