22 found
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  1. Analysis and Synthesis in Mathematics,.Michael Otte & Marco Panza (eds.) - 1997 - Kluwer Academic Publishers.
  2. Limits of Constructivism: Kant, Piaget and Peirce.Michael Otte - 1998 - Science & Education 7 (5):425-450.
  3.  4
    Analysis and Synthesis in Mathematics: History and Philosophy.Michael Otte & Marco Panza - 1997 - Springer Verlag.
    The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.
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  4. Analysis and Synthesis in Mathematics From the Perspective of Charles S. Peirce's Philosophy.Michael Otte - forthcoming - Boston Studies in the Philosophy of Science.
     
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  5.  14
    Introduction.Lorraine Daston & Michael Otte - 1991 - Science in Context 4 (2):223-232.
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  6. Grenzen der Mathematisierung: Von der grundlegenden Bedeutung der Anwendungen.Johannes Lenhard & Michael Otte - 2005 - Philosophia Naturalis 42 (1):15-47.
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  7. Der Charakter der Mathematik Zwischen Philosophie Und Wissenschaft.Michael Otte - 1989 - Philosophica 43:79-126.
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  8. Analysis and synthesis in mathematics, Boston studies in the philosophy of science, vol. 196.Michaël Otte & Marco Panza - 1999 - Revue Philosophique de la France Et de l'Etranger 189 (1):99-99.
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  9. Die Philosophie der Mathematik bei Charles S. Peirce im Kontext seines "evolutionären Realismus". Eine Untersuchung zum Peirceschen Kontinuitätsprinzip.Michael Otte & Michael H. G. Hoffmann - 1994 - Dialektik. Enzyklopädische Zeitschrift Für Philosophie Und Wissenschaften 1994:181–186.
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  10. Estimation of Optical Flow Based on Higher-Order Spatiotemporal Derivatives in Interlaced and Non-Interlaced Image Sequences.Michael Otte & Hans-Hellmut Nagel - 1995 - Artificial Intelligence 78 (1-2):5-43.
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  11. Gegenstand und Methode in der Geschichte der Mathematik.Michael Otte - 1992 - Philosophia Naturalis 29 (1):31-68.
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  12. Reviews: Mathematics and Logic-Analysis and Synthesis in Mathematics. History and Philosophy. [REVIEW]Michael Otte, Marco Panza & I. Grattan-Guinness - 1998 - Annals of Science 55 (4):436-437.
  13.  50
    Two Principles of Leibniz's Philosophy in Relation to the History of Mathematics.Michael Otte - 1993 - Theoria 8 (1):113-125.
  14.  19
    The Applicability of Mathematics as a Philosophical Problem: Mathematization as Exploration.Johannes Lenhard & Michael Otte - 2018 - Foundations of Science 23 (4):719-737.
    This paper discerns two types of mathematization, a foundational and an explorative one. The foundational perspective is well-established, but we argue that the explorative type is essential when approaching the problem of applicability and how it influences our conception of mathematics. The first part of the paper argues that a philosophical transformation made explorative mathematization possible. This transformation took place in early modernity when sense acquired partial independence from reference. The second part of the paper discusses a series of examples (...)
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  15.  17
    Space, Complementarity, and “Diagrammatic Reasoning”.Michael Otte - 2011 - Semiotica 2011 (186):275-296.
    In the development of pure mathematics during the nineteenth and twentieth centuries, two very different movements had prevailed. The so-called rigor movement of arithmetization, which turned into set theoretical foundationalism, on the one hand, and the axiomatic movement, which originated in Poncelet's or Peirce's emphasis on the continuity principle, on the other hand. Axiomatical mathematics or mathematics as diagrammatic reasoning represents a genetic perspective aiming at generalization, whereas mathematics as arithmetic or set theory is mainly concerned with foundation and separation. (...)
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  16. Kontinuitätsprinzip und Prinzip der Identität des Ununterscheidbaren.Michael Otte - 1993 - Studia Leibnitiana 25 (1):70-89.
    The dynamics of the historical growth of mathematics as well as natural science is reflected by the interaction of the continuity principle and the principle of the identity of indiscernibles. Aristotle, for example on the one side is responsible for introducing the continuity principle into natural history. On the other hand he is regarded as the great representative of a logic which rests upon the assumption of the possibility of clear divisions and rigorous classification. In modern times the Aristotelian antithesis (...)
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  17. Mathematical Creativity and the Character of Mathematical Objects.Michael Otte - 1999 - Logique Et Analyse 42 (167-168):387-410.
     
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  18. Mathematik und Verallgemeinerung: Peirce'semiotisch-pragmatische Sicht.Michael Otte - 1997 - Philosophia Naturalis 34 (2):175-222.
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  19.  39
    Proof-Analysis and Continuity.Michael Otte - 2004 - Foundations of Science 11 (1-2):121-155.
    During the first phase of Greek mathematics a proof consisted in showing or making visible the truth of a statement. This was the epagogic method. This first phase was followed by an apagogic or deductive phase. During this phase visual evidence was rejected and Greek mathematics became a deductive system. Now epagoge and apagoge, apart from being distinguished, roughly according to the modern distinction between inductive and deductive procedures, were also identified on account of the conception of generality as continuity. (...)
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  20.  10
    Constructivism and Objects of Mathematical Theory.Michael Otte - 1992 - In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations. De Gruyter. pp. 296--313.
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  21.  26
    Style as a Historical Category.Michael Otte - 1991 - Science in Context 4 (2):233-264.
    The ArgumentIn writing the history of science, the fluctuations between two meanings of the concept of style are of special interest: a simple or direct meaning of this concept referring to a means of expression and of presentation, and a philosophical interpretation of this term referring to “a world of objective spiritual order.” The last two chapters of this paper consider the perspective of the simple meaning of the concept, the first two chapters take the philosophical meaning as their starting (...)
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  22.  23
    Analyse und Synthese oder von Leibniz und Kant zum axiomatischen Denken.Johannes Lenhard & Michael Otte - 2002 - Philosophia Naturalis 39 (2):259-292.
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