What is Lakatos's 'proofs and refutations'?
My concept of 'proofs and refutations' describes the dynamic nature of mathematical discovery. I argued that proofs are not merely demonstrations of self-evident truths, but rather attempts to articulate and defend conjectures. These proofs, however, often contain hidden assumptions or ambiguities that lead to counterexamples. The subsequent process of refutation and proof-revision is what drives mathematical progress. Instead of discrete, final proofs, we have a continuous, often messy, dialectic of conjecture, proof, and attempted refutation, leading to progressively refined understanding.
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