<*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]

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<*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]

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