David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
International Studies in the Philosophy of Science 8 (2):113 – 124 (1994)
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)|
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
Thomas S. Kuhn (1996/2012). The Structure of Scientific Revolutions. University of Chicago Press.
Bernard Arthur Owen Williams (1985). Ethics and the Limits of Philosophy. Harvard University Press.
David Bloor (1991). Knowledge and Social Imagery. University of Chicago Press.
Harold I. Brown (1988). Rationality. Routledge.
Citations of this work BETA
No citations found.
Similar books and articles
Jerome Frazee (1990). A New Symbolic Representation for the Algebra of Sets. History and Philosophy of Logic 11 (1):67-75.
Jeffrey A. Oaks (2007). Medieval Arabic Algebra as an Artificial Language. Journal of Indian Philosophy 35 (5-6):543-575.
Sergiu Rudeanu (1993). On Łukasiewicz-Moisil Algebras of Fuzzy Sets. Studia Logica 52 (1):95 - 111.
T. S. Blyth & J. Fang (2011). On Endomorphisms of Ockham Algebras with Pseudocomplementation. Studia Logica 98 (1-2):237-250.
David J. Foulis (2006). The Universal Group of a Heyting Effect Algebra. Studia Logica 84 (3):407 - 424.
Yoshihito Tanaka (2007). An Infinitary Extension of Jankov's Theorem. Studia Logica 86 (1):111 - 131.
Ladislav Kvasz (2006). The History of Algebra and the Development of the Form of its Language. Philosophia Mathematica 14 (3):287-317.
Daniel D. Merrill (2005). Augustus De Morgan's Boolean Algebra. History and Philosophy of Logic 26 (2):75-91.
D. Macbeth (2012). Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice. Philosophia Mathematica 20 (1):58-85.
Albrecht Heeffer (2008). The Emergence of Symbolic Algebra as a Shift in Predominant Models. Foundations of Science 13 (2):149--161.
Added to index2009-01-28
Total downloads6 ( #439,916 of 1,790,117 )
Recent downloads (6 months)1 ( #426,071 of 1,790,117 )
How can I increase my downloads?