Results for ' Mathematics, general'

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  1.  29
    Mathematical Generality, Letter-Labels, and All That.F. Acerbi - 2020 - Phronesis 65 (1):27-75.
    This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully (...), and the ontological commitments underlying the stylistic practice. (shrink)
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  2.  96
    Contextualizing concepts using a mathematical generalization of the quantum formalism.Liane Gabora & Diederik Aerts - 2002 - Journal of Experimental and Theoretical Artificial Intelligence 14 (4):327-358.
    We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...)
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  3. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...)
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  4. Mathematics and Explanatory Generality.Alan Baker - 2017 - Philosophia Mathematica 25 (2):194-209.
    According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...)
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  5.  34
    Generalized equivalence: A pattern of mathematical expression.T. A. McKee - 1985 - Studia Logica 44 (3):285 - 289.
    A simple propositional operator is introduced which generalizes pairwise equivalence and occurs widely in mathematics. Attention is focused on a replacement theorem for this notion of generalized equivalence and its use in producing further generalized equivalences.
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  6.  36
    Mathematical, Philosophical and Semantic Considerations on Infinity : General Concepts.José-Luis Usó-Doménech, Josué Antonio Nescolarde Selva & Mónica Belmonte Requena - 2016 - Foundations of Science 21 (4):615-630.
    In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians (...)
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  7.  21
    Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China.Karine Chemla - 2003 - Science in Context 16 (3).
  8.  31
    Generality, mathematical elegance, and evolution of numerical/object identity.Felice L. Bedford - 2001 - Behavioral and Brain Sciences 24 (4):654-655.
    Object identity, the apprehension that two glimpses refer to the same object, is offered as an example of combining generality, mathematics, and evolution. We argue that it applies to glimpses in time (apparent motion), modality (ventriloquism), and space (Gestalt grouping); that it has a mathematically elegant solution of nested geometries (Euclidean, Similarity, Affine, Projective, Topology); and that it is evolutionarily sound despite our Euclidean world. [Shepard].
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  9.  11
    Proof, Generality and the Prescription of Mathematical Action: A Nanohistorical Approach to Communication.Karine Chemla - 2015 - Centaurus 57 (4):278-300.
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  10.  6
    Fundamental Mathematics. Prepared for the General Course Mathematics 1 in the College.E. P. Northrop, R. S. Fouch, I. R. Hershner, S. P. Hughart, W. S. Karush & J. S. Leech - 1950 - Journal of Symbolic Logic 14 (4):242-243.
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  11.  76
    Two general methods of extending mathematical theory creative process in mathematics.Marvin Barsky - 1969 - Philosophia Mathematica (1-2):22-27.
  12.  2
    Generalization and the Impossible: Issues in the search for generalized mathematics around 1900.Paul Ziche - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 209-228.
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  13.  5
    Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves.Eberhard Knobloch - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
  14.  5
    General mathematical physics and schemas, application to the theory of particles.J. L. Destouches - 1965 - Dialectica 19 (3‐4):345-348.
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  15.  8
    Empirical Generalizations on the Growth of Mathematical Notations.Florian Cajori - 1924 - Isis 6:391-394.
  16.  12
    Empirical Generalizations on the Growth of Mathematical Notations.Florian Cajori - 1924 - Isis 6 (3):391-394.
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  17.  4
    The Oxford Handbook of Generality in Mathematics and the Sciences.Karine Chemla, Renaud Chorlay & David Rabouin (eds.) - 2016 - New York, NY, USA: Oxford University Press UK.
    Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how individuals have valued generality and how they have worked with specific types of " (...)" entities, procedures, and arguments. (shrink)
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  18. Why proofs by mathematical induction are generally not explanatory.Marc Lange - 2009 - Analysis 69 (2):203-211.
    Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would be.
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  19.  17
    Abduction, Generalization, and Abstraction in Mathematical Problem Solving.Vic Cifarelli - 1998 - Semiotics:97-113.
  20. Outlines of a Mathematical Theory of General Problems.Paulo Veloso - 1984 - Philosophia Naturalis 21 (2/4):354-367.
     
