Kurt Gödel

1906-1978 · Austrian-American · Mathematical logic, philosophy of mathematics, metalogic, philosophy of language

Mathematics is reality.

When Kurt Gödel presented his incompleteness theorems at a Vienna conference in 1930, he demolished the grandest ambition of modern mathematics: Hilbert's program to ground all mathematics in a complete, consistent formal system. Gödel proved that any such system must contain true statements it cannot prove — and cannot prove its own consistency. One of the most stunning results in intellectual history, from a logician who entered the Vienna Circle as a student and left as its silent refutation.

Topics Kurt Gödel addresses

• the incompleteness theorems
• the second incompleteness theorem
• truth versus provability
• the completeness theorem for first-order logic
• ω-consistency
• mathematical platonism
• conceptual realism and the perception of concepts
• the constructible universe L
• the axiom of choice
• the continuum hypothesis
• the generalized continuum hypothesis
• Cohen's forcing and independence results
• new axioms for set theory
• the disjunction thesis
• minds and machines
• absolutely unsolvable Diophantine problems
• Hilbert's program
• formalism in mathematics
• against logical positivism
• the Carnap critique
• Husserlian phenomenology and mathematical intuition
• rationalistic optimism
• the Leibnizian program
• the modal ontological argument

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