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Applying unrigorous mathematics: Heaviside's operational calculus.

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  • 1School of Philosophy, Religion and History of Science, University of Leeds, Leeds LS2 9JT, UK.

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Summary

This study explores the use of unrigorous mathematics in physics, proposing a new "robustly inferential conception" (RIC) to better represent these scientific practices. This approach offers a more natural way to understand how imprecise mathematical tools lead to scientific discoveries.

Keywords:
InferentialismMapping accountMathematical representationMathematical rigorOliver HeavisideOperational calculus

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Area of Science:

  • Philosophy of Science
  • History of Physics
  • Mathematical Applications

Background:

  • Unrigorous mathematical applications are common in physics but philosophically underexplored.
  • Existing philosophical accounts, like the mapping account, inadequately represent these practices.

Purpose of the Study:

  • To analyze the philosophical implications of using unrigorous mathematics in scientific representations.
  • To propose an alternative framework for understanding these applications.

Main Methods:

  • Critique of prominent philosophical accounts of mathematical representation in science.
  • Development and defense of the robustly inferential conception (RIC).
  • Case study analysis of Heaviside's operational calculus.

Main Results:

  • The mapping account fails to capture key aspects of unrigorous mathematical applications in physics.
  • The robustly inferential conception (RIC) provides a more natural and accurate representation.
  • Heaviside's work exemplifies the utility of RIC.

Conclusions:

  • A new philosophical framework (RIC) is needed to understand the role of unrigorous mathematics in scientific progress.
  • RIC better accommodates historical and contemporary practices in physics.
  • This work highlights the importance of inferential processes in mathematical scientific representation.