| Descript. |
XIII, 170 pages 1 illustrations : online resource. |
| Phys Desc |
text file PDF rda |
| Series |
Logic, Epistemology, and the Unity of Science,
2214-9775 ; 42
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Logic, Epistemology, and the Unity of Science, 2214-9775 ; 42
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| Contents |
Brouwer, Dummett and the bar theorem.-Creative subject and bar theorem.-Natural intuitionistic semantics and generalized Beth semantics.-Connection between the principle of inductive evidence and the bartheorem.-On the Brouwerian concept of negative continuity.-Classical and intuitionistic semantical groundedness.-Brouwers equivalence between virtual and inextensible order -- An intuitionistic notion of hypothetical truth for which strong completeness intuitionistically holds.-Propositions and judgements in Martin-Löf.-Negationless Intuitionism.-Temporal and atemporal truth in intuitionistic mathematics.-Arbitrary reference in mathematical reasoning.-The priority of arithmetical truth over arithmetical provability -- The impredicativity of the intuitionistic meaning of logical constants.-The intuitionistic meaning of logical constants and fallible models. |
| Summary |
This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers both new and previously published it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwers idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwers work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics. |
| Sys Details |
eBook access requires you to log in as a Federation University Australia library user |
| Notes |
Springer eBooks |
| Subject |
Philosophy.
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Logic.
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Mathematics -- Philosophy.
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Logic, Symbolic and mathematical.
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Philology.
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| Other Author |
SpringerLink (Online service)
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| ISBN |
9783319743578 |
| ISBN/ISSN |
10.1007/978-3-319-74357-8 doi |
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