Results for 'Finsler geometry'

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  1.  55
    Finsler Geometry and Relativistic Field Theory.R. G. Beil - 2003 - 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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  2. De la vie après la mort, Paul Finsler, mathématiques et métaphysique.Paul Finsler, Emmanuel Angebault & Daniel Parrochia - 2001 - Revue Philosophique de la France Et de l'Etranger 191 (4):530-531.
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  3.  27
    Gravitational Field Equations Based on Finsler Geometry.G. S. Asanov - 1983 - Foundations of Physics 13 (5):501-527.
    The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = K lj lj of the Finslerian curvature tensorK l j hk (x, y). The relevant Lagrangian is constructed by the replacement of the directional variabley i inK by a vector fieldy i (x), (...)
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  4. Born’s Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant.Carlos Castro - 2012 - Foundations of Physics 42 (8):1031-1055.
    The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of (...)
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  5.  22
    On Superluminal Particles and the Extended Relativity Theories.Carlos Castro - 2012 - Foundations of Physics 42 (9):1135-1152.
    Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because (...)
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  6.  34
    The Construction of Teleparallel Finsler Connections and the Emergence of an Alternative Concept of Metric Compatibility.José G. Vargas & Douglas G. Torr - 1997 - Foundations of Physics 27 (6):825-843.
    The issue of whether teleparallel nonlinear connections exist is resolved by their explicit construction on Finslerian metrics that arise in the Robertson test theory of special relativity (RTTSR), and on the Minkowski metric in particular. The method is an adaptation to the Finsler bundle of a similar construction for teleparallel linear connections. It suggests the existence of a concept of metric compatibility alternative toω μλ +ω λμ = 0 for teleparallel nonlinear connections. A sophisticated system of partial differential equations (...)
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  7. Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets.John L. Bell - unknown
    I describe two approaches to modelling the universe, the one having its origin in topos theory and differential geometry, the other in set theory. The first is synthetic differential geometry. Traditionally, there have been two methods of deriving the theorems of geometry: the analytic and the synthetic. While the analytical method is based on the introduction of numerical coordinates, and so on the theory of real numbers, the idea behind the synthetic approach is to furnish the subject (...)
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  8. Core Knowledge of Geometry in an Amazonian Indigene Group.Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke - 2006 - 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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  9. Kant on Geometry and Spatial Intuition.Michael Friedman - 2012 - 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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  10. Hume on Space, Geometry, and Diagrammatic Reasoning.Graciela De Pierris - 2012 - 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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  11.  48
    Spinoza's Geometry of Power.Valtteri Viljanen - 2011 - 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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  12.  80
    New Foundations for Physical Geometry: The Theory of Linear Structures.Tim Maudlin - 2014 - Oxford University Press.
    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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  13.  37
    The Dynamical Approach as Practical Geometry.Syman Stevens - 2015 - 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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  14.  33
    A Philosopher Looks at Non-Commutative Geometry.Nick Huggett - manuscript
    This paper introduces some basic ideas and formalism of physics in non-commutative geometry. My goals are three-fold: first to introduce the basic formal and conceptual ideas of non-commutative geometry, and second to raise and address some philosophical questions about it. Third, more generally to illuminate the point that deriving spacetime from a more fundamental theory requires discovering new modes of `physically salient' derivation.
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  15. The Twofold Role of Diagrams in Euclid’s Plane Geometry.Marco Panza - 2012 - 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.  77
    Relativity and Geometry.Roberto Torretti - 1983 - 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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  17. Flexible Intuitions of Euclidean Geometry in an Amazonian Indigene Group.Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene - 2011 - 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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  18.  93
    The Geometry of Standard Deontic Logic.Alessio Moretti - 2009 - 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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  19. Carnap’s Conventionalism in Geometry.Stefan Lukits - 2013 - Grazer Philosophische Studien 88 (1):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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  20. The Ethics of Geometry: A Genealogy of Modernity.David Rapport Lachterman - 1989 - 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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  21. What Frege Meant When He Said: Kant is Right About Geometry.Teri Merrick - 2006 - Philosophia Mathematica 14 (1):44-75.
    This paper argues that Frege's notoriously long commitment to Kant's thesis that Euclidean geometry is synthetic _a priori_ is best explained by realizing that Frege uses ‘intuition’ in two senses. Frege sometimes adopts the usage presented in Hermann Helmholtz's sign theory of perception. However, when using ‘intuition’ to denote the source of geometric knowledge, he is appealing to Hermann Cohen's use of Kantian terminology. We will see that Cohen reinterpreted Kantian notions, stripping them of any psychological connotation. Cohen's defense (...)
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  22. Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry.Rafał Gruszczyński & Andrzej Pietruszczak - 2009 - 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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  23. Geometry as a Universal Mental Construction.Véronique Izard, Pierre Pica, Danièle Hinchey, Stanislas Dehane & Elizabeth Spelke - 2011 - In Stanislas Dehaene & Elizabeth Brannon (eds.), Space, Time and Number in the Brain. Oxford University Press.
    Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The (...)
