Results for 'Euclidean Plane'

198 found
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  1. 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 (...)
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  2. A kinematic model for a partially resolved dynamical system in a Euclidean.Mohammed Sanduk - 2012 - Journal of Mathematical Modelling and Application 1 (6):40-51.
    The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and (...)
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  3. An Extension of Heron’s Formula to Tetrahedra, and the Projective Nature of Its Zeros.Havel Timothy - manuscript
    A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which (...)
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  4. The Flying Termite.Laszlo Katona (ed.) - 2014 - Vernon Press.
    ABSTRACT of The Flying Termite by L.L. Katona -/- In this book I would like to show the term “intelligence“ has a universal, non-anthropomorphic meaning. We can perceive intelligence in dogs, dolphins or gorillas without understanding of it, but intelligence can be also seen in many other things from insects and the Solar System to elementary particles or the rules of a triangle. But that doesn’t mean intelligence comes from Intelligent Design, yet alone a Designer, they seems to be the (...)
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  5. 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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  6. 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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  7. Lakatos and the Euclidean Programme.A. C. Paseau & Wesley Wrigley - forthcoming - In Roman Frigg, Jason Alexander, Laurenz Hudetz, Miklos Rédei, Lewis Ross & John Worrall (eds.), The Continuing Influence of Imre Lakatos's Philosophy: a Celebration of the Centenary of his Birth. Springer.
    Euclid’s Elements inspired a number of foundationalist accounts of mathematics, which dominated the epistemology of the discipline for many centuries in the West. Yet surprisingly little has been written by recent philosophers about this conception of mathematical knowledge. The great exception is Imre Lakatos, whose characterisation of the Euclidean Programme in the philosophy of mathematics counts as one of his central contributions. In this essay, we examine Lakatos’s account of the Euclidean Programme with a critical eye, and suggest (...)
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  8. The Euclidean Mousetrap.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 attain the (...)
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  9. 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 intuitions (...)
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  10. On the relationship between plane and solid geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
    Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned (...)
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  11. Visual foundations of Euclidean Geometry.Véronique Izard, Pierre Pica & Elizabeth Spelke - 2022 - Cognitive Psychology 136 (August):101494.
    Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the (...)
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  12. NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited).Florentin Smarandache - 2021 - Neutrosophic Sets and Systems 46 (1):456-477.
    In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, (...)
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  13. 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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  14. After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics.Janet Folina - 2018 - Journal for the History of Analytical Philosophy 6 (3).
    The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical (...)
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  15. 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 geometry have 'intuitive content' in (...)
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  16. 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 the (...)
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  17. Cognitive processing of spatial relations in Euclidean diagrams.Yacin Hamami, Milan N. A. van der Kuil, Ineke J. M. van der Ham & John Mumma - 2020 - Acta Psychologica 205:1--10.
    The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first (...)
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  18. Four-Way Turiyam based Characterization of Non-Euclidean Geometry.Prem Kumar Singh - 2023 - Journal of Neutrosophic and Fuzzy Ststems 5 (2):69-80.
    Recently, a problem is addressed while dealing the data with Non-Euclidean Geometry and its characterization. The mathematician found negation of fifth postulates of Euclidean geometry easily and called as Non-Euclidean geometry. However Riemannian provided negation of second postulates also which still considered as Non-Euclidean. In this case the problem arises what will happen in case negation of other Euclid Postulates exists. Same time total total or partial negation of Euclid postulates fails as hybrid Geometry. It become (...)
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  19. 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 objects and figures. Geometric (...)
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  20. NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited).Florentin Smarandache - 2021 - Neutrosophic Sets and Systems 46 (1):456-477.
    In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry.
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  21. On the representational role of Euclidean diagrams: representing qua samples.Tamires Dal Magro & Matheus Valente - 2021 - Synthese 199 (1-2):3739-3760.
    We advance a theory of the representational role of Euclidean diagrams according to which they are samples of co-exact features. We contrast our theory with two other conceptions, the instantial conception and Macbeth’s iconic view, with respect to how well they accommodate three fundamental constraints on theories of the Euclidean diagrammatic practice— that Euclidean diagrams are used in proofs whose results are wholly general, that Euclidean diagrams indicate the co-exact features that the geometer is allowed to (...)
