Results for 'non Euclidean geometry'

997 found
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  1. Kant's Views on Non-Euclidean Geometry.Michael 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 (...) have 'intuitive content' in order to show that both Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (shrink)
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  2. Spatial Perception and Geometry in Kant and Helmholtz.Gary Hatfield - 1984 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:569 - 587.
    This paper examines Helmholtz's attempt to use empirical psychology to refute certain of Kant's epistemological positions. Particularly, Helmholtz believed that his work in the psychology of visual perception showed Kant's doctrine of the a priori character of spatial intuition to be in error. Some of Helmholtz's arguments are effective, but this effectiveness derives from his arguments to show the possibility of obtaining evidence that the structure of physical space is non-Euclidean, and these arguments do not depend on his theory (...)
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  3. Conventionalism in Reid’s ‘Geometry of Visibles’.Edward Slowik - 2003 - Studies in the History and Philosophy of Science 34:467-489.
    The role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the “geometry of visibles”, is the subject of this investigation. 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 (...)
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  4. 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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  5. Euclidean Geometry is a Priori.Boris Culina - manuscript
    In the article, an argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modelling, not the world, but our activities in the world.
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  6. 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 (...) map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)
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  7. 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 (...)
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  8.  29
    On the Relationship Between Geometric Objects and Figures in Euclidean Geometry.Mario Bacelar Valente - 2021 - In Diagrammatic Representation and Inference. 12th International Conference, Diagrams 2021. pp. 71-78.
    In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric (...)
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  9. Achievements and Fallacies in Hume's Account of Infinite Divisibility.James Franklin - 1994 - Hume Studies 20 (1):85-101.
    Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. (...)
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  10. An Elementary System of Axioms for Euclidean Geometry Based on Symmetry Principles.Boris Čulina - 2018 - Axiomathes 28 (2):155-180.
    In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides (...)
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  11.  77
    Urbis Et Orbis: Non-Euclidean Space of History.Alex V. Halapsis - 2015 - The European Philosophical and Historical Discourse 1 (2):37-42.
    Social space is superimposed on the civilization map of the world whereas the social time is correlated with the duration of civilization existence. Within own civilization the concept space is non-homogeneous, there are “singled out points” — “concept factories”. As social structures, cities may exist rather long, sometimes during several millennia, but as concept centres they are limited by the duration of civilization existence. If civilization is a “concept universe”, nobody and nothing may cross the boundaries, which include cities as (...)
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  12. REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are (...)
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  13. The Euclidean Mousetrap: Schopenhauer’s Criticism of the Synthetic Method in Geometry.Jason M. Costanzo - 2008 - Idealistic Studies 38 (3):209-220.
    In his doctoral dissertation On the Principle of Sufficient Reason, Arthur Schopenhauer there outlines a critique of Euclidean geometry on the basis of the changing nature of mathematics, and hence of demonstration, as a result of Kantian idealism. According to Schopenhauer, Euclid treats geometry synthetically, proceeding from the simple to the complex, from the known to the unknown, “synthesizing” later proofs on the basis of earlier ones. Such a method, although proving the case logically, nevertheless fails to (...)
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  14. A New Definition of A Priori Knowledge: In Search of a Modal Basis.Tuomas E. Tahko - 2008 - Metaphysica 9 (2):57-68.
    In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a (...)
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  15.  38
    The Philosophy of Perception : An Explanation of Realism, Idealism and the Nature of Reality.Rochelle Forrester - unknown
    This paper investigates the nature of reality by looking at the philosophical debate between realism and idealism and at scientific investigations in quantum physics and at recent studies of animal senses, neurology and cognitive psychology. The concept of perceptual relativity is examined and this involves looking at sense perception in other animals and various examples of perceptual relativity in science. It will be concluded that the universe is observer dependent and that there is no reality independent of the observer, which (...)
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  16.  90
    Themersonowie i Witkacy, czyli nieeuklidesowa przygoda smoka Żabrołaka (The Themersons and Witkacy or non-euclidean adventure of the Gaberbocchus).Marek Sredniawa - 2016 - Sztuka Edycji 9 (1):57-68.
