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Bibliographic Item (1.0)
- Imre Lakatos (edited by John Worral and Elie Zahar)
- Proofs and Refutations
- Cambridge University Press 1976
- =PHILOSOPHY MATHEMATICS PROOFS SOCIAL PROCESS
- 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.
- He makes it clear that proofs are often refuted. Mathematics grows by a
process of proof, refutation, and reproof.
- The exception improves the rule more often than not.
- The author wanted to decrease the dogmatism of mathematics, and in
particular the dogma that mathematical knowledge grows by deducing truth
from known truths.
- 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.
- The end result of years of exploration is an axiomatic structure like
Euclid. But this structure is not how the field developed.
- Lakatos tabulates specific ways of tackling facts that don't fit the
theorem and its (putative) proof.
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