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  22. 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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  23.  16
    Kant's Views on Non-Euclidean Geometry.Michael Cuffaro - 2012 - In Lampert Fabio (ed.), Proceedings of the Canadian Society for History and Philosophy of Mathematics. Springer. pp. 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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  24. Color for the perceptual organization of the pictorial plane: Victor Vasarely's legacy to Gestalt psychology.Birgitta Dresp-Langley & Adam Reeves - 2020 - Heliyon 6 (6):e04375.
    Victor Vasarely's (1906–1997) important legacy to the study of human perception is brought to the forefront and discussed. A large part of his impressive work conveys the appearance of striking three-dimensional shapes and structures in a large-scale pictorial plane. Current perception science explains such effects by invoking brain mechanisms for the processing of monocular (2D) depth cues. Here in this study, we illustrate and explain local effects of 2D color and contrast cues on the perceptual organization in terms of (...)
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  25. Design of Label Sorting Algorithm Program as Batik Pattern Drawer with Euclidean Distance Method.Budi Setiyono, Sumardi & Solichul Huda - 2018 - International Journal of Engineering and Information Systems (IJEAIS) 3 (2):36-46.
    Abstract: The development of technology pushes human to increase productivity by changing manual system to automatic system. Modernization affect almost all aspect especially in art. Batik is a ancestor legacy of indonesian people that recogized by UNESCO as culture legacy of Indonesia yet batik industries are not develop as much. Modernization in batik art is expected to optimize its productivity. This research design algorithm and the program in MATLAB that used for controlling movement protype of batik maker 2 dof cartesian (...)
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  26. 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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  27. The connection between mathematics and philosophy on the discrete–structural plane of thinking: the discrete–structural model of the world.Eldar Amirov - 2017 - Гілея: Науковий Вісник 126 (11):266-270.
    The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...)
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  28.  63
    Real Examples of NeutroGeometry & AntiGeometry.Florentin Smarandache - 2023 - Neutrosophic Sets and Systems 55.
    For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] (...)
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  29. La Neutro-Geometría y la Anti-Geometría como Alternativas y Generalizaciones de las Geometrías no Euclidianas.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 20 (1):91-104.
    In this paper we extend Neutro-Algebra and Anti-Algebra to geometric spaces, founding Neutro/Geometry and AntiGeometry. While Non-Euclidean Geometries resulted from the total negation of a specific axiom (Euclid's Fifth Postulate), AntiGeometry results from the total negation of any axiom or even more axioms of any geometric axiomatic system (Euclidean, Hilbert, etc. ) and of any type of geometry such as Geometry (Euclidean, Projective, Finite, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.), and Neutro-Geometry results from the partial (...)
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  30. Introduction to Image Processing via Neutrosophic Techniques.A. A. Salama, Florentin Smarandache & Mohamed Eisa - 2014 - Neutrosophic Sets and Systems 5:59-64.
    This paper is an attempt of proposing the processing approach of neutrosophic technique in image processing. As neutrosophic sets is a suitable tool to cope with imperfectly defined images, the properties, basic operations distance measure, entropy measures, of the neutrosophic sets method are presented here. İn this paper we, introduce the distances between neutrosophic sets: the Hamming distance, the normalized Hamming distance, the Euclidean distance and normalized Euclidean distance. We will extend the concepts of distances to the case (...)
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  31. Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9):1-56.
    The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...)
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  32. 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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  33. 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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  34. Exploring marginality among Filipino Catholics in Japan: A proposed heuristic device.Willard Enrique Macaraan - 2020 - Religions 11 (161):1-17.
    The Church seeks to be inclusive; one that opens her doors to everyone. For many Filipino Catholics (FCs) in Japan, their ecclesial existence is marked by a history of negotiation as “guests” hosted by the Japanese Catholics (JCs). Within this field of host–guest interplay, this paper explores the dynamics of sociospatial seclusion by employing the ideation of marginality pro ered by Loic Wacquant’s study on urban ghettos. The paper argues that the guest-identity of FCs must not be understood as a (...)
