Results for 'Geometric Symbols'

963 found
Order:
  1.  46
    Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick. Helena M. Pycior.Joan Richards - 1998 - Isis 89 (4):728-729.
  2.  40
    Analytical symbols and geometrical figures in eighteenth-century calculus.Giovanni Ferraro - 2001 - Studies in History and Philosophy of Science Part A 32 (3):535-555.
    Leibnizian-Newtonian calculus was a theory that dealt with geometrical objects; the figure continued to play one of the fundamental roles it had played in Greek geometry: it susbstituted a part of reasoning. During the eighteenth century a process of de-geometrization of calculus took place, which consisted in the rejection of the use of diagrams and in considering calculus as an 'intellectual' system where deduction was merely linguistic and mediated. This was achieved by interpreting variables as universal quantities and introducing the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  3.  29
    Helena M. Pycior, Symbols, Impossible Numbers, and Geometric Entanglement. British Algebra through the Commentaries On Newton's Universal Arithmetick.Helena M. Pycior - 1998 - Erkenntnis 49 (3):415-419.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  45
    Helena M. Pycior, symbols, impossible numbers, and geometric entanglement. British algebra through the commentaries on Newton's universal arithmetick.Volker Peckhaus - 1998 - Erkenntnis 49 (3):415-419.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  5.  82
    Solving Geometric Analogy Problems Through Two‐Stage Analogical Mapping.Andrew Lovett, Emmett Tomai, Kenneth Forbus & Jeffrey Usher - 2009 - Cognitive Science 33 (7):1192-1231.
    Evans’ 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high‐level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  6.  70
    A geometric proof of the completeness of the łukasiewicz calculus.Giovanni Panti - 1995 - Journal of Symbolic Logic 60 (2):563-578.
    We give a self-contained geometric proof of the completeness theorem for the infinite-valued sentential calculus of Łukasiewicz.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  7.  63
    Geometric Representations for Minimalist Grammars.Peter Beim Graben & Sabrina Gerth - 2012 - Journal of Logic, Language and Information 21 (4):393-432.
    We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  10
    Comparison of intradimensional and extradimensional shifts using geometric and symbolic stimuli.Thomas D. Kennedy & Charles D. Gersten - 1976 - Bulletin of the Psychonomic Society 7 (5):458-460.
  9.  24
    Concept Learning: A Geometrical Model.Peter G.?Rdenfors - 2001 - Proceedings of the Aristotelian Society 101 (2):163 - 183.
    In contrast to symbolic or associationist representations, I advocate a third form of representing information that employs geometrical structures. I argue that this form is appropriate for modelling concept learning. By using the geometrical structures of what I call conceptual spaces, I define properties and concepts. A learning model that shows how properties and concepts can be learned in a simple but naturalistic way is then presented. I also discuss the advantages of the geometric approach over the symbolic and (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  10. Reviews: Mathematics and Logic-Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick. [REVIEW]Helena M. Pycior & M. Seltman - 1998 - Annals of Science 55 (4):438-439.
  11. Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - 2023 - Review of Symbolic Logic 16 (1):298-337.
    Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, (...) and Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  12.  86
    Weakly one-based geometric theories.Alexander Berenstein & Evgueni Vassiliev - 2012 - Journal of Symbolic Logic 77 (2):392-422.
    We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: "weak one-basedness", absence of type definable "almost quasidesigns", and "generic linearity". Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  13.  64
    Cognitive Artifacts for Geometric Reasoning.Mateusz Hohol & Marcin Miłkowski - 2019 - Foundations of Science 24 (4):657-680.
    In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  14. Concept learning: A geometrical model.Peter Gärdenfors - 2001 - Proceedings of the Aristotelian Society 101 (2):163–183.
    In contrast to symbolic or associationist representations, I advocate a third form of representing information that employs geometrical structures. I argue that this form is appropriate for modelling concept learning. By using the geometrical structures of what I call conceptual spaces, I define properties and concepts. A learning model that shows how properties and concepts can be learned in a simple but naturalistic way is then presented. I also discuss the advantages of the geometric approach over the symbolic and (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  15.  59
    The Semantics of Political Symbols.Andrei Babaitsev - 2008 - Proceedings of the Xxii World Congress of Philosophy 44:5-9.
