Search results for 'Geometry Philosophy' (try it on Scholar)

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  1. Vincenzo De Risi (2007). Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space. Birkhäuser.score: 132.0
    This book reconstructs, both from the historical and theoretical points of view, Leibniz's geometrical studies, focusing in particular on the research Leibniz ...
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  2. Jeremy Heis (2011). Ernst Cassirer's Neo-Kantian Philosophy of Geometry. British Journal for the History of Philosophy 19 (4):759 - 794.score: 102.0
    One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but (...)
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  3. Frank J. Leavitt (1991). Kant's Schematism and His Philosophy of Geometry. Studies in History and Philosophy of Science Part A 22 (4):647-659.score: 102.0
    Kant's philosophy of geometry rests upon his doctrine of the "schematism" which I argue is formally identical to the ability to grass the middle term of an Aristotelian syllogism. The doctrine fails to avoid obscurities which were already present in Plato, Aristotle, and Hume.
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  4. A. Richardson (2003). The Geometry of Knowledge: Lewis, Becker, Carnap and the Formalization of Philosophy in the 1920s. Studies in History and Philosophy of Science Part A 34 (1):165-182.score: 102.0
    On an ordinary view of the relation of philosophy of science to science, science serves only as a topic for philosophical reflection, reflection that proceeds by its own methods and according to its own standards. This ordinary view suggests a way of writing a global history of philosophy of science that finds substantially the same philosophical projects being pursued across widely divergent scientific eras. While not denying that this view is of some use regarding certain themes of and (...)
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  5. David Rapport Lachterman (1989). The Ethics of Geometry: A Genealogy of Modernity. Routledge.score: 102.0
    The Ethics of Geometry is a study of the relationship between philosophy and mathematics. Essential differences in the ethos of mathematics, for example, the customary ways of undertaking and understanding mathematical procedures and their objects, provide insight into the fundamental issues in the quarrel of moderns with ancients. Two signal features of the modern ethos are the priority of problem-solving over theorem-proving, and the claim that constructability by human minds or instruments establishes the existence of relevant entities. These (...)
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  6. Peg Rawes (2008). Space, Geometry and Aesthetics: Through Kant and Towards Deleuze. Palgrave Macmillan.score: 102.0
    Peg Rawes examines a "minor tradition" of aesthetic geometries in ontological philosophy. Developed through Kant’s aesthetic subject she explores a trajectory of geometric thinking and geometric figurations--reflective subjects, folds, passages, plenums, envelopes and horizons--in ancient Greek, post-Cartesian and twentieth-century Continental philosophies, through which productive understandings of space and embodies subjectivities are constructed. Six chapters, explore the construction of these aesthetic geometric methods and figures in a series of "geometric" texts by Kant, Plato, Proclus, Spinoza, Leibniz, Bergson, Husserl and Deleuze. (...)
     
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  7. David W. Wood (2012). "Mathesis of the Mind": A Study of Fichte's Wissenschaftslehre and Geometry. Rodopi.score: 102.0
    This is the first major study in any language on J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a (...)
     
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  8. L. Kvasz (2011). Kant's Philosophy of Geometry--On the Road to a Final Assessment. Philosophia Mathematica 19 (2):139-166.score: 96.0
    The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable (...)
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  9. Joongol Kim (2006). Concepts and Intuitions in Kant's Philosophy of Geometry. Kant-Studien 97 (2):138-162.score: 96.0
    This paper is an exposition and defense of Kant’s philosophy of geometry. The main thesis is that Euclidean geometry investigates the properties of geometrical objects in an inner space that is given to us a priori (pure space) and hence is a priori and synthetic. This thesis is supported by arguing that Euclidean geometry requires certain intuitive objects (Sect. 1), that these objects are a priori constructions in pure space (Sect. 2), and finally that the role (...)
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  10. Jamie Tappenden (1995). Geometry and Generality in Frege's Philosophy of Arithmetic. Synthese 102 (3):319 - 361.score: 96.0
    This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and (...) and the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)
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  11. Vadim Batitsky (1998). From Inexactness to Certainty: The Change in Hume's Conception of Geometry. [REVIEW] Journal for General Philosophy of Science 29 (1):1-20.score: 96.0
    Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry (...)
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  12. Valtteri Viljanen (2011). Spinoza's Geometry of Power. Cambridge University Press.score: 90.0
    This work examines the unique way in which Benedict de Spinoza (1632-77) combines two significant philosophical principles: that real existence requires causal power and that geometrical objects display exceptionally clearly how things have properties in virtue of their essences. Valtteri Viljanen argues that underlying Spinoza's psychology and ethics is a compelling metaphysical theory according to which each and every genuine thing is an entity of power endowed with an internal structure akin to that of geometrical objects. This allows Spinoza to (...)
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  13. Roberto Torretti (1983/1996). Relativity and Geometry. Dover Publications.score: 84.0
    High-level study discusses Newtonian principles and 19th-century views on electrodynamics and the aether, covers Einstein’s electrodynamics of moving bodies, Minkowski geometry and other topics. A rich exposition of the elements of the Special and General Theory of Relativity.
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  14. Carsten Klein (2001). Conventionalism and Realism in Hans Reichenbach's Philosophy of Geometry. International Studies in the Philosophy of Science 15 (3):243 – 251.score: 84.0
    Hans Reichenbach's so-called geometrical conventionalism is often taken as an example of a positivistic philosophy of science, based on a verificationist theory of meaning. By contrast, we shall argue that this view rests on a misinterpretation of Reichenbach's major work in this area, the Philosophy of Space and Time (1928). The conception of equivalent descriptions, which lies at the heart of Reichenbach's conventionalism, should be seen as an attempt to refute Poincaré's geometrical relativism. Based upon an examination of (...)
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  15. Mary Domski (2003). The Constructible and the Intelligible in Newton's Philosophy of Geometry. Philosophy of Science 70 (5):1114-1124.score: 84.0
    In the preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice.” Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton's unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in (...)
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  16. Tim Maudlin (2014). New Foundations for Physical Geometry: The Theory of Linear Structures. Oup Oxford.score: 84.0
    Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
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  17. Diego L. Rapoport (2011). Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-Reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics. [REVIEW] Foundations of Physics 41 (1):33-76.score: 84.0
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...)
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  18. Thierry Paquot & Christiane Younès (eds.) (2005). Géométrie, Mesure du Monde: Philosophie, Architecture, Urbain. La Découverte.score: 84.0
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  19. Francesca Biagioli (2013). Between Kantianism and Empiricism: Otto Hölder's Philosophy of Geometry. Philosophia Scientiæ 17 (17-1):71-92.score: 80.0
    La philosophie de la géométrie de Hölder, si l’on s’en tient à une lecture superficielle, est la part la plus problématique de son épistémologie. Il soutient que la géométrie est fondée sur l’expérience à la manière de Helmholtz, malgré les objections sérieuses de Poincaré. Néanmoins, je pense que la position de Hölder mérite d’être discutée pour deux motifs. Premièrement, ses implications méthodologiques furent importantes pour le développement de son épistémologie. Deuxièmement, Poincaré utilise l’opposition entre le kantisme et l’empirisme comme un (...)
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  20. E. G. Zahar (1997). Poincarés Philosophy of Geometry, or Does Geometric Conventionalism Deserve its Name? Studies in History and Philosophy of Science Part B 28 (2):183-218.score: 78.0
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  21. Alexander Bird (1996). Squaring the Circle: Hobbes on Philosophy and Geometry. Journal of the History of Ideas 57 (2):217–31.score: 78.0
    Hobbes' geometrical disputes are significant since they highlight several important strands in his thought - issues concerning the right to make definitions, his anti-clericalism, the maker's knowledge argument and his objections to algebra. These are examined, and the foundational position, according to Hobbes, of geomentry in relation to philosophy, science and technology, explained and discussed.
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  22. Ted Humphrey (1973). The Historical and Conceptual Relations Between Kant's Metaphysics of Space and Philosophy of Geometry. Journal of the History of Philosophy 11 (4):483-512.score: 78.0
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  23. R. Torretti (2003). Philosophy and Geometry: Theoretical and Historical Issues - Lorenzo Magnani, Kluwer Academic Publishers, Dordrecht, 2001, Pp. XIX + 249, US $88. ISBN 0-792-36933-. [REVIEW] Studies in History and Philosophy of Science Part B 34 (1):158-160.score: 78.0
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  24. Alberto Coffa (1983). Geometry and Semantics: An Examination of Putnam's Philosophy of Geometry. In. In R. Cohen & L. Laudan (eds.), Physics, Philosophy, and Psychoanalysis. D. Reidel. 1--30.score: 78.0
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  25. L. Magnani (2001). Philosophy and Geometry. Kluwer Academic Publisher.score: 78.0
    The total irrelevance of absolute space to scientific observation and experiment led him early to a most radical conclusion: experience cannot teach us anything about the true structure of space; consequently, the choice of a geometry for the ...
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  26. Marcin Wolski (2004). Notes on the Geometry of Logic and Philosophy. Logic and Logical Philosophy 10:223.score: 78.0
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  27. Peter Baofu (2009). The Future of Post-Human Geometry: A Preface to a New Theory of Infinity, Symmetry, and Dimensionality. Cambridge Scholars.score: 78.0
     
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  28. Veit Pittioni (1989). Geometry and Philosophy. Philosophy and History 22 (2):132-133.score: 78.0
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  29. Daniel Sutherland (2010). Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant. In Michael Friedman, Mary Domski & Michael Dickson (eds.), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science. Open Court.score: 78.0
  30. Douglas Jesseph (1990). Berkeley's Philosophy of Geometry. Archiv für Geschichte der Philosophie 72 (3):301-332.score: 74.0
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  31. M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.score: 72.0
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in (...)
