Crosilla, L (2015) Error and Predicativity. In: Beckmann, A, Mitrana, V and Soskova, M, (eds.) Evolving Computability. Lecture Notes in Computer Science. CiE 2015: 11th Conference on Computability in Europe, 29 Jun - 03 Jul 2015, Bucharest, Romania. Springer , pp. 13-22. ISBN 978-3-319-20027-9
Abstract
The article surveys ideas emerging within the predicative tradition in the foundations of mathematics, and attempts a reading of predicativity constraints as highlighting different levels of understanding in mathematics. A connection is made with two kinds of error which appear in mathematics: local and foundational errors. The suggestion is that ideas originating in the predicativity debate as a reply to foundational errors are now having profound influence to the way we try to address the issue of local errors. Here fundamental new interactions between computer science and mathematics emerge.
Metadata
Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | © 2015, Springer International Publishing Switzerland. This is a post-peer-review, pre-copyedit version of an article published in Evolving Computability (Lecture Notes in Computer Science). The final authenticated version is available online at: https:// doi.org/10.1007/978-3-319-20028-6_2. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Type Theory; Peano Arithmetic; Inductive Definition; Actual Infinity; Order Arithmetic |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Philosophy, Religion and History of Science (Leeds) > School of Philosophy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Aug 2018 14:39 |
Last Modified: | 16 Aug 2018 14:46 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/978-3-319-20028-6_2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:110424 |