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  21.  27
    Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence.Caroline Hornung, Christine Schiltz, Martin Brunner & Romain Martin - 2014 - Frontiers in Psychology 5.
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  22.  16
    Concepts of general topology in constructive mathematics and in sheaves.R. J. Grayson - 1981 - Annals of Mathematical Logic 20 (1):1.
  23.  22
    Concepts of general topology in constructive mathematics and in sheaves, II.R. J. Grayson - 1982 - Annals of Mathematical Logic 23 (1):55.
  24.  4
    Reverse mathematics: proofs from the inside out.John Stillwell - 2018 - Princeton: Princeton University Press.
    This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In (...)
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  25. Absolute generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - New York: Oxford University Press.
    The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.
  26.  25
    A Kantian account of mathematical modelling and the rationality of scientific theory change: The role of the equivalence principle in the development of general relativity.Jonathan Everett - 2018 - Studies in History and Philosophy of Science Part A 71:45-57.
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  27.  47
    Derivational robustness, credible substitute systems and mathematical economic models: the case of stability analysis in Walrasian general equilibrium theory.D. Wade Hands - 2016 - European Journal for Philosophy of Science 6 (1):31-53.
    This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers (...)
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  28.  17
    David W. Kueker. Generalized interpolation and definability. Annals of mathematical logic, vol. 1 no. 4 , pp. 423–468.E. G. K. López-Escobar - 1974 - Journal of Symbolic Logic 39 (2):337-338.
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  29.  2
    1. The General Character of Mathematical Logic.Philip McShane - 2001 - In Phenomenology and Logic: The Boston College Lectures on Mathematical Logic and Existentialism. University of Toronto Press. pp. 3-37.
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  30.  4
    History of Mathematics. Volume 1. General Survey of the History of Elementary Mathematics. David Eugene Smith.George Sarton - 1924 - Isis 6 (3):440-444.
  31.  4
    Mathematical logic through Python.Yannai A. Gonczarowski - 2022 - New York, NY: Cambridge University Press. Edited by Noam Nisan.
    An introduction to Mathematical Logic using a unique pedagogical approach in which the students implement the underlying conceps as well as almost all the mathematical proofs in the Python programming language. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. The covered mathematical material includes Propositional Logic and first-order Predicate Logic, culminating in a proof of Gödel's Completeness Theorem. A "sneak peak" into Gödel's Incompleteness Theorem is also provided.
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  32.  5
    Learning in mathematically-based domains: Understanding and generalizing obstacle cancellations.Jude W. Shavlik & Gerald F. DeJong - 1990 - Artificial Intelligence 45 (1-2):1-45.
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  33.  9
    Pierce R. S.. A generalization of atomic Boolean algebras. Pacific journal of mathematics, vol. 9 , pp. 175–182.Carol R. Karp - 1962 - Journal of Symbolic Logic 27 (1):100-100.
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  34.  6
    A course of philosophy and mathematics: toward a general theory of reality.Nicolas K. Laos - 2021 - New York: Nova Science Publishers.
    The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, including significant aspects of set theory, topology, mathematical logic, number systems, abstract algebra, linear algebra, and the theory of differential equations. From this perspective, it can be treated as a mathematical textbook. Third, it makes a student and a researcher in (...)
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  35. Mathematical logic and the foundations of mathematics: an introductory survey.G. T. Kneebone - 1963 - Mineola, N.Y.: Dover Publications.
    Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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  36.  2
    Speculative Philosophy as a Generalized Mathematics.Ronny Desmet - 2008 - Chromatikon 4:37-49.
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  37. Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. TIESZEN - 1993 - Studia Logica 52 (3):484-486.
    The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological (...)
     
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  38.  68
    Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
    This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...)
  39.  11
    The Relation of Mathematics to General Formal Logic [with Discussion].Mrs Sophie Bryant, Shadworth H. Hodgson & E. C. Benecke - 1902 - Proceedings of the Aristotelian Society 2:105 - 143.
  40.  4
    The relation of mathematics to general formal logic.Sophie Bryant - 1902 - Proceedings of the Aristotelian Society 2:105.
  41.  11
    Toward a General Mathematical Theory of Behavior.Edward W. Barankin - 1971 - Annals of the Japan Association for Philosophy of Science 4 (1):1-34.
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  42. Short-circuiting the definition of mathematical knowledge for an Artificial General Intelligence.Samuel Alexander - 2020 - Cifma.
    We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which (...)
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  43. Hilbert Mathematics versus Gödel Mathematics. III. Hilbert Mathematics by Itself, and Gödel Mathematics versus the Physical World within It: both as Its Particular Cases.Vasil Penchev - 2023 - Philosophy of Science eJournal (Elsevier: SSRN) 16 (47):1-46.
    The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...)
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  44. Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  45.  65
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: Routledge.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general (...)
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  46.  27
    The mathematical experience.Philip J. Davis - 1981 - Boston: Birkhäuser. Edited by Reuben Hersh & Elena Marchisotto.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
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  47.  83
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: London.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general (...)
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  48.  2
    Does mathematical study develop logical thinking?: testing the theory of formal discipline.Matthew Inglis - 2017 - New Jersey: World Scientific. Edited by Nina Attridge.
    "This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...)
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  49. Hilbert Mathematics Versus Gödel Mathematics. IV. The New Approach of Hilbert Mathematics Easily Resolving the Most Difficult Problems of Gödel Mathematics.Vasil Penchev - 2023 - Philosophy of Science eJournal (Elsevier: SSRN) 16 (75):1-52.
    The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of (...)
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  50. Alternative mathematics and alternative theoretical physics: The method for linking them together.Antonino Drago - 1996 - Epistemologia 19 (1):33-50.
    I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.
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