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

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  1.  48
    Graciela De Pierris (2012). Hume on Space, Geometry, and Diagrammatic Reasoning. Synthese 186 (1):169-189.
    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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  2. Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
    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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  3. Giangiacomo Gerla & Bonaventura Paolillo (2010). Whitehead's Pointfree Geometry and Diametric Posets. Logic and Logical Philosophy 19 (4):289-308.
    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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  4. Rafał Gruszczyński & Andrzej Pietruszczak (2009). Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry. Logic and Logical Philosophy 18 (2):145-188.
    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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  5.  95
    John Corcoran (2014). ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY. Bulletin of Symbolic Logic 20 (1):131-2.
    John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the (...)
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  6. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Core Knowledge of Geometry in an Amazonian Indigene Group. Science 311 (5759)::381-4.
    Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.
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  7.  24
    Valtteri Viljanen (2011). Spinoza's Geometry of Power. Cambridge University Press.
    This work examines the unique way in which Benedict de Spinoza 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 offer (...)
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  8.  75
    Stefan Lukits (2014). Carnap's Conventionalism in Geometry. Grazer Philosophische Studien 88:123-138.
    Against Thomas Mormann's argument that differential topology does not support Carnap's conventionalism in geometry we show their compatibility. However, Mormann's emphasis on the entanglement that characterizes topology and its associated metrics is not misplaced. It poses questions about limits of empirical inquiry. For Carnap, to pose a question is to give a statement with the task of deciding its truth. Mormann's point forces us to introduce more clarity to what it means to specify the task that decides between competing (...)
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  9.  49
    Roberto Torretti (1983). Relativity and Geometry. Dover Publications.
    This high-level study discusses Newtonian principles and 19th-century views on electrodynamics and the aether. Additional topics include Einstein's electrodynamics of moving bodies, Minkowski spacetime, gravitational geometry, time and causality, and other subjects. Highlights include a rich exposition of the elements of the special and general theories of relativity.
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  10.  50
    Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Core Knowledge of Geometry in an Amazonian Indigene Group. Science 3115759:381-384.
    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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  11.  64
    Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene (2011). Flexible Intuitions of Euclidean Geometry in an Amazonian Indigene Group. Pnas 23.
    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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  12.  22
    Gary Hatfield (2015). Natural Geometry in Descartes and Kepler. Res Philosophica 92 (1):117-148.
    According to Kepler and Descartes, the geometry of the triangle formed by the two eyes when focused on a single point affords perception of the distance to that point. Kepler characterized the processes involved as associative learning. Descartes described the processes as a “ natural geometry.” Many interpreters have Descartes holding that perceivers calculate the distance to the focal point using angle-side-angle, calculations that are reduced to unnoticed mental habits in adult vision. This article offers a purely psychophysiological (...)
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  13.  92
    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.
    Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the de Sitter solutions in terms of a family of radial functions R that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared 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 with the (...)
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  14. 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.
    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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  15.  77
    Marco Panza (2012). The Twofold Role of Diagrams in Euclid's Plane Geometry. Synthese 186 (1):55-102.
    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.  21
    Norman Daniels (1974). Thomas Reid's Inquiry: The Geometry of Visibles and the Case for Realism. New York,B. Franklin.
    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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  17.  75
    Alessio Moretti (2009). The Geometry of Standard Deontic Logic. Logica Universalis 3 (1):19-57.
    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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  18.  5
    Victor Pambuccian (2005). The Complexity of Plane Hyperbolic Incidence Geometry Is∀∃∀∃. Mathematical Logic Quarterly 51 (3):277-281.
    We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.
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  19.  61
    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.
    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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  20.  87
    Richard Pettigrew (2009). Aristotle on the Subject Matter of Geometry. Phronesis 54 (3):239-260.
    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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  21. David Rapport Lachterman (1989). The Ethics of Geometry: A Genealogy of Modernity. Routledge.
    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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  22.  89
    Lydia Patton (2010). Review: Hyder, The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry. [REVIEW] Notre Dame Philosophical Reviews 2010 (7).
    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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  23.  38
    Guido Rizzi & Matteo Luca Ruggiero (2002). Space Geometry of Rotating Platforms: An Operational Approach. [REVIEW] Foundations of Physics 32 (10):1525-1556.
    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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  24.  17
    Hannes Ole Matthiessen (forthcoming). Empirical Conditions for a Reidean Geometry of Visual Experience. Topoi.
    Thomas Reid's Geometry of Visibles, according to which the geometrical properties of an object's perspectival appearance equal the geometrical properties of its projection on the inside of a sphere with the eye in its centre allows for two different interpretations. It may (1) be understood as a theory about phenomenal visual space – i.e. an account of how things appear to human observers from a certain point of view – or it may (2) be seen as a mathematical model (...)
