Results for 'Mathematical reasoning'

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  1. Mathematical Reasoning: Analogies, Metaphors, and Images.Lyn D. English (ed.) - 1997 - L. Erlbaum Associates.
    Presents the latest research on how reasoning with analogies, metaphors, metonymies, and images can facilitate mathematical understanding. For math education, educational psychology, and cognitive science scholars.
     
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  2. The Parallel Structure of Mathematical Reasoning.Andrew Aberdein - 2012 - In Alison Pease & Brendan Larvor (eds.), Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012. Society for the Study of Artificial Intelligence and the Simulation of Behaviour. pp. 7--14.
    This paper proposes an account of mathematical reasoning as parallel in structure: the arguments which mathematicians use to persuade each other of their results comprise the argumentational structure; the inferential structure is composed of derivations which offer a formal counterpart to these arguments. Some conflicts about the foundations of mathematics correspond to disagreements over which steps should be admissible in the inferential structure. Similarly, disagreements over the admissibility of steps in the argumentational structure correspond to different views about (...)
     
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  3. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value.John Corcoran - 1971 - Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a (...)
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  4.  69
    Peirce on the Role of Poietic Creation in Mathematical Reasoning.Daniel G. Campos - 2007 - Transactions of the Charles S. Peirce Society 43 (3):470 - 489.
    : C.S. Peirce defines mathematics in two ways: first as "the science which draws necessary conclusions," and second as "the study of what is true of hypothetical states of things" (CP 4.227–244). Given the dual definition, Peirce notes, a question arises: Should we exclude the work of poietic hypothesis-making from the domain of pure mathematical reasoning? (CP 4.238). This paper examines Peirce's answer to the question. Some commentators hold that for Peirce the framing of mathematical hypotheses requires (...)
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  5.  56
    Mathematical Reasoning: Induction, Deduction and Beyond.David Sherry - 2006 - Studies in History and Philosophy of Science Part A 37 (3):489-504.
    Mathematics used to be portrayed as a deductive science. Stemming from Polya, however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof and (...)
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  6.  10
    Deducing False Propositions From True Ideas: Nieuwentijt on Mathematical Reasoning.Sylvia Pauw - forthcoming - Synthese:1-19.
    This paper argues that, for Bernard Nieuwentijt, mathematical reasoning on the basis of ideas is not the same as logical reasoning on the basis of propositions. Noting that the two types of reasoning differ helps make sense of a peculiar-sounding claim Nieuwentijt makes, namely that it is possible to mathematically deduce false propositions from true abstracted ideas. I propose to interpret Nieuwentijt’s abstracted ideas as incomplete mental copies of existing objects. I argue that, according to Nieuwentijt, (...)
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  7.  54
    What Perception is Doing, and What It is Not Doing, in Mathematical Reasoning.Dennis Lomas - 2002 - British Journal for the Philosophy of Science 53 (2):205-223.
    What is perception doing in mathematical reasoning? To address this question, I discuss the role of perception in geometric reasoning. Perception of the shape properties of concrete diagrams provides, I argue, a surrogate consciousness of the shape properties of the abstract geometric objects depicted in the diagrams. Some of what perception is not doing in mathematical reasoning is also discussed. I take issue with both Parsons and Maddy. Parsons claims that we perceive a certain type (...)
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  8. Children's Mathematical Reasoning with the Turtle Metaphor.Douglas H. Clements & Julie Sarama - 1997 - In Lyn D. English (ed.), Mathematical Reasoning: Analogies, Metaphors, and Images. L. Erlbaum Associates. pp. 313--337.
     
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  9. Constructive Ambiguity in Mathematical Reasoning.E. R. Grosholz - 2005 - In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics. College Publications. pp. 1--23.
     
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  10.  20
    Sex Differences in Mathematical Reasoning Ability in Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes.Camilla Persson Benbow - 1988 - Behavioral and Brain Sciences 11 (2):169-183.
  11. Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338.John Corcoran - 2014 - MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted (...)
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  12.  6
    Agent Based Mathematical Reasoning.Christoph Benzmüller, Mateja Jamnik, Manfred Kerber & Volker Sorge - 1999 - Electronic Notes in Theoretical Computer Science, Elsevier 23 (3):21-33.
    In this contribution we propose an agent architecture for theorem proving which we intend to investigate in depth in the future. The work reported in this paper is in an early state, and by no means finished. We present and discuss our proposal in order to get feedback from the Calculemus community.
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  13. An Introduction to Mathematical Reasoning.Boris Iglewicz - 1973 - New York: Macmillan.
     
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  14.  12
    Reasoning with the Infinite: From the Closed World to the Mathematical Universe.Michel Blay - 1999 - University of Chicago Press.
    "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion. ...
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  15. Analogues of the Liar Paradox in Systems of Epistemic Logic Representing Meta-Mathematical Reasoning and Strategic Rationality in Non-Cooperative Games.Robert Charles Koons - 1987 - Dissertation, University of California, Los Angeles
    The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...)
     
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  16. An Introduction to Mathematical Reasoning: Lectures on Numbers, Sets, and Functions.Peter J. Eccles - 1997 - Cambridge University Press.
    The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of (...)
     
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  17. Mathematical Reasoning.C. Susan Robinson & John R. Hayes - 1978 - In Russell Revlin & Richard E. Mayer (eds.), Human Reasoning. Distributed Solely by Halsted Press. pp. 195.
  18.  6
    Evaluating Explanations of Sex Differences in Mathematical Reasoning Scores.Robert Rosenthal - 1988 - Behavioral and Brain Sciences 11 (2):207-208.
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    Arbitrary Reference in Mathematical Reasoning.Enrico Martino - 2001 - Topoi 20 (1):65-77.
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    Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice.Danielle Macbeth - 2012 - Philosophia Mathematica 20 (1):58-85.
    Throughout its long history, mathematics has involved the use ofsystems of written signs, most notably, diagrams in Euclidean geometry and formulae in the symbolic language of arithmetic and algebra in the mathematics of Descartes, Euler, and others. Such systems of signs, I argue, enable one to embody chains of mathematical reasoning. I then show that, properly understood, Frege’s Begriffsschrift or concept-script similarly enables one to write mathematical reasoning. Much as a demonstration in Euclid or in early (...)
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  21. Mathematical Reasoning and Heuristics.Carlo Cellucci & Donald Gillies (eds.) - 2005 - College Publications.
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  22.  9
    Alan Bundy. The Computer Modelling of Mathematical Reasoning. Academic Press, London Etc. 1983, Xiv + 322 Pp. [REVIEW]Vladimir Lifschitz - 1987 - Journal of Symbolic Logic 52 (2):555-557.
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    Sex-Related Differences in Precocious Mathematical Reasoning Ability: Not Illusory, Not Easily Explained.Camilla Persson Benbow - 1988 - Behavioral and Brain Sciences 11 (2):217-232.
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    Two Styles of Reasoning in Scientific Practices: Experimental and Mathematical Traditions.Mieke Boon - 2011 - International Studies in the Philosophy of