Make It So: Imperatival Foundations for Mathematics

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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.

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Author Profiles

Chris Scambler
New York University
Neil Barton
University of Oslo
Ethan Russo
New York University

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References found in this work

Philosophy and Model Theory.Tim Button & Sean P. Walsh - 2018 - Oxford, UK: Oxford University Press. Edited by Sean Walsh & Wilfrid Hodges.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.

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