Ten Misconceptions from the History of Analysis and Their Debunking

@article{Blaszczyk2013TenMF,
  title={Ten Misconceptions from the History of Analysis and Their Debunking},
  author={P. Blaszczyk and M. Katz and D. Sherry},
  journal={Foundations of Science},
  year={2013},
  volume={18},
  pages={43-74}
}
  • P. Blaszczyk, M. Katz, D. Sherry
  • Published 2013
  • Philosophy, Mathematics
  • Foundations of Science
  • The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from… CONTINUE READING
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    References

    SHOWING 1-10 OF 169 REFERENCES
    Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus
    • 59
    • PDF
    A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography
    • 32
    • PDF
    Zooming in on infinitesimal 1–.9.. in a post-triumvirate era
    • 27
    • PDF
    Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond
    • 54
    • PDF
    A History of Analysis
    • 62
    God, king, and geometry: revisiting the introduction to Cauchys Cours danalyse
    • 6
    • PDF
    THE TENSION BETWEEN INTUITIVE INFINITESIMALS AND FORMAL MATHEMATICAL ANALYSIS
    • 10
    • PDF
    How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining
    • 8
    The Concepts of the Calculus
    • 28