The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.
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Book Description
Editorial Reviews
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'The two volumes edited by M.Detlefsen without doubt constitute an important and valuable reference for research on the very intricate network of concepts, theories and theses connected with the concept of proof.' - Erkenntnis
About the Author
Michael Detlefsen is Professor of Philosophy at the University of Notre Dame, where he also serves as editor of the Notre Dame Journal of Formal Logic.
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Inside This Book
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First Sentence:
The question, "Which is the right logic?" Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
epistemic biography, finitary general propositions, finitary generalizations, arithmetical justification, primitive recursive formulas, generalized inductive definitions, sentences formulable, arithmetized syntax, intuitive logical thinking, posteriori grounded, virtual reasons, finitary propositions, finitary reasoning, priori grounded, ideal mathematics, abstract proofs, syntactic reading, step from premises, infinite induction, finitary mathematics, derivability conditions, possible warrants, locative element, semantic reflection, undischarged assumptions Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Oxford University Press, Cambridge University Press, Journal of Symbolic Logic, Harvard University Press, Gödel Second Incompleteness Theorem, First Incompleteness Theorem, Journal of Philosophical Logic, Selected Readings, Hilbert's Foundations of Geometry, Hilbert's Thesis, Isaac Levi, Kurt Gödel Collected Works, Mathematische Annalen, Charles Parsons, Die Grundlegung, Gödel's Second Incompleteness Theorem, Gottlob Frege, Journal of Philosophy, Second Theorem, Weak Conservation, Alfred Tarski, Basil Blackwell, Cornell University Press, Fundamenta Mathematicae New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
The question, "Which is the right logic?" Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
epistemic biography, finitary general propositions, finitary generalizations, arithmetical justification, primitive recursive formulas, generalized inductive definitions, sentences formulable, arithmetized syntax, intuitive logical thinking, posteriori grounded, virtual reasons, finitary propositions, finitary reasoning, priori grounded, ideal mathematics, abstract proofs, syntactic reading, step from premises, infinite induction, finitary mathematics, derivability conditions, possible warrants, locative element, semantic reflection, undischarged assumptions Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Oxford University Press, Cambridge University Press, Journal of Symbolic Logic, Harvard University Press, Gödel Second Incompleteness Theorem, First Incompleteness Theorem, Journal of Philosophical Logic, Selected Readings, Hilbert's Foundations of Geometry, Hilbert's Thesis, Isaac Levi, Kurt Gödel Collected Works, Mathematische Annalen, Charles Parsons, Die Grundlegung, Gödel's Second Incompleteness Theorem, Gottlob Frege, Journal of Philosophy, Second Theorem, Weak Conservation, Alfred Tarski, Basil Blackwell, Cornell University Press, Fundamenta Mathematicae New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 48
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9
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- Foundations of Geometry by David Hilbert on 7 pages
- Handbook of Mathematical Logic (Studies in Logic and the Foundations of Mathematics) by J. Barwise on 5 pages
- Provability, Computability and Reflection, Volume 90 (Studies in Logic and the Foundations of Mathematics) by Lev D. Beklemishev on 5 pages
- Collected Works, Vol. 3: Unpublished Essays and Lectures by Kurt Godel on 4 pages
- Philosophy of Mathematics: Selected Readings by Paul Benacerraf on page 23, page 75, and page 135
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- Philosophy of Science, Logic and Mathematics in the 20th Century: Routledge History of Philosophy Volume 9 by Stuart G. Shanker in Front Matter, and page 118
- Naturalism in Mathematics by Penelope Maddy in Back Matter
- The Search for Certainty: A Philosophical Account of Foundations of Mathematics by Marcus Giaquinto in Back Matter
- Set Theory and Its Philosophy: A Critical Introduction by Michael Potter in Back Matter
- The Problem of the Unity of Science: Proceedings of the Annual Meeting of the International Academy of the Philosophy of Science, Copenhagen-Aarhus, Denmark, 31 May-3 June 2000 by Jan Faye on page 63
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