History, methodology and early algebra

Abstract The limits of ?criterial rationality? (that is, rationality as rule?following) have been extensively explored in the philosophy of science by Kuhn and others. In this paper I attempt to extend this line of enquiry into mathematics by means of a pair of case studies in early algebra. The first case is the Ars Magna (Nuremburg 1545) by Jerome Cardan (1501?1576), in which a then recently?discovered formula for finding the roots of some cubic equations is extended to cover all cubics and proved. The second is the formulation by Albert Girard (1595?1632) of an early version of the fundamental theorem of algebra in his L'invention nouvelle en l'algèbre (Amsterdam, 1629). I conclude that in these cases at least, the questions raised in the philosophy of science debate can also be asked of the history of mathematics, and that a modest methodological anarchism is the appropriate stance
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/02698599408573488
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,520
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
The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - University of Chicago Press.
Knowledge and Social Imagery.David Bloor - 1991 - University of Chicago Press.
Rationality.Harold I. Brown - 1988 - Routledge.

View all 7 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
A New Symbolic Representation for the Algebra of Sets.Jerome Frazee - 1990 - History and Philosophy of Logic 11 (1):67-75.
Medieval Arabic Algebra as an Artificial Language.Jeffrey A. Oaks - 2007 - Journal of Indian Philosophy 35 (5-6):543-575.
On Łukasiewicz-Moisil Algebras of Fuzzy Sets.Sergiu Rudeanu - 1993 - Studia Logica 52 (1):95 - 111.
An Infinitary Extension of Jankov's Theorem.Yoshihito Tanaka - 2007 - Studia Logica 86 (1):111 - 131.
Augustus De Morgan's Boolean Algebra.Daniel D. Merrill - 2005 - History and Philosophy of Logic 26 (2):75-91.
Added to PP index

Total downloads
7 ( #531,630 of 2,180,839 )

Recent downloads (6 months)
1 ( #299,822 of 2,180,839 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums