Search results for 'geometry' (try it on Scholar)

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  1. Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.score: 24.0
    I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why (...)
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  2. Lydia Patton (2010). Review: Hyder, The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry. [REVIEW] Notre Dame Philosophical Reviews 2010 (7).score: 24.0
    Hyder constructs two historical narratives. First, he gives an account of Helmholtz's relation to Kant, from the famous Raumproblem, which preoccupied philosophers, geometers, and scientists in the mid-19th century, to Helmholtz's arguments in his four papers on geometry from 1868 to 1878 that geometry is, in some sense, an empirical science (chapters 5 and 6). The second theme is the argument for the necessity of central forces to a determinate scientific description of physical reality, an abiding concern of (...)
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  3. Alessio Moretti (2009). The Geometry of Standard Deontic Logic. Logica Universalis 3 (1):19-57.score: 24.0
    Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...)
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  4. Giangiacomo Gerla (2007). Point-Free Geometry and Verisimilitude of Theories. Journal of Philosophical Logic 36 (6):707 - 733.score: 24.0
    A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the (...)
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  5. Richard Pettigrew (2009). Aristotle on the Subject Matter of Geometry. Phronesis 54 (3):239-260.score: 24.0
    I offer a new interpretation of Aristotle's philosophy of geometry, which he presents in greatest detail in Metaphysics M 3. On my interpretation, Aristotle holds that the points, lines, planes, and solids of geometry belong to the sensible realm, but not in a straightforward way. Rather, by considering Aristotle's second attempt to solve Zeno's Runner Paradox in Book VIII of the Physics , I explain how such objects exist in the sensibles in a special way. I conclude by (...)
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  6. Katherine Dunlop (2009). Why Euclid's Geometry Brooked No Doubt: J. H. Lambert on Certainty and the Existence of Models. Synthese 167 (1):33 - 65.score: 24.0
    J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid’s fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid’s in justification. (...)
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  7. Stephen Palmquist (2007). Emergence, Evolution, and the Geometry of Logic: Causal Leaps and the Myth of Historical Development. [REVIEW] Foundations of Science 12 (1):9-37.score: 24.0
    After sketching the historical development of “emergence” and noting several recent problems relating to “emergent properties”, this essay proposes that properties may be either “emergent” or “mergent” and either “intrinsic” or “extrinsic”. These two distinctions define four basic types of change: stagnation, permanence, flux, and evolution. To illustrate how emergence can operate in a purely logical system, the Geometry of Logic is introduced. This new method of analyzing conceptual systems involves the mapping of logical relations onto geometrical figures, following (...)
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  8. Mirja Helena Hartimo (2008). From Geometry to Phenomenology. Synthese 162 (2):225 - 233.score: 24.0
    Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the (...)
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  9. Roberto Torretti (1983/1996). Relativity and Geometry. Dover Publications.score: 24.0
    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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  10. Carlos Castro (2007). On Dark Energy, Weyl's Geometry, Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly. Foundations of Physics 37 (3):366-409.score: 24.0
    Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the (Anti) de Sitter solutions in terms of a family of radial functions R(r) that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared (UV/IR) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of ${10^{- 123} M_{\rm Planck}^4}$ is derived in agreement (...)
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  11. Graciela De Pierris (2012). Hume on Space, Geometry, and Diagrammatic Reasoning. Synthese 186 (1):169-189.score: 24.0
    Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working within (...)
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  12. Jamie Tappenden (2000). Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments? Notre Dame Journal of Formal Logic 41 (3):271-315.score: 24.0
    It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of (...)
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  13. R. G. Beil (2003). Finsler Geometry and Relativistic Field Theory. Foundations of Physics 33 (7):1107-1127.score: 24.0
    Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.
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  14. Guido Rizzi & Matteo Luca Ruggiero (2002). Space Geometry of Rotating Platforms: An Operational Approach. [REVIEW] Foundations of Physics 32 (10):1525-1556.score: 24.0
    We study the space geometry of a rotating disk both from a theoretical and operational approach; in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call “relative space:” it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the “physical space of the rotating platform.” (...)
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  15. Marco Panza (2012). The Twofold Role of Diagrams in Euclid's Plane Geometry. Synthese 186 (1):55-102.score: 24.0
    Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless (...)
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  16. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Core Knowledge of Geometry in an Amazonian Indigene Group. Science 3115759:381-384.score: 24.0
    Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our (...)
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  17. Mark Israelit (2005). On Measuring Standards in Weyl's Geometry. Foundations of Physics 35 (10):1769-1782.score: 24.0
    In Weyl’s geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of length in the interior of atoms are given, so that atoms can serve as measuring standards. The Weyl space becomes a well founded framework for classical theories of electromagnetism and gravitation.
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  18. René Jagnow (2006). Edmund Husserl on the Applicability of Formal Geometry. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. 67--85.score: 24.0
    In this paper, I reconstruct Edmund Husserl's view on the relationship between formal inquiry and the life-world, using the example of formal geometry. I first outline Husserl's account of geometry and then argue that he believed that the applicability of formal geometry to intuitive space (the space of everyday-experience) guarantees the conceptual continuity between different notions of space.
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  19. Jairo da Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.score: 24.0
    Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of (...)
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  20. Rabin Banerjee, Biswajit Chakraborty, Subir Ghosh, Pradip Mukherjee & Saurav Samanta (2009). Topics in Noncommutative Geometry Inspired Physics. Foundations of Physics 39 (12):1297-1345.score: 24.0
    In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.
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  21. Emil J. Martinec (2013). Evolving Notions of Geometry in String Theory. Foundations of Physics 43 (1):156-173.score: 24.0
    The unfolding of string theory has led to a successive refinement and generalization of our understanding of geometry and topology. A brief overview of these developments is given.
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  22. Valtteri Viljanen (2011). Spinoza's Geometry of Power. Cambridge University Press.score: 24.0
    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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  23. Tim Maudlin (2014). New Foundations for Physical Geometry: The Theory of Linear Structures. Oup Oxford.score: 24.0
    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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  24. 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: 24.0
    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 as (...)
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  25. Cristina Coppola, Giangiacomo Gerla & Annamaria Miranda (2010). Point-Free Foundation of Geometry and Multivalued Logic. Notre Dame Journal of Formal Logic 51 (3):383-405.score: 24.0
    Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
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  26. Norman Daniels (1974). Thomas Reid's Inquiry: The Geometry of Visibles and the Case for Realism. New York,B. Franklin.score: 24.0
    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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  27. Guillermo Rosado Haddock (2012). Husserl's Conception of Physical Theories and Physical Geometry in the Time of the Prolegomena : A Comparison with Duhem's and Poincaré's Views. [REVIEW] Axiomathes 22 (1):171-193.score: 24.0
    This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations , and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune (...)
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  28. Jairo José Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.score: 24.0
    Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of (...)
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  29. Dinesh Singh, Nader Mobed & Pierre-Philippe Ouimet (2010). Signatures of Noncommutative Geometry in Muon Decay for Nonsymmetric Gravity. Foundations of Physics 40 (12):1789-1799.score: 24.0
    It is shown how to identify potential signatures of noncommutative geometry within the decay spectrum of a muon in orbit near the event horizon of a microscopic Schwarzschild black hole. This possibility follows from a re-interpretation of Moffat’s nonsymmetric theory of gravity, first published in Phys. Rev. D 19:3554, 1979, where the antisymmetric part of the metric tensor manifests the hypothesized noncommutative geometric structure throughout the manifold. It is further shown that for a given sign convention, the predicted signatures (...)
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  30. Rafał Gruszczyński & Andrzej Pietruszczak (2008). Full Development of Tarski's Geometry of Solids. Bulletin of Symbolic Logic 14 (4):481-540.score: 24.0
    In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 (...)
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  31. Dejan Todorovic (2001). Is Kinematic Geometry an Internalized Regularity? Behavioral and Brain Sciences 24 (4):641-651.score: 24.0
    A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and kinematic (...)
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  32. Jesse Alama (2014). The Simplest Axiom System for Hyperbolic Geometry Revisited, Again. Studia Logica 102 (3):609-615.score: 24.0
    Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.
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  33. Cristina Coppola & Giangiacomo Gerla (2013). Special Issue on Point-Free Geometry and Topology. Logic and Logical Philosophy 22 (2):139-143.score: 24.0
    In the first section we briefly describe methodological assumptions of point-free geometry and topology. We also outline history of geometrical theories based on the notion of emph{region}. The second section is devoted to concise presentation of the content of the LLP special issue on point-free theories of space.
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  34. Rafał Gruszczyński & Andrzej Pietruszczak (2009). Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry. Logic and Logical Philosophy 18 (2):145-188.score: 24.0
    This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by (...)
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  35. Guillermo E. Rosado Haddock (2012). Husserl's Conception of Physical Theories and Physical Geometry in the Time of the Prolegomena: A Comparison with Duhem's and Poincaré's Views. Axiomathes 22 (1):171-193.score: 24.0
    This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations, and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with (...)
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  36. Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene (2011). Flexible Intuitions of Euclidean Geometry in an Amazonian Indigene Group. Pnas 23.score: 24.0
    Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto (...)
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  37. John Harding (2013). Decidability of the Equational Theory of the Continuous Geometry CG(\Bbb {F}). Journal of Philosophical Logic 42 (3):461-465.score: 24.0
    For $\Bbb {F}$ the field of real or complex numbers, let $CG(\Bbb {F})$ be the continuous geometry constructed by von Neumann as a limit of finite dimensional projective geometries over $\Bbb {F}$ . Our purpose here is to show the equational theory of $CG(\Bbb {F})$ is decidable.
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  38. D. Farnsworth (ed.) (1972). Methods of Local and Global Differential Geometry in General Relativity. New York,Springer-Verlag.score: 24.0
  39. Giangiacomo Gerla & Bonaventura Paolillo (2010). Whitehead's Pointfree Geometry and Diametric Posets. Logic and Logical Philosophy 19 (4):289-308.score: 24.0
    This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to (...)
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  40. Alessio Moretti (2010). The Critics of Paraconsistency and of Many-Valuedness and the Geometry of Oppositions. Logic and Logical Philosophy 19 (1-2):63-94.score: 24.0
    In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...)
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  41. 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: 24.0
    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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  42. David Rapport Lachterman (1989). The Ethics of Geometry: A Genealogy of Modernity. Routledge.score: 24.0
    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 figures (...)
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  43. Victor Pambuccian (2011). The Simplest Axiom System for Plane Hyperbolic Geometry Revisited. Studia Logica 97 (3):347 - 349.score: 24.0
    Using the axiom system provided by Carsten Augat in [1], it is shown that the only 6-variable statement among the axioms of the axiom system for plane hyperbolic geometry (in Tarski's language L B =), we had provided in [3], is superfluous. The resulting axiom system is the simplest possible one, in the sense that each axiom is a statement in prenex form about at most 5 points, and there is no axiom system consisting entirely of at most 4-variable (...)
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  44. Peg Rawes (2008). Space, Geometry and Aesthetics: Through Kant and Towards Deleuze. Palgrave Macmillan.score: 24.0
    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. In (...)
     
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  45. David W. Wood (2012). "Mathesis of the Mind": A Study of Fichte's Wissenschaftslehre and Geometry. Rodopi.score: 24.0
    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 synthetic and (...)
     
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  46. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Examining Knowledge of Geometry : Response to Wulf and Delson. Science 312 (5778):1309-1310.score: 22.0
    La connaissances noyau de la géométrie euclidienne est liée au raisonnement déductif et non à la reconnaissance de motifs perceptuels.
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  47. Vincenzo De Risi (2007). Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space. Birkhäuser.score: 21.0
    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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  48. Robert French (1987). The Geometry of Visual Space. Noûs 21 (June):115-133.score: 21.0
  49. Anne Newstead & Franklin James, The Epistemology of Geometry I: The Problem of Exactness. Proceedings of the Australasian Society for Cognitive Science 2009.score: 21.0
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...)
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