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Foundations of Science

, Volume 23, Issue 4, pp 719–737 | Cite as

The Applicability of Mathematics as a Philosophical Problem: Mathematization as Exploration

  • Johannes Lenhard
  • Michael Otte
Article
  • 78 Downloads

Abstract

This paper discerns two types of mathematization, a foundational and an explorative one. The foundational perspective is well-established, but we argue that the explorative type is essential when approaching the problem of applicability and how it influences our conception of mathematics. The first part of the paper argues that a philosophical transformation made explorative mathematization possible. This transformation took place in early modernity when sense acquired partial independence from reference. The second part of the paper discusses a series of examples from the history of mathematics that highlight the complementary nature of the foundational and exploratory types of mathematization.

Keywords

Mathematization Applicability Exploration Semiotics 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Philosophy and Institute for Interdisciplinary ResearchBielefeld UniversityBielefeldGermany
  2. 2.Bielefeld UniversityBielefeldGermany

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