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  32. D. Garber (2010). Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space, by Vincenzo De Risi. Mind 119 (474):472-478.score: 72.0
    (No abstract is available for this citation).
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  33. Diego L. Rapoport (2009). Surmounting the Cartesian Cut with Philosophy, Physics, Cybernetics and Geometry; Self.Reference, Torsion, the Klein Bottle, Multivalued Logics and Quantum Mechanics. foundations of physics 39 (09).score: 72.0
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology -after Merleau-Ponty, Heidegger and Rosen- and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...)
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  34. Norman Daniels (1974). Thomas Reid's Inquiry: The Geometry of Visibles and the Case for Realism. New York,B. Franklin.score: 72.0
    Chapter I: The Geometry of Visibles 1 . The N on- Euclidean Geometry of Visibles In the chapter "The Geometry of Visibles" in Inquiry into the Human Mind, ...
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  35. Stephen Palmquist (2000). The Tree of Philosophy. Philopsychy Press.score: 72.0
    Based on the author's Introduction to Philosophy lectures in Hong Kong, this book has been translated into Chinese and Indonesian and has sold over 10,000 copies. Unlike a typical textbook, the author punctuates his objective descriptions of the classical philosophical theories in metaphysics, logic, applied philosophy and ontology, with highly personal examples of how philosophical reflection can stimulate insights. Like a typical textbook, every chapter ends with a list of questions for further thought and a list of recommended (...)
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  36. Roger B. Angel (1982). Philosophy of Geometry From Riemann to Poincaré Roberto Torretti Dordrecht and Boston: D. Reidel Publishing Company, 1978. Pp. Xiii, 459. $50.00 U.S. [REVIEW] Dialogue 21 (02):384-391.score: 72.0
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  37. I. Toth & J. Kaplansky (1998). "As Philolaos the Pythagorean Said": Philosophy, Geometry, Freedom. Diogenes 46 (182):43-71.score: 72.0
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  38. Martin Carrier, Geometric Facts and Geometric Theory : Helmholtz and 20th-Century Philosophy of Physical Geometry.score: 72.0
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  39. Richard J. Hall (1965). A Philosophy of Geometry. Philosophia Mathematica (1):13-31.score: 72.0
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  40. Stavros Kiriakakis (2003). Lorenzo Magnani, Philosophy and Geometry, Theoretical and Historical Issues. Philosophical Inquiry 25 (3-4):262-266.score: 72.0
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  41. S. L. (1982). Philosophy of Geometry From Riemann to Poincaré. Review of Metaphysics 35 (3):633-634.score: 72.0
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  42. William Sacksteder (1992). Three Diverse Sciences in Hobbes: First Philosophy, Geometry, and Physics. Review of Metaphysics 45 (4):739 - 772.score: 72.0
  43. S. Albert Kivinen (1984). Stenius on the Philosophy of Geometry. Theoria 50 (2-3):212-240.score: 72.0
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  44. Steven J. Bartlett (1981). Philosophy of Geometry From Riemann to Poincare. By Roberto Torretti. The Modern Schoolman 58 (2):136-136.score: 72.0
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  45. Pierre Cassou Nogues (1999). Recherches de Husserl Pour Une Philosophie de la Géométrie/Husserl's Research on the Philosophy of Geometry. Revue d'Histoire des Sciences 52 (2):179-206.score: 72.0
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  46. Nicholas Griffin & Roberto Torretti (1981). Philosophy of Geometry From Riemann to Poincare. Philosophical Quarterly 31 (125):374.score: 72.0
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  47. Ulrich Majer (2006). The Relation of Logic and Intuition in Kant's Philosophy of Science, Particularly Geometry. In. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. 47--66.score: 72.0
  48. Alessio Moretti (2012). Why the Logical Hexagon? Logica Universalis 6 (1-2):69-107.score: 72.0
    The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the “logical square” (or “square of opposition”), of which it is a much more general and powerful “relative”. The discovery of the former did not raise interest, (...)
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  49. Dana Ashkenazi & Zvi Lotker (2014). The Quasicrystals Discovery as a Resonance of the Non-Euclidean Geometry Revolution: Historical and Philosophical Perspective. Philosophia 42 (1):25-40.score: 72.0
    In this paper, we review the history of quasicrystals from their sensational discovery in 1982, initially “forbidden” by the rules of classical crystallography, to 2011 when Dan Shechtman was awarded the Nobel Prize in Chemistry. We then discuss the discovery of quasicrystals in philosophical terms of anomalies behavior that led to a paradigm shift as offered by philosopher and historian of science Thomas Kuhn in ‘The Structure of Scientific Revolutions’. This discovery, which found expression in the redefinition of the concept (...)
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