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History and Philosophy of Logic
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Module 4
Formal Systems and Their Philosophical Limits
1
Frege-Hilbert: Axioms, Truth & Definitions
Analyse the Frege-Hilbert controversy on the nature of axioms as truths versus implicit definitions.
2
Hilbert's Programme: Philosophical Goals
Assess the philosophical goals of Hilbert's programme for the foundations of mathematics.
3
Gödel's Incompleteness and Hilbert's Programme
Analyse the philosophical significance of Gödel's first incompleteness theorem for Hilbert's programme.
4
Gödel's Incompleteness: Truth Beyond Proof
Evaluate the claim that the first incompleteness theorem shows that mathematical truth outruns formal proof.
5
Gödel's Second Incompleteness Theorem and Foundationalism
Assess the philosophical impact of the second incompleteness theorem on foundationalist programmes in mathematics.
6
Gödel, Minds, and Mechanism: A Critical Look at Lucas-Penrose
Critically evaluate the Lucas-Penrose argument that Gödel's theorems refute mechanism about the mind.
Previous module
The Crisis of Logicism and Its Aftermath
Next module
The Nature of Logical Consequence