    With the use symbols by political subjects arises the problem of their understanding. Groups of symbols can be created in such a way to contain a message. The state coat of arms is a political symbol, in which is concentrated a number of meanings and significance. The coat of arms — it is a symbol garnished with colossal endless meaning and potential withing its power. Besides this, the state coat of arms appears in numbers like mandalas: it is (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  16.  56
    A geometric zero-one law.Robert H. Gilman, Yuri Gurevich & Alexei Miasnikov - 2009 - Journal of Symbolic Logic 74 (3):929-938.
    Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. If x is an element of X, let $B_n (x)$ be the ball of radius n around x. Suppose that X is infinite, connected and of bounded degree. A first-order sentence ϕ in the language of X is almost surely true (resp. a. s. false) for finite substructures of X if for every x ∈ X, the fraction of substructures of $B_n (x)$ (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17. Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle.Juris Steprāns - 2005 - Bulletin of Symbolic Logic 11 (4):517-525.
    It is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark  
  18.  18
    Generic Expansions of Geometric Theories.Somaye Jalili, Massoud Pourmahdian & Nazanin Roshandel Tavana - forthcoming - Journal of Symbolic Logic:1-22.
    As a continuation of ideas initiated in [19], we study bi-colored (generic) expansions of geometric theories in the style of the Fraïssé–Hrushovski construction method. Here we examine that the properties $NTP_{2}$, strongness, $NSOP_{1}$, and simplicity can be transferred to the expansions. As a consequence, while the corresponding bi-colored expansion of a red non-principal ultraproduct of p-adic fields is $NTP_{2}$, the expansion of algebraically closed fields with generic automorphism is a simple theory. Furthermore, these theories are strong with $\operatorname {\mathrm (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  19.  38
    Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction.Lukas M. Verburgt - 2016 - Annals of Science 73 (1):40-67.
    ABSTRACTThis paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  20.  86
    Hilbert, Duality, and the Geometrical Roots of Model Theory.Günther Eder & Georg Schiemer - 2018 - Review of Symbolic Logic 11 (1):48-86.
    The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’sFoundations of Geometry(1899) and its mathematical roots in nineteenth-century projective geometry. A central innovation of Hilbert’s book was to provide semantically minded independence proofs for various fragments of Euclidean geometry, thereby contributing to the development of the model-theoretic point of view in logical theory. Though it is generally acknowledged that the development of model theory is intimately bound up with innovations in 19th century geometry (in particular, the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  21.  36
    Concept Representation and the Geometric Model of Mind.Włodzisław Duch - 2022 - Studies in Logic, Grammar and Rhetoric 67 (1):151-167.
    Current cognitive architectures are either working at the abstract, symbolic level, or the low, emergent level related to neural modeling. The best way to understand phenomena is to see, or imagine them, hence the need for a geometric model of mental processes. Geometric models should be based on an intermediate level of modeling that describe mental states in terms of features relevant from the first-person perspective but also linked to neural events. Concepts should be represented as geometrical objects (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  22.  43
    Symbol and Function in Contemporary Architecture.Curtis L. Carter - 2008 - Proceedings of the Xxii World Congress of Philosophy 1:15-25.
    The focus here will be on the tension between architecture’s symbolic role and its function as a space to house and present art. ‘Symbolic’ refers both to a building as an aesthetic or sculptural form and secondly to its role in expressing civic identity. ‘Function’ refers to the intended purpose or practical use apart from its role as a form of art. As an art form, it serves important symbolic purposes; its practical purposes are linked to serving individual and community (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  23. Model theory: Geometrical and set-theoretic aspects and prospects.Angus Macintyre - 2003 - Bulletin of Symbolic Logic 9 (2):197-212.
    I see model theory as becoming increasingly detached from set theory, and the Tarskian notion of set-theoretic model being no longer central to model theory. In much of modern mathematics, the set-theoretic component is of minor interest, and basic notions are geometric or category-theoretic. In algebraic geometry, schemes or algebraic spaces are the basic notions, with the older “sets of points in affine or projective space” no more than restrictive special cases. The basic notions may be given sheaf-theoretically, or (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  24.  88
    Idealization and external symbolic storage: the epistemic and technical dimensions of theoretic cognition.Peter Woelert - 2012 - Phenomenology and the Cognitive Sciences 11 (3):335-366.
    This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently follows (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  25.  67
    The emergence of symbolic algebra as a shift in predominant models.Albrecht Heeffer - 2008 - Foundations of Science 13 (2):149--161.
    Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  26.  26
    Reflections on the Notion of Culture in the History of Mathematics: The Example of “Geometrical Equations”.François Lê - 2016 - Science in Context 29 (3):273-304.