    Stanisław Ignacy Witkiewicz and Franciszka and Stefan Themerson constitute a rare constellation of outstanding artists of the 20th century avant-garde. Their best known contributions were a concept of Pure Form and an idea of Semantic Poetry respectively. They all shared multiplicity and diversity of interests and areas of not only artistic activities. Philosophy and science influenced to large extent form and content of their works. Despite their mutual interest in each other’s work they had never met personally and no correspondence (...)
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  17.  70
    The C-Aplpha Non Exclusion Principle and the Vastly Different Internal Electron and Muon Center of Charge Vacuum Fluctuation Geometry.Jim Wilson - forthcoming - Physics Essays.
    The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...)
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  18. 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 (...)
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  19. 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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  20. On Explanations From Geometry of Motion.Juha Saatsi - 2018 - British Journal for the Philosophy of Science 69 (1):253–273.
    This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from "geometry of motion" with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.
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  21.  71
    Spinoza's Geometry of Power.Valtteri Viljanen - 2011 - Cambridge: 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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  22. Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing.Birgitta Dresp-Langley - 2016 - Symmetry 127 (8).
    Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and (...) of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)
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  23. 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 (...)
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  24. Geometry for a Brain. Optimal Control in a Network of Adaptive Memristors.Ignazio Licata & Germano Resconi - 2013 - Adv. Studies Theor. Phys., (no.10):479-513.
    In the brain the relations between free neurons and the conditioned ones establish the constraints for the informational neural processes. These constraints reflect the systemenvironment state, i.e. the dynamics of homeocognitive activities. The constraints allow us to define the cost function in the phase space of free neurons so as to trace the trajectories of the possible configurations at minimal cost while respecting the constraints imposed. Since the space of the free states is a manifold or a non orthogonal space, (...)
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  25. The Cognitive Geometry of War.Barry Smith - 1997 - In Peter Koller & Klaus Puhl (eds.), Current Issues in Political Philosophy: Justice in Society and World Order. Vienna: Hölder-Pichler-Tempsky. pp. 394--403.
    When national borders in the modern sense first began to be established in early modern Europe, non-contiguous and perforated nations were a commonplace. According to the conception of the shapes of nations that is currently preferred, however, nations must conform to the topological model of circularity; their borders must guarantee contiguity and simple connectedness, and such borders must as far as possible conform to existing topographical features on the ground. The striving to conform to this model can be seen at (...)
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  26. The Contact Algebra of the Euclidean Plane has Infinitely Many Elements.Thomas Mormann - manuscript
    Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to (...)
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  27. Berkeley and Proof in Geometry.Richard J. Brook - 2012 - Dialogue 51 (3):419-435.
    Berkeley in his Introduction to the Principles of Human knowledge uses geometrical examples to illustrate a way of generating “universal ideas,” which allegedly account for the existence of general terms. In doing proofs we might, for example, selectively attend to the triangular shape of a diagram. Presumably what we prove using just that property applies to all triangles.I contend, rather, that given Berkeley’s view of extension, no Euclidean triangles exist to attend to. Rather proof, as Berkeley would normally assume, (...)
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  28.  82
    Modal Logics for Parallelism, Orthogonality, and Affine Geometries.Philippe Balbiani & Valentin Goranko - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):365-397.
    We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.
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  29. Remarks on the Geometry of Complex Systems and Self-Organization.Luciano Boi - 2012 - In Vincenzo Fano, Enrico Giannetto, Giulia Giannini & Pierluigi Graziani (eds.), Complessità e Riduzionismo. © ISONOMIA – Epistemologica, University of Urbino. pp. 28-43.
    Let us start by some general definitions of the concept of complexity. We take a complex system to be one composed by a large number of parts, and whose properties are not fully explained by an understanding of its components parts. Studies of complex systems recognized the importance of “wholeness”, defined as problems of organization (and of regulation), phenomena non resolvable into local events, dynamics interactions in the difference of behaviour of parts when isolated or in higher configuration, etc., in (...)