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  24.  47
    Bridging the Gap Between Analytic and Synthetic Geometry: Hilbert’s Axiomatic Approach.Eduardo N. Giovannini - 2016 - 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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  25.  39
    Empirical Conditions for a Reidean Geometry of Visual Experience.Hannes Ole Matthiessen - 2016 - Topoi 35 (2):511-522.
    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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  26. Deleuze, Leibniz and Projective Geometry in the Fold.Simon Duffy - 2010 - Angelaki 15 (2):129-147.
    Explications of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in 'The Fold: Leibniz and the Baroque' focus predominantly on the role of the infinitesimal calculus developed by Leibniz.1 While not underestimat- ing the importance of the infinitesimal calculus and the law of continuity as reflected in the calculus of infinite series to any understanding of Leibniz’s metaphysics and to Deleuze’s reconstruction of it in The Fold, what I propose to examine in this paper is the role played by other (...)
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  27.  39
    Thomas Reid’s Inquiry: The Geometry of Visibles and the Case for Realism.Norman DANIELS - 1974 - 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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  28. Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?Jamie Tappenden - 2000 - 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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  29.  60
    Natural Geometry in Descartes and Kepler.Gary Hatfield - 2015 - 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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  30. Whitehead's Pointfree Geometry and Diametric Posets.Giangiacomo Gerla & Bonaventura Paolillo - 2010 - 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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  31. ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY.John Corcoran - 2014 - 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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  32. Emergence, Evolution, and the Geometry of Logic: Causal Leaps and the Myth of Historical Development. [REVIEW]Stephen Palmquist - 2007 - 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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  33.  8
    The Conventionality of Simultaneity in Einstein’s Practical Chrono-Geometry.Mario Bacelar Valente - 2017 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 32 (2):177-190.
    While Einstein considered that sub specie astern the correct philosophical position regarding geometry was that of the conventionality of geometry, he felt that provisionally it was necessary to adopt a non-conventional stance that he called practical geometry. here we will make the case that even when adopting Einstein’s views we must conclude that practical geometry is conventional after all. Einstein missed the fact that the conventionality of simultaneity leads to a conventional element in the chrono-geometry, (...)
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  34. Natural Philosophy, Deduction, and Geometry in the Hobbes-Boyle Debate.Marcus P. Adams - 2017 - Hobbes Studies 30 (1):83-107.
    This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding of (...)
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  35. Aristotle on the Subject Matter of Geometry.Richard Pettigrew - 2009 - 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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  36. Kant's Views on Non-Euclidean Geometry.Michael E. Cuffaro - 2012 - 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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  37.  41
    Conventionalism In Reid’s ‘Geometry Of Visibles’.Edward Slowik - 2003 - 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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  38. Point-Free Geometry and Verisimilitude of Theories.Giangiacomo Gerla - 2007 - 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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  39.  14
    The Complexity of Plane Hyperbolic Incidence Geometry Is∀∃∀∃.Victor Pambuccian - 2005 - 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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  40.  55
    Space Geometry of Rotating Platforms: An Operational Approach. [REVIEW]Guido Rizzi & Matteo Luca Ruggiero - 2002 - 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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  41.  70
    From Inexactness to Certainty: The Change in Hume's Conception of Geometry.Vadim Batitsky - 1998 - 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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  42.  15
    Explaining the Geometry of Desert.Neil Feit & Stephen Kershnar - 2004 - Public Affairs Quarterly 18 (4):273-298.
    In the past decade, three philosophers in particular have recently explored the relation between desert and intrinsic value. Fred Feldman argues that consequentialism need not give much weight – or indeed any weight at all – to the happiness of persons who undeservedly experience pleasure. He defends the claim that the intrinsic value of a state of affairs is determined by the “fit” between the amount of well-being that a person receives and the amount of well-being that the person deserves. (...)
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  43.  38
    Full Development of Tarski's Geometry of Solids.Rafał Gruszczyński & Andrzej Pietruszczak - 2008 - 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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  44.  17
    The Simplest Axiom System for Hyperbolic Geometry Revisited, Again.Jesse Alama - 2014 - Studia Logica 102 (3):609-615.
    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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  45.  52
    Husserl on Geometry and Spatial Representation.Jairo José da Silva - 2012 - 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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  46. On Dark Energy, Weyl’s Geometry, Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly.Carlos Castro - 2007 - 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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  47.  63
    David Hyder. The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry. Viii + 229 Pp., Bibl., Index. Berlin/New York: Walter de Gruyter, 2009. $105. [REVIEW]Gary Hatfield - 2012 - Isis 103 (4):769-770.
    David Hyder.The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry. viii + 229 pp., bibl., index. Berlin/New York: Walter de Gruyter, 2009.
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  48.  23
    Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories.Sergiu I. Vacaru - 2013 - Foundations of Physics 43 (6):719-732.
    Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally (...)
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  49.  43
    Topics in Noncommutative Geometry Inspired Physics.Rabin Banerjee, Biswajit Chakraborty, Subir Ghosh, Pradip Mukherjee & Saurav Samanta - 2009 - 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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  50.  27
    Forms of the Pasch Axiom in Ordered Geometry.Victor Pambuccian - 2010 - 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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