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Lakatos76

  1. Imre Lakatos (edited by John Worral and Elie Zahar)
  2. Proofs and Refutations
  3. Cambridge University Press 1976
  4. =PHILOSOPHY MATHEMATICS PROOFS SOCIAL PROCESS
  5. Describes an advanced seminar in mathematics where the students duplicate the key points in the history of a particularly elegant theorem in the theory of polyhedra.
  6. He makes it clear that proofs are often refuted. Mathematics grows by a process of proof, refutation, and reproof.
  7. The exception improves the rule more often than not.
  8. The author wanted to decrease the dogmatism of mathematics, and in particular the dogma that mathematical knowledge grows by deducing truth from known truths.
  9. He shows that actual mathematics develops in an illogical fashion because it grows by discovering the underlying assumptions as well as by working from these to prove conclusions.
  10. The end result of years of exploration is an axiomatic structure like Euclid. But this structure is not how the field developed.
  11. Lakatos tabulates specific ways of tackling facts that don't fit the theorem and its (putative) proof.
  12. See [DeMilloLiptonPerlis79]

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