Crosilla, L (2018) Predicativity and Feferman. In: Jӓger, G and Sieg, W, (eds.) Feferman on Foundations: Logic, Mathematics, Philosophy. Outstanding Contributions to Logic, 13 . Springer , Cham, Switzerland , pp. 423-447. ISBN 978-3-319-63332-9
Abstract
Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clari fication of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predicativity have since taken a life of their own, but have also produced a deeper understanding of the notion of predicativity, therefore witnessing the "light logic throws on problems in the foundations of mathematics." (Feferman 1998, p. vii) Predicativity has been at the center of a considerable part of Feferman's work: over the years he has explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics. The aim of this note is to outline the principal features of predicativity, from its original motivations at the start of the past century to its logical analysis in the 1950-60's. The hope is to convey why predicativity is a fascinating subject, which has attracted Feferman's attention over the years.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © Springer International Publishing AG, part of Springer Nature 2017. This is an author produced version of a chapter published in "Feferman on Foundations: Logic, Mathematics, Philosophy". Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Impredicative definitions; Predicativity given the natural numbers; Vicious circle principle; Invariance; Γ0 |
Dates: |
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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: | 07 Feb 2017 12:10 |
Last Modified: | 30 Mar 2020 00:38 |
Status: | Published |
Publisher: | Springer |
Series Name: | Outstanding Contributions to Logic |
Identification Number: | 10.1007/978-3-319-63334-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111839 |