European Journal for Philosophy of Science

, Volume 8, Issue 3, pp 735–759 | Cite as

Explanation and abstraction from a backward-error analytic perspective

  • Nicolas FillionEmail author
  • Robert H. C. Moir
Original paper in Philosophy of Science


We argue that two powerful error-theoretic concepts (backward error and conditioning) provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of (possibly idealized) neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems.


Rational reconstruction Error theory Explanation Idealization Abstraction 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophySimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceWestern UniversityLondonCanada

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