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  25.  43
    R. G. Beil (2003). Finsler Geometry and Relativistic Field Theory. Foundations of Physics 33 (7):1107-1127.
    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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  26.  24
    Michael E. Cuffaro (2012). Kant's Views on Non-Euclidean Geometry. Proceedings of the Canadian Society for History and Philosophy of Mathematics 25:42-54.
    Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have 'intuitive content' in (...)
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  27.  20
    E. Slowik (2003). Conventionalism in Reid's 'Geometry of Visibles'. Studies in History and Philosophy of Science Part A 34 (3):467-489.
    The subject of this investigation is the role of conventions in the formulation of Thomas Reid's theory of the geometry of vision, which he calls the 'geometry of visibles'. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid's 'geometry of visibles' and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a (...)
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  28. Giangiacomo Gerla (2007). Point-Free Geometry and Verisimilitude of Theories. Journal of Philosophical Logic 36 (6):707 - 733.
    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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  29.  32
    Mark Israelit (2005). On Measuring Standards in Weyl's Geometry. Foundations of Physics 35 (10):1769-1782.
    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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  30.  5
    Syman Stevens (2015). The Dynamical Approach as Practical Geometry. Philosophy of Science 82 (5):1152-1162.
    This article introduces Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity, and argues that it may be construed as a relationalist form of Einstein’s ‘practical geometry’. This construal of the dynamical approach is shown to be compatible with related chapters of Brown’s text and also with recent descriptions of the dynamical approach by Pooley and others.
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  31.  4
    Victor Pambuccian (2010). Forms of the Pasch Axiom in Ordered Geometry. Mathematical Logic Quarterly 56 (1):29-34.
    We prove that, in the framework of ordered geometry, the inner form of the Pasch axiom does not imply its outer form . We also show that OP can be properly split into IP and the weak Pasch axiom.
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  32.  10
    Eduardo N. Giovannini (2016). Bridging the Gap Between Analytic and Synthetic Geometry: Hilbert’s Axiomatic Approach. Synthese 193 (1):31-70.
    The paper outlines an interpretation of one of the most important and original contributions of David Hilbert’s monograph Foundations of Geometry , namely his internal arithmetization of geometry. It is claimed that Hilbert’s profound interest in the problem of the introduction of numbers into geometry responded to certain epistemological aims and methodological concerns that were fundamental to his early axiomatic investigations into the foundations of elementary geometry. In particular, it is shown that a central concern that (...)
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  33.  26
    Vadim Batitsky (1998). From Inexactness to Certainty: The Change in Hume's Conception of Geometry. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 29 (1):1-20.
    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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  34.  5
    Victor Pambuccian (2001). Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry. Mathematical Logic Quarterly 47 (1):129-136.
    In this paper we provide quantifier-free, constructive axiomatizations for 2-dimensional absolute, Euclidean, and hyperbolic geometry. The main novelty consists in the first-order languages in which the axiom systems are formulated.
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  35.  24
    Emil J. Martinec (2013). Evolving Notions of Geometry in String Theory. Foundations of Physics 43 (1):156-173.
    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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  36.  8
    Victor Pambuccian (1992). Ternary Operations as Primitive Notions for Plane Geometry II. Mathematical Logic Quarterly 38 (1):345-348.
    We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.
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  37.  46
    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.
    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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  38.  59
    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.
    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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  39.  21
    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.
    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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  40.  21
    Rabin Banerjee, Biswajit Chakraborty, Subir Ghosh, Pradip Mukherjee & Saurav Samanta (2009). Topics in Noncommutative Geometry Inspired Physics. Foundations of Physics 39 (12):1297-1345.
    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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  41.  34
    Jairo da Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
    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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  42.  51
    Mirja Helena Hartimo (2008). From Geometry to Phenomenology. Synthese 162 (2):225 - 233.
    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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  43.  9
    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.
    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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  44.  15
    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.
    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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  45.  33
    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.
    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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  46.  11
    Rafael Grimson, Bart Kuijpers & Walied Othman (2012). Quantifier Elimination for Elementary Geometry and Elementary Affine Geometry. Mathematical Logic Quarterly 58 (6):399-416.
    We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry , based on extending equation image and equation image, respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.
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  47.  5
    Hoshang Heydari (2015). Geometry and Structure of Quantum Phase Space. Foundations of Physics 45 (7):851-857.
    The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry. The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, and a compatible (...)
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  48.  28
    Rafał Gruszczyński & Andrzej Pietruszczak (2008). Full Development of Tarski's Geometry of Solids. Bulletin of Symbolic Logic 14 (4):481-540.
    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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  49.  23
    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.
    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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  50.  21
    Jairo José Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
    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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