- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Make It So: Imperatival Foundations for Mathematics
Abstract
This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.Author Profiles
Other Versions
No versions found
My notes
Similar books and articles
Representations and the Foundations of Mathematics.Sam Sanders - 2022 - Notre Dame Journal of Formal Logic 63 (1):1-28.
Logical Foundations of Set Theory and Mathematics.Mary Tiles - 2002 - In Dale Jacquette (ed.), A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 365–376.
Metaphysics and the Foundations of Mathematics.Vasilii Ya Perminov - 2012 - Russian Studies in Philosophy 50 (4):24-42.
Toward a History of Mathematics Focused on Procedures.Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze & David Sherry - 2017 - Foundations of Science 22 (4):763-783.
Set Theory and Structures.Neil Barton & Sy-David Friedman - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 223-253.
Set Theory and Structures.Sy-David Friedman & Neil Barton - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 223-253.
Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
Proof Theory.Jeremy Avigad - 2012 - In Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy. Cham: Springer. pp. 177-190.
Remarks on the Foundations of Mathematics. [REVIEW]T. W. - 1957 - Review of Metaphysics 10 (4):726-726.
Analytics
Added to PP
2023-09-12
Downloads
384 (#62,969)
6 months
123 (#49,604)
2023-09-12
Downloads
384 (#62,969)
6 months
123 (#49,604)
Historical graph of downloads
Author Profiles
References found in this work
Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford, England: Oxford University Press.
Philosophy and Model Theory.Tim Button & Sean P. Walsh - 2018 - Oxford, UK: Oxford University Press. Edited by Sean Walsh & Wilfrid Hodges.
From Kant to Hilbert: a source book in the foundations of mathematics.William Ewald (ed.) - 1996 - New York: Oxford University Press.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-6b65f85844-fbfkv uwo