· 2015
Proofs and Refutations: The Logic of Mathematical Discovery
- 1,278citations
- 2015year
Short summary
Imre Lakatos's "Proofs and Refutations" argues that mathematics grows through a dynamic process of proposing proofs, critiquing them, and improving upon them, rather than being a static collection of truths.
AI-generated from the title and abstract; the full text is not read.
Key points
- Mathematics develops via a cycle of proof attempts and critiques.
- This process accounts for the dynamic complexity of mathematical practice.
- The book uses a teacher-student dialogue format to explore solutions to problems.
- It aims to provide a philosophy of mathematics that balances static and dynamic aspects.
AI-generated from the title and abstract; the full text is not read.
Abstract
Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers
The authors' abstract, as published at the source., 2015 · DOI ↗
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Field: History and Philosophy of Science
History and Philosophy of ScienceArts and Humanities