Results for 'euclidean geometry'

439 found
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  1. Euclidean Geometry is a Priori.Boris Culina - manuscript
    An argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modeling, not the world, but our activities in the world.
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  2. 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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  3. 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), (...)
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  4. 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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  5. 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.) (...)
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  6. 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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  7. (1 other version)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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  8. 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 (...)
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  9. 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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  10. 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 (...)
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  11. 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: Searching for the Foundations of Mathematical Thought. 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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  12. 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 (...)
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  13.  93
    "Mathesis of the Mind": A Study of Fichte’s Wissenschaftslehre and Geometry.David W. Wood - 2012 - New York, NY: New York/Amsterdam: Editions Rodopi (Brill Publishers). Fichte-Studien-Supplementa Vol. 29.
    This is a study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external, formal & internal, cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to 'ordinary' Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an 'ursprüngliche' or original geometry. – That is to say, a synthetic and constructivistic conception of (...) grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. -/- Accordingly, this study classifies Fichte’s philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or a “mathesis of the mind.” -/- . (shrink)
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  14. 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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  15. 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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  16. 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 (...)
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  17. 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 (...)
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  18. (1 other version)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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  19. 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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  20. 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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  21. 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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  22.  85
    The Nuances of Deprogramming Zeros.Parker Emmerson - 2024 - Journal of Liberated Mathematics.
    Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties of (...)
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  23. 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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  24. 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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  25. Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics.Vasil Penchev - 2023 - Astrophysics, Cosmology and Gravitation Ejournal 2 (52):1-82.
    Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...)
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  26. A hub-and-spoke model of geometric concepts.Mario Bacelar Valente - 2023 - Theoria : An International Journal for Theory, History and Fundations of Science 38 (1):25-44.
    The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of (...)
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  27. 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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  28. 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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  29. Arguments for the Continuity of Matter in Kant and Du Châtelet.Aaron Wells - forthcoming - Kant Studien.
    In the Metaphysical Foundations of Natural Science, Kant attempts to argue a priori from the indefinite divisibility of space to the indefinite metaphysical divisibility of matter. This is one type of argument from the continuity of space—purportedly established by Euclidean geometry—to the continuity of matter. I compare Kant's argument to parallel reasoning in Du Châtelet, whose work he knew. Both philosophers appeal to idealism about matter in their reasoning, yet also face difficulties in explaining why continuity, though not (...)
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  30. 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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  31. How Many Points are there in a Line Segment? – A new answer from Discrete-Cellular Space viewpoint.Victor Christianto & Florentin Smarandache - manuscript
    While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. (...)
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  32. SAD computers and two versions of the Church–Turing thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
    Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the (...)
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  33.  93
    Hypothesis and Convention in Poincaré’s Defense of Galilei Spacetime.Scott Walter - 2009 - In Michael Heidelberger & Gregor Schiemann (eds.), The Significance of the Hypothetical in Natural Science. De Gruyter. pp. 193-220.
    According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré's Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this (...)
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  34. Reconstructing the Unity of Mathematics circa 1900.David J. Stump - 1997 - Perspectives on Science 5 (3):383-417.
    Standard histories of mathematics and of analytic philosophy contend that work on the foundations of mathematics was motivated by a crisis such as the discovery of paradoxes in set theory or the discovery of non-Euclidean geometries. Recent scholarship, however, casts doubt on the standard histories, opening the way for consideration of an alternative motive for the study of the foundations of mathematics—unification. Work on foundations has shown that diverse mathematical practices could be integrated into a single framework of axiomatic (...)
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  35. Collected Papers (on various scientific topics), Volume XIII.Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic (...)
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  36. 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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  37. What is the Value of Geometric Models to Understand Matter?Francoise Monnoyeur (ed.) - 2015 - palermo italy: review of Ontology.
    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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  38. 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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  39. A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic 50 (1):149-185.
    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 and Malament. 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 : a predicate of betwenness and a four (...)
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  40. 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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  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. Posthumanist Phenomenology and Artificial Intelligence.Avery Rijos - unknown - Medium.
    This paper examines the ontological and epistemological implications of artificial intelligence (AI) through posthumanist philosophy, integrating the works of Deleuze, Foucault, and Haraway with contemporary computational methodologies. It introduces concepts such as negative augmentation, praxes of revealing, and desedimentation, while extending ideas like affirmative cartographies, ethics of alterity, and planes of immanence to critique anthropocentric assumptions about identity, cognition, and agency. By redefining AI systems as dynamic assemblages emerging through networks of interaction and co-creation, the paper challenges traditional dichotomies such (...)
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  43. Posthumanist Phenomenology and Artificial Intelligence.Avery Rijos - 2024 - Philosophy Papers (Philpapers).
    This paper examines the ontological and epistemological implications of artificial intelligence (AI) through posthumanist philosophy, integrating the works of Deleuze, Foucault, and Haraway with contemporary computational methodologies. It introduces concepts such as negative augmentation, praxes of revealing, and desedimentation, while extending ideas like affirmative cartographies, ethics of alterity, and planes of immanence to critique anthropocentric assumptions about identity, cognition, and agency. By redefining AI systems as dynamic assemblages emerging through networks of interaction and co-creation, the paper challenges traditional dichotomies such (...)
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  44. 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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  45. 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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  46. Linguistic Geometry and its Applications.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose (...)
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  47. 2D geometry predicts perceived visual curvature in context-free viewing.Birgitta Dresp-Langley - 2015 - Computational Intelligence and Neuroscience 2015 (708759):1-9.
    Planar geometry was exploited for the computation of symmetric visual curves in the image plane, with consistent variations in local parameters such as sagitta, chordlength, and the curves’ height-to-width ratio, an indicator of the visual area covered by the curve, also called aspect ratio. Image representations of single curves (no local image context) were presented to human observers to measure their visual sensation of curvature magnitude elicited by a given curve. Nonlinear regression analysis was performed on both the individual (...)
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  48. Geometry of motion: some elements of its historical development.Mario Bacelar Valente - 2019 - ArtefaCToS. Revista de Estudios de la Ciencia y la Tecnología 8 (2):4-26.
    in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion (...)
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  49. 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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  50. Logic, Geometry And Probability Theory.Federico Holik - 2013 - SOP Transactions On Theoretical Physics 1:128 - 137.
    We discuss the relationship between logic, geometry and probability theory under the light of a novel approach to quantum probabilities which generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories.
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