Results for 'Mathematics, general'

1000+ found
Order:
  1.  17
    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)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  86
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   28 citations  
  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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   22 citations  
  5. 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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   25 citations  
  6.  1
    The Oxford Handbook of Generality in Mathematics and the Sciences.Karine Chemla, Renaud Chorlay & David Rabouin (eds.) - 2016 - 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)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  31
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  8.  18
    Generality Above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China.Karine Chemla - 2003 - Science in Context 16 (3).
  9.  31
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10.  27
    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].
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  11.  9
    Proof, Generality and the Prescription of Mathematical Action: A Nanohistorical Approach to Communication.Karine Chemla - 2015 - Centaurus 57 (4):278-300.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  12.  10
    Empirical Generalizations on the Growth of Mathematical Notations.Florian Cajori - 1924 - Isis 6 (3):391-394.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  13.  7
    Empirical Generalizations on the Growth of Mathematical Notations.Florian Cajori - 1924 - Isis 6:391-394.
  14.  16
    Abduction, Generalization, and Abstraction in Mathematical Problem Solving.Vic Cifarelli - 1998 - Semiotics:97-113.
  15.  3
    General Mathematical Physics and Schemas, Application to the Theory of Particles.J. L. Destouches - 1965 - Dialectica 19 (3‐4):345-348.
    Direct download  
     
    Export citation  
     
    Bookmark  
  16.  4
    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.
  17.  68
    Two General Methods of Extending Mathematical Theory Creative Process in Mathematics.Marvin Barsky - 1969 - Philosophia Mathematica (1-2):22-27.
  18.  5
    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.
    Direct download  
     
    Export citation  
     
    Bookmark  
  19.  1
    A Course of Philosophy and Mathematics: Toward a General Theory of Reality.Nicolas 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  20.  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.
    Direct download  
     
    Export citation  
     
    Bookmark  
  21. Outlines of a Mathematical Theory of General Problems.Paulo Veloso - 1984 - Philosophia Naturalis 21 (2/4):354-367.
     
    Export citation  
     
    Bookmark  
  22. Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - Topics in Cognitive Science 5 (2):231-250.
    The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  23. Short-Circuiting the Definition of Mathematical Knowledge for an Artificial General Intelligence.Samuel Alexander - forthcoming - Lecture Notes in Computer Science.
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  24.  23
    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.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  25.  10
    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.
  26.  14
    Concepts of General Topology in Constructive Mathematics and in Sheaves.R. J. Grayson - 1981 - Annals of Mathematical Logic 20 (1):1.
  27.  18
    Concepts of General Topology in Constructive Mathematics and in Sheaves, II.R. J. Grayson - 1982 - Annals of Mathematical Logic 23 (1):55.
  28.  22
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  29.  22
    The Universal Generalization Problem.Carlo Cellucci - 2009 - Logique Et Analyse 52.
    The universal generalization problem is the question: What entitles one to conclude that a property established for an individual object holds for any individual object in the domain? This amounts to the question: Why is the rule of universal generalization justified? In the modern and contemporary age Descartes, Locke, Berkeley, Hume, Kant, Mill, Gentzen gave alternative solutions of the universal generalization problem. In this paper I consider Locke’s, Berkeley’s and Gentzen’s solutions and argue that they are problematic. Then I consider (...)
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  30. 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 (...)
     
    Export citation  
     
    Bookmark  
  31.  23
    The Mathematical Experience: Study Edition.Philip J. Davis - 1981 - Birkhäuser.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
    Direct download  
     
    Export citation  
     
    Bookmark   140 citations  
  32.  40
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  33.  15
    Robinson Julia. General Recursive Functions. Proceedings of the American Mathematical Society, Vol. 1 No. 6 , Pp. 703–718. [REVIEW]Martin Davis - 1951 - Journal of Symbolic Logic 16 (4):280-280.
  34. Logic and Foundations of Mathematics: Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.Andrea Cantini, Ettore Casari & Pierluigi Minari (eds.) - 1999 - Dordrecht, Netherland: Springer.
    The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  35. Fenstad Jens E.. General Recursion Theory. An Axiomatic Approach. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, and New York, 1980, XI + 225 Pp. [REVIEW]Douglas Cenzer - 1982 - Journal of Symbolic Logic 47 (3):696-698.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  36.  30
    Raymond M. Smullyan. A Generalization of Intuitionistic and Modal Logics. Truth, Syntax and Modality, Proceedings of the Temple University Conference on Alternative Semantics, Edited by Hugues Leblanc, Studies in Logic and the Foundations of Mathematics, Vol. 68, North-Holland Publishing Company, Amsterdam and London1973, Pp. 274–293. [REVIEW]Melvin Fitting - 1977 - Journal of Symbolic Logic 42 (2):316.
  37.  3
    Giorgio Israel (General Editor). Correspondence of Luigi Cremona (1830–1903): Conserved in the Department of Mathematics, “Sapienza” Università di Roma. 2 Volumes. 1,824 Pp., Bibl., Index. Turnhout: Brepols, 2017. €190 (Cloth). [REVIEW]Angelo Guerraggio - 2020 - Isis 111 (3):683-684.
  38.  15
    Gerneth Dal Charles. Generalization of Menger's Result on the Structure of Logical Formulas. Bulletin of the American Mathematical Society, Vol. 54 , Pp. 803–804. [REVIEW]Alonzo Church - 1948 - Journal of Symbolic Logic 13 (4):224-224.
  39.  4
    The Relation of Mathematics to General Formal Logic.Sophie Bryant - 1902 - Proceedings of the Aristotelian Society 2:105.
  40.  8
    E. P. Northrop. Fundamental Mathematics. Prepared for the General Course Mathematics 1 in the College. Second Edition, Planographed. The University of Chicago Bookstore, Chicago1946, Xi + 24 + 12 + 16 + 14 + 100 + 42 + 3 + 25 + 36 + 31 + 40 + 44 + 1 Pp. [REVIEW]J. C. Cooley - 1948 - Journal of Symbolic Logic 13 (3):142-143.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  41.  25
    Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW]I. Grattan-Guinness - 2011 - Logica Universalis 5 (1):21-73.
    A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  42.  8
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  43.  9
    Fitting Melvin. Fundamentals of Generalized Recursion Theory. Studies in Logic and the Foundations of Mathematics, Vol. 105. North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1981, Xx + 307 Pp. [REVIEW]Peter G. Hinman - 1986 - Journal of Symbolic Logic 51 (4):1078-1079.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  44.  7
    Toward a General Mathematical Theory of Behavior.Edward W. Barankin - 1971 - Annals of the Japan Association for Philosophy of Science 4 (1):1-34.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  45.  15
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  46.  43
    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, (...)
  47. 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 (...)
     
    Export citation  
     
    Bookmark   12 citations  
  48. 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  49.  17
    Turquette A. R.. A General Theory of K-Place Stroke Functions in 2-Valued Logic. Proceedings of the American Mathematical Society, Vol. 13 , Pp. 822–824. [REVIEW]Arto Salomaa - 1964 - Journal of Symbolic Logic 29 (3):143-143.
  50. Mathematical Logic and the Foundations of Mathematics: An Introductory Survey.G. T. Kneebone - 1963 - New York, NY, USA: 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.
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
1 — 50 / 1000