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  35. Geachianism.Patrick Todd - 2011 - Oxford Studies in Philosophy of Religion 3:222-251.
    The plane was going to crash, but it didn't. Johnny was going to bleed to death, but he didn't. Geach sees here a changing future. In this paper, I develop Geach's primary argument for the (almost universally rejected) thesis that the future is mutable (an argument from the nature of prevention), respond to the most serious objections such a view faces, and consider how Geach's view bears on traditional debates concerning divine foreknowledge and human freedom. As I hope to (...)
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  36.  87
    Are The Least Time Path Principle and Snell's Law of Reflection Equivalent?Radhakrishnamurty Padyala - manuscript
    We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical reflector, (...)
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  37. Una vita oltre la maschera: Panimmagismo e immanenza.Pierluca D'Amato - 2016 - Philosophy Kitchen 1 (5):89-101.
    As all philosophical concepts, also the concept of person constitutes itself referring to a particular problem. The analysis drafted by Marcel Mauss regarding the genesis of the aforementioned category permits to analyse the problematic nucleus to which such concept refers to, disclosing that it responds to the necessity of solving the ancient problem of the link between mind and body in a specific perspective. In this respect, Bergsonian theory of images represents a solid attempt of passing not only the habitual (...)
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  38. Set Size and the Part–Whole Principle.Matthew W. Parker - 2013 - Review of Symbolic Logic (4):1-24.
    Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories (...)
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  39. 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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  40. The Topology of Communities of Trust.Mark Alfano - 2016 - Russian Sociological Review 15 (4):30-56.
    Hobbes emphasized that the state of nature is a state of war because it is characterized by fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the topology (...)
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  41. Backing Away from Libertarian Self-Ownership.David Sobel - 2012 - Ethics 123 (1):32-60.
    Libertarian self-ownership views have traditionally maintained that we enjoy very powerful deontological protections against any infringement upon our property. This stringency yields very counter-intuitive results when we consider trivial infringements such as very mildly toxic pollution or trivial risks such having planes fly overhead. Maintaining that other people's rights against all infringements are very powerful threatens to undermine our liberty, as Nozick saw. In this paper I consider the most sophisticated attempts to rectify this problem within a libertarian self-ownership framework. (...)
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  42. The Epistemic Status of the Imagination.Joshua Myers - 2021 - Philosophical Studies 178 (10):3251-3270.
    Imagination plays a rich epistemic role in our cognitive lives. For example, if I want to learn whether my luggage will fit into the overhead compartment on a plane, I might imagine trying to fit it into the overhead compartment and form a justified belief on the basis of this imagining. But what explains the fact that imagination has the power to justify beliefs, and what is the structure of imaginative justification? In this paper, I answer these questions by (...)
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  43. The Faithfulness Problem.Mario Bacelar Valente - 2022 - Principia: An International Journal of Epistemology 26 (3):429-447.
    When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical (...)
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  44. Do the Laws of Physics Forbid the Operation of Time Machines?John Earman, Chris Smeenk & Christian Wüthrich - 2009 - Synthese 169 (1):91 - 124.
    We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...)
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  45. 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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  46. Base-extension Semantics for Modal Logic.Eckhardt Timo & Pym David - forthcoming - Logic Journal of the IGPL.
    In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , (...)
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  47. Indivisible Parts and Extended Objects.Dean W. Zimmerman - 1996 - The Monist 79 (1):148-180.
    Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of (...)
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  48. 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. Of (...)
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  49. Effects of saturation and contrast polarity on the figure-ground organization of color on gray.Birgitta Dresp-Langley & Adam Reeves - 2014 - Frontiers in Psychology 5:1-9.
    Poorly saturated colors are closer to a pure grey than strongly saturated ones and, therefore, appear less “colorful”. Color saturation is effectively manipulated in the visual arts for balancing conflicting sensations and moods and for inducing the perception of relative distance in the pictorial plane. While perceptual science has proven quite clearly that the luminance contrast of any hue acts as a self-sufficient cue to relative depth in visual images, the role of color saturation in such figure-ground organization has (...)
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  50. 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 mathematical (...)
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