    ArgumentThis paper challenges the use of the notion of “culture” to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to “geometrical equations,” objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to “geometrical equations,” and (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27.  37
    Four concepts from "geometrical" stability theory in modules.T. G. Kucera & M. Prest - 1992 - Journal of Symbolic Logic 57 (2):724-740.
  28. Sure-wins under coherence: a geometrical perspective.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi - 2019 - In Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.
    In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  29.  68
    Inequivalent representations of geometric relation algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
    It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark  
  30.  37
    Bornstein Benedykt. Geometrical logic. The structures of thought and space. Bibliotheca Universitatis Liberae Polonae, ser. B, no. 8 . Wolna Wszechnica Polska, Warsaw 1939, 114 pp. [REVIEW]Saunders Mac Lane - 1939 - Journal of Symbolic Logic 4 (3):133-134.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  31.  52
    Certain Modern Ideas and Methods: “Geometric Reality” in the Mathematics of Charlotte Angas Scott.Jemma Lorenat - 2020 - Review of Symbolic Logic 13 (4):681-719.
    Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  32.  61
    Bruno Poizat. Groupes stables. Une tentative de conciliation entre la géométric algébrique et la logique mathématique. Nur al-Mantiq wal-Ma'rifah, Villeurbanne1987, vi + 215 pp. [REVIEW]James Loveys - 1989 - Journal of Symbolic Logic 54 (4):1494-1496.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  33.  26
    Tsao-Chen Tang. Algebraic postulates and a geometric interpretation for the Lewis calculus of strict implication. Bulletin of the American Mathematical Society, vol. 44 , pp. 737–744. [REVIEW]Charles A. Baylis - 1939 - Journal of Symbolic Logic 4 (1):27-27.
  34.  38
    Sergeǐ S. Goncharov. Schetnye bulevy algebry i razreshimost′. Russian original of the preceding. Sibirskaya shkola algebry i logiki. Nauchnaya Kniga, Novosibirsk1996, 364 + xii pp. - Anand Pillay. Geometric stability theory. Oxford logic guides, no. 32. Clarendon Press, Oxford University Press, Oxford, New York, etc., 1996, x + 361 pp. [REVIEW]Boris Zil'Ber - 1998 - Journal of Symbolic Logic 63 (3):1190-1190.
  35.  44
    Jonahan Chapman and Frederick Rowbottom. Relative category theory and geometric morphisms. A logical approach. Oxford logic guides, no. 16., Clarendon press, Oxford University Press, Oxford and New York1992, xi + 263 pp. [REVIEW]I. Moerdijk - 1995 - Journal of Symbolic Logic 60 (2):694-695.
  36.  15
    Sacred geometry: your personal guide.Bernice Cockram - 2020 - New York, NY: Wellfleet Press.
    With In Focus Sacred Geometry, learn the fascinating history behind this ancient tradition as well as how to decipher the geometrical symbols, formulas, and patterns based on mathematical patterns. People have searched for the meaning behind mathematical patterns for thousands of years. At its core, sacred geometry seeks to find the universal patterns that are found and applied to the objects surrounding us, such as the designs found in temples, churches, mosques, monuments, art, architecture, and nature. Learn the fundamental (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  37. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  38.  8
    An introduction to mathematical reasoning.Boris Iglewicz - 1973 - New York,: Macmillan. Edited by Judith Stoyle.
    What is mathematics; Symbolic logic; A reviw of number and notation; Further review topics; Introduction to proofs; Direct proof I; Direct Proog II; Indirect proof; Analogy abnd geometric proof.
    Direct download  
     
    Export citation  
     
    Bookmark  
  39. Likeness-Making and the Evolution of Cognition.Hajo Greif - 2021 - Biology and Philosophy 37 (1):1-24.
    Paleontological evidence suggests that human artefacts with intentional markings might have originated already in the Lower Paleolithic, up to 500.000 years ago and well before the advent of ‘behavioural modernity’. These markings apparently did not serve instrumental, tool-like functions, nor do they appear to be forms of figurative art. Instead, they display abstract geometric patterns that potentially testify to an emerging ability of symbol use. In a variation on Ian Hacking’s speculative account of the possible role of “likeness-making” in (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  40.  46
    What is a number?: mathematical concepts and their origins.Robert Tubbs - 2009 - Baltimore: Johns Hopkins University Press.
    Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  41.  31
    Synthetic and analytic geometries in the publications of Jakob Steiner and Julius Plücker.Jemma Lorenat - 2016 - Archive for History of Exact Sciences 70 (4):413-462.
