Foundations of applied mathematics I

Synthese 199 (1-2):4151-4193 (2021)
  Copy   BIBTEX


This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
What is applied mathematics?James Robert Brown - 1997 - Foundations of Science 2 (1):21-37.
Logical foundations of applied mathematics.V. V. Nalimov - 1974 - Synthese 27 (1-2):211 - 250.
Reflections on mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Apriority and applied mathematics.Robert A. Holland - 1992 - Synthese 92 (3):349 - 370.
Remarks about a “General Science of Reasoning”.Michel Paty - 2004 - Vienna Circle Institute Yearbook 11:185-193.
Mathematics and the "Language Game".Alan Ross Anderson - 1958 - Review of Metaphysics 11 (3):446 - 458.
Univalent Foundations and the UniMath Library.Anthony Bordg - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag.


Added to PP

33 (#473,861)

6 months
9 (#295,075)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

The Nothing from Infinity paradox versus Plenitudinous Indeterminism.Nicholas Shackel - 2022 - European Journal for Philosophy of Science 12 (online early):1-14.
Standard Formalization.Jeffrey Ketland - 2022 - Axiomathes 32 (3):711-748.

Add more citations

References found in this work

Models in Science (2nd edition).Roman Frigg & Stephan Hartmann - 2021 - The Stanford Encyclopedia of Philosophy.
Philosophy of logic.Willard Van Orman Quine - 1970 - Cambridge, Mass.: Harvard University Press. Edited by Simon Blackburn & Keith Simmons.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.

View all 98 references / Add more references