Incomplete understanding of complex numbers Girolamo Cardano: a case study in the acquisition of mathematical concepts

Synthese 191 (17):4231-4252 (2014)
  Copy   BIBTEX

Abstract

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters

Author's Profile

Denis Buehler
Institut Jean Nicod

Analytics

Added to PP
2014-09-03

Downloads
504 (#35,366)

6 months
184 (#17,290)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?