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Jack Douglas

Axioms and Illusions: The Limits of Knowledge and Proof

Axioms and Illusions: The Limits of Knowledge and Proof

Introduction The worlds of mathematics, science and philosophy all share a central pursuit: knowledge. In mathematics, a statement must be proved in order to be accepted as an undeniable fact. However, a fundamental reality of mathematics is that there will always exist truths which cannot be proven. This raises the
17 Oct 2026 8 min read
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