TY - JOUR

T1 - Dirac and the dispensability of mathematics

AU - Bueno, Otávio

N1 - Funding Information:
My thanks go to Jody Azzouni, Mark Colyvan, Steven French, Alirio Rosales, Harvey Siegel, and Bas van Fraassen for helpful discussions. In particular, Mark Colyvan and Jody Azzouni provided extensive and insightful comments on earlier versions of this paper, for which I am extremely grateful. Their comments led to substantial improvements. Finally, I would like to acknowledge the comments of two anonymous referees, which also led to several changes in the final version of this paper. The material is based upon work supported by a grant from the National Science Foundation, NSF 01-157, NIRT. All opinions expressed here are mine and do not necessarily reflect those of the National Science Foundation.

PY - 2005/9

Y1 - 2005/9

N2 - In this paper, I examine the role of the delta function in Dirac's formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The indispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its dispensability. I first discuss the significance of the delta function in Dirac's work, and explore the strategy that he devised to overcome its use. I then argue that even if mathematical theories turned out to be indispensable, this wouldn't justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac's discovery of antimatter, there's no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac's work.

AB - In this paper, I examine the role of the delta function in Dirac's formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The indispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its dispensability. I first discuss the significance of the delta function in Dirac's work, and explore the strategy that he devised to overcome its use. I then argue that even if mathematical theories turned out to be indispensable, this wouldn't justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac's discovery of antimatter, there's no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac's work.

KW - Antimatter

KW - Application of mathematics

KW - Delta function

KW - Dirac

KW - Indispensability argument

KW - Quantum mechanics

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U2 - 10.1016/j.shpsb.2005.03.002

DO - 10.1016/j.shpsb.2005.03.002

M3 - Article

AN - SCOPUS:23844493141

VL - 36

SP - 465

EP - 490

JO - Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

JF - Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

SN - 1355-2198

IS - 3

ER -