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  30. Inequality in the Universe, Imaginary Numbers and a Brief Solution to P=NP? Problem.Mesut Kavak - manuscript
    While I was working about some basic physical phenomena, I discovered some geometric relations that also interest mathematics. In this work, I applied the rules I have been proven to P=NP? problem over impossibility of perpendicularity in the universe. It also brings out extremely interesting results out like imaginary numbers which are known as real numbers currently. Also it seems that Euclidean Geometry is impossible. The actual geometry is Riemann Geometry and complex numbers are real.
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  31.  54
    Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
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  32. What is the Value of Geometric Models to Understand Matter?Francoise Monnoyeur - 2015 - Epekeina 6 (2):1-13.
    This article analyzes the value of geometric models to understand matter with the examples of the Platonic model for the primary four elements (fire, air, water, and earth) and the models of carbon atomic structures in the new science of crystallography. How the geometry of these models is built in order to discover the properties of matter is explained: movement and stability for the primary elements, and hardness, softness and elasticity for the carbon atoms. These geometric models appear to (...)
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  33. Miracles and the Perfection of Being: The Theological Roots of Scientific Concepts.Alex V. Halapsis - 2016 - Anthropological Measurements of Philosophical Research 9:70-77.
    Purpose of the article is to study the Western worldview as a framework of beliefs in probable supernatural encroachment into the objective reality. Methodology underpins the idea that every cultural-historical community envisions the reality principles according to the beliefs inherent to it which accounts for the formation of the unique “universes of meanings”. The space of history acquires the Non-Euclidean properties that determine the specific cultural attitudes as well as part and parcel mythology of the corresponding communities. Novelty consists (...)
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  34. Mathematics - an Imagined Tool for Rational Cognition.Boris Culina - manuscript
    Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths (...)
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  35. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  36. In the Light of Time.Arto Annila - 2009 - Proceedings of Royal Society A 465:1173–1198.
    The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, (...)
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  37. The Media of Relativity.Jimena Canales - 2015 - Technology and Culture 56 (3):610-645.
    How are fundamental constants, such as c for the speed of light, related to particular technological environments? Our understanding of the constant c and Einstein’s relativistic cosmology depended on key experiences and lessons learned in connection to new forms of telecommunications, first used by the military and later adapted for commercial purposes. Many of Einstein’s contemporaries understood his theory of relativity by reference to telecommunications, some referring to it as “signal-theory” and “message theory.” Prominent physicists who contributed to it (Hans (...)
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  38.  95
    A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic:1-37.
    We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and (...)
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  39. Out of Nowhere: Introduction: The Emergence of Spacetime.Nick Huggett & Christian Wuthrich - 2021
    This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces the problem of emergence of spacetime in quantum gravity. It introduces the main philosophical challenge to spacetime emergence and sketches our preferred solution to it.
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  40. A BRIEF OUTLINE OF THE POSSIBLE BASICS OF COSMOLOGY IN THE 22nd CENTURY, AND WHAT IT MEANS FOR RELIGION.Rodney Bartlett - manuscript
    This article’s conclusion is that the theories of Einstein are generally correct and will still be relevant in the next century (there will be modifications necessary for development of quantum gravity). Those Einsteinian theories are Special Relativity, General Relativity, and the title of a paper he published in 1919 which asked if gravitation plays a role in the composition of elementary particles of matter. This paper was the bridge between General Relativity and the Unified Field Theory he sought during the (...)
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  41. Marriages of Mathematics and Physics: A Challenge for Biology.Arezoo Islami & Giuseppe Longo - 2017 - Progress in Biophysics and Molecular Biology 131:179-192.
    The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the (...)
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  42. More Trouble for Regular Probabilitites.Matthew W. Parker - 2012
    In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...)
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  43. Immobility Theory.Ninh Khac Son - manuscript
    The content of the manuscript represents a bold idea system, it is beyond the boundaries of all existing knowledge but the method of reasoning and logic is also very strict and scientific. The purpose of the manuscript is to unify the natural categories (natural philosophy, natural geometry, quantum mechanics, astronomy,…), and to open a new direction for most other sciences. Abstract of the manuscript: About Philosophy: • Proved the existence of time and non-dilation. • Proved that matter is always (...)
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  44. Demystifying Emergence.David Yates - 2016 - Ergo: An Open Access Journal of Philosophy 3:809-841.
    Are the special sciences autonomous from physics? Those who say they are need to explain how dependent special science properties could feature in irreducible causal explanations, but that’s no easy task. The demands of a broadly physicalist worldview require that such properties are not only dependent on the physical, but also physically realized. Realized properties are derivative, so it’s natural to suppose that they have derivative causal powers. Correspondingly, philosophical orthodoxy has it that if we want special science properties to (...)
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  45. Bohm's Approach and Individuality.Paavo Pylkkänen, Basil Hiley & Ilkka Pättiniemi - 2016 - In Alexandre Guay & Thomas Pradeu (eds.), Individuals Across the Sciences. Oxford, UK: Oxford University Press.
    Ladyman and Ross argue that quantum objects are not individuals and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory, according to which particles do have denite trajectories at all times. However, LR interpret the research by Brown et al. as implying that "raw stuff" or haecceities are needed for the individuality of particles of BT, (...)
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  46. True Grid.Barry Smith - 2001 - In D. Montello (ed.), Spatial Information Theory: Foundations of Geographic Information Science. New York: Springer. pp. 14-27.
    The Renaissance architect, moral philosopher, cryptographer, mathematician, Papal adviser, painter, city planner and land surveyor Leon Battista Alberti provided the theoretical foundations of modern perspective geometry. Alberti’s work on perspective exerted a powerful influence on painters of the stature of Albrecht Dürer, Leonardo da Vinci and Piero della Francesca. But his Della pittura of 1435–36 contains also a hitherto unrecognized ontology of pictorial projection. We sketch this ontology, and show how it can be generalized to apply to representative devices (...)
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  47. Kant, Polysolipsism, and the Real Unity of Experience.Richard Brown - manuscript
    [written in 2002/2003 while I was a graduate student at the University of Connecticut and ultimately submitted as part of my qualifying exam for the Masters of Philosophy] The question I am interested in revolves around Kant’s notion of the unity of experience. My central claim will be that, apart from the unity of experiencings and the unity of individual substances, there is a third unity: the unity of Experience. I will argue that this third unity can be conceived of (...)
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  48. Consciousness All the Way Down? An Analysis of McGinn's Critique of Panexperientialism.Christian de Quincey - 1994 - Journal of Consciousness Studies 1 (2):217-229.
    This paper examines two objections by Colin McGinn to panexperientialist metaphysics as a solution to the mind-body problem. It begins by briefly stating how the `ontological problem' of the mind-body relationship is central to the philosophy of mind, summarizes the difficulties with dualism and materialism, and outlines the main tenets of panexperientialism. Panexperientialists, such as David Ray Griffin, claim that theirs is one approach to solving the mind-body problem which does not get stuck in accounting for interaction nor in the (...)
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  49.  13
    Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map.Birgitta Dresp-Langley - 2021 - Symmetry 13:299.
    Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this (...)
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    Knowledge Beyond Reason in Spinoza’s Epistemology: Scientia Intuitiva and Amor Dei Intellectualis in Spinoza’s Epistemology.Anne Newstead - forthcoming - Australasian Philosophical Review 4 (Revisiting Spinoza's Rationalism).
    Genevieve Lloyd’s Spinoza is quite a different thinker from the arch rationalist caricature of some undergraduate philosophy courses devoted to “The Continental Rationalists”. Lloyd’s Spinoza does not see reason as a complete source of knowledge, nor is deductive rational thought productive of the highest grade of knowledge. Instead, that honour goes to a third kind of knowledge—intuitive knowledge (scientia intuitiva), which provides an immediate, non-discursive knowledge of its singular object. To the embarrassment of some hard-nosed philosophers, intellectual intuition has an (...)
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