15 found
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  1. Using Invariances in Geometrical Diagrams: Della Porta, Kepler and Descartes on Refraction.Albrecht Heeffer - 2017 - In Yaakov Zik, Giora Hon & Arianna Borrelli (eds.), The Optics of Giambattista Della Porta : A Reassessment. Springer Verlag.
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  2.  45
    The emergence of symbolic algebra as a shift in predominant models.Albrecht Heeffer - 2008 - Foundations of Science 13 (2):149--161.
    Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide (...)
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  3.  16
    Historical Objections Against the Number Line.Albrecht Heeffer - 2011 - Science & Education 20 (9):863-880.
  4.  11
    The symbolic model for algebra: Functions and mechanisms.Albrecht Heeffer - 2010 - In W. Carnielli L. Magnani (ed.), Model-Based Reasoning in Science and Technology. Springer. pp. 519--532.
  5. Script and Symbolic Writing in Mathematics and Natural Philosophy.Maarten Van Dyck & Albrecht Heeffer - 2014 - Foundations of Science 19 (1):1-10.
    We introduce the question whether there are specific kinds of writing modalities and practices that facilitated the development of modern science and mathematics. We point out the importance and uniqueness of symbolic writing, which allowed early modern thinkers to formulate a new kind of questions about mathematical structure, rather than to merely exploit this structure for solving particular problems. In a very similar vein, the novel focus on abstract structural relations allowed for creative conceptual extensions in natural philosophy during the (...)
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  6.  24
    Epistemic Justification and Operational Symbolism.Albrecht Heeffer - 2014 - Foundations of Science 19 (1):89-113.
    By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280–1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of mathematical practices (...)
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  7.  13
    Philosophical aspects of symbolic reasoning in early modern mathematics.Albrecht Heeffer & Maarten Van Dyck - 2010 - London: College Publications.
    The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exist which enable us to express all knowledge? This book (...)
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  8. Bibliographie d’Henri Bosmans.Jean-François Stoffel, Albrecht Heeffer & Michel Hermans - 2010 - In Michel Hermans & Jean-François Stoffel (eds.), Le Père Henri Bosmans sj (1852-1928), historien des mathématiques : actes des Journées d’études organisées les 12 et 13 mai 2006 au Centre interuniversitaire d’études des religions et de la laïcité de l’Université libre de Bruxelles et le 15 mai 2008 aux. Académie royale de Belgique. pp. 253-298.
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  9.  58
    On the nature and origin of algebraic symbolism.Albrecht Heeffer - 2009 - In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. World Scientific. pp. 1--27.
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  10. Strikt finitistische rekenkunde zonder vrees.Albrecht Heeffer - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):188-191.
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  11.  42
    Surmounting obstacles: circulation and adoption of algebraic symbolism.Albrecht Heeffer - 2012 - Philosophica 87 (4):5-25.
    This introductory paper provides an overview of four contributions on the epistemological functions of mathematical symbolism as it emerged in Arabic and European treatises on algebra. The evolution towards symbolic algebra was a long and difficult process in which many obstacles had to be overcome. Three of these obstacles, related to the circulation and adoption of symbolism, are highlighted in this special volume: 1) the transition of material practices of algebraic calculation to discursive practices and text production, 2) the transition (...)
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  12.  12
    Beloften en teleurstellingen van artificiële intelligentie voor wetenschappelijke ontdekkingen.Albrecht Heeffer - 2021 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 113 (1):55-80.
    Promises and disappointments of artificial intelligence for scientific discovery Recent successes within Artificial Intelligence with deep learning techniques in board games gave rise to the ambition to apply these learning methods to scientific discovery. This model for discovering new scientific laws is based on data-driven generalization in large databases with observational data using neural networks. In this study we want to review and critical assess an earlier research programme by the name of BACON. Though BACON was based on different AI (...)
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  13.  46
    Regiomontanus and Chinese mathematics.Albrecht Heeffer - 2008 - Philosophica 82 (1):87-114.
    This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem (CRT) through the Shù shū Jiǔ zhāng (SSJZ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ. CRT problems appear in earlier European arithmetic and can be solved by the method (...)
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  14.  48
    Recensies-Pieter J. Van strien, psychologie Van de wetenschap: Creativiteit, serendipiteit, de persoonlijke factor en de sociale context.Albrecht Heeffer - 2012 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 104 (3):237.
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  15.  35
    Handling Inconsistencies in the Early Calculus: An Adaptive Logic for the Design of Chunk and Permeate Structures.Jesse Heyninck, Peter Verdée & Albrecht Heeffer - 2018 - Journal of Philosophical Logic 47 (3):481-511.
    The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism proposed by Brown and Priest in, 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of this application (...)
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