Foundations of applied mathematics I

Synthese 199 (1-2):4151-4193 (2021)
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Abstract

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.

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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.

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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.

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