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

Authors
Denis Buehler
Institut Jean Nicod
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
Keywords Mental content  Anti-Individualism  Conceptual Role Theory  Concepts  History of mathematics
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11229-014-0527-x
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,408
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Origins of Objectivity.Tyler Burge - 2010 - Oxford University Press.
Naming and Necessity.Saul Kripke - 1980 - In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge. pp. 431-433.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

View all 32 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Tecendo uma teia: aquisição de conceitos e papel inferencial.John Sarnecki - 2012 - Veritas – Revista de Filosofia da Pucrs 57 (3):138-162.
From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
Concepts and Conceptual Change.Paul R. Thagard - 1990 - Synthese 82 (2):255-74.
Phenomenal Concepts, Color Experience, and Mary's Puzzle.Diana I. Pérez - 2011 - Teorema: International Journal of Philosophy (3):113-133.
Animal Minds and the Possession of Concepts.Albert Newen & Andreas Bartels - 2007 - Philosophical Psychology 20 (3):283 – 308.
Introduction.Neil Tennant - 2008 - Philosophia Mathematica 16 (1):1-3.
The Emperor’s New Concepts.Neil Tennant - 2002 - Noûs 36 (s16):345-377.
Causes as Probability Raisers of Processes.Jonathan Schaffer - 2001 - Journal of Philosophy 98 (2):75-92.

Analytics

Added to PP index
2014-09-03

Total views
115 ( #87,337 of 2,420,815 )

Recent downloads (6 months)
2 ( #351,362 of 2,420,815 )

How can I increase my downloads?

Downloads

My notes