    In their publications during the 1820s, Jakob Steiner and Julius Plücker frequently derived the same results while claiming different methods. This paper focuses on two such results in order to compare their approaches to constructing figures, calculating with symbols, and representing geometric magnitudes. Underlying the repetitive display of similar problems and theorems, Steiner and Plücker redefined synthetic and analytic methods in distinctly personal practices.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  42.  40
    Mathematics, Science and the Cambridge Tradition.Nuno Ornelas Martins - 2012 - Economic Thought 1 (2).
    In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  43.  20
    Temporal display of gestures in diagrammatic proof.Leclercq Bruno - 2021 - Metodo. International Studies in Phenomenology and Philosophy 9 (1):119-142.
    According to the deductivist view of mathematics which became the rule during the nineteenth century, formal proofs working with symbolic formulas replaced the intuitive knowledge that used to be gained by the step-by-step construction of geometric fgures and diagrams. Twentieth century epistemological refection on symbolic formulas and formal proofs, however, took them to be diagrams respectively exhibiting formal relations and transformations. The claim was also made that, for such diagrams to be proofs, temporal displays of transformations—and of other speech (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  44.  35
    Formen der Anschauungforms of Intuition: An Essay on the Philosophy of Mathematics: Eine Philosophie der Mathematik.Pirmin Stekeler-Weithofer - 2008 - Walter de Gruyter.
    What are pure geometric forms? In what sense are there an infinite number of points on a line? What is the relationship between empirically correct statements about real bodily figures (or movements) and the ideal truths of a pure mathematical geometry (also in space-time)? Starting from Kant and Wittgenstein, the book demonstrates how our dealings with figures and symbols is to be understood beyond the technical mastery of forms of calculation and proof.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  45.  43
    Introduction to mathematics: number, space, and structure.Scott A. Taylor - 2023 - Providence, Rhode Island: American Mathematical Society.
    This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  46.  18
    Concept learning and nonmonotonic reasoning.Peter Gärdenfors - 2005 - In Henri Cohen & Claire Lefebvre (eds.), Handbook of Categorization in Cognitive Science (Second Edition). pp. 977-999.
    Humans learn new concepts extremely fast. One or two examples of a new concept are often sufficient for us to grasp its meaning. Traditional theories of concept formation, such as symbolic or connectionist representations, have problems explaining the quick learning exhibited by humans. In contrast to these representations, I advocate a third form of representing categories, which employs geometric structures. I argue that this form is appropriate for modeling concept learning. By using the geometric structures of what I (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  47.  18
    The ingredients of a successful atomic exhibition in Cold War Italy.Donatella Germanese - 2023 - Annals of Science 80 (1):10-37.
    The organization of the mobile atomic exhibition, Mostra Atomica, designed by the United States Information Service to travel through Italy in 1954–55, had to meet technical, scientific, artistic, and political challenges. The head of the group in charge of the exhibition was architect Peter G. Harnden whose pedigree in the intelligence and training in architecture were an ideal match for leading the unit dedicated to exhibitions. The political sensitivity of the Mostra Atomica also required the intervention of the Italian Ministry (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  48. 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.
    Direct download  
     
    Export citation  
     
    Bookmark   52 citations  
  49.  13
    Newton on Quadratures: A Brief Outline.Niccolò Guicciardini - 2023 - In Marius Stan & Christopher Smeenk (eds.), Theory, Evidence, Data: Themes from George E. Smith. Springer. pp. 197-222.
    The purpose of this chapter is to give a brief outline of Newton’s methods for “squaring” a curve, which in Leibnizian terms one would call “integrations.” These methods are rarely considered by scholars, even by Newton scholars, with the exception of those, who like George—the dedicatee of this volume—are familiar with the “technical” Newton. My purpose here is not to address the specialists in the history of seventeenth-century mathematics, but rather to offer a reader-friendly primer in Newton’s “quadrature” techniques. I (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  50.  21
    The Paradox Topos.Lisa Gorton - 2000 - Journal of the History of Ideas 61 (2):343-346.
    In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.2 (2000) 343-346 [Access article in PDF] The Paradox Topos Lisa Gorton As William Egginton points out, 1 when Dante and Beatrice step outside the cosmos, they step into another set of concentric spheres. 2 These surround our (supposedly) geocentric cosmos, and yet they center upon God. The image affronts our logic of space. If these concentric spheres encompass us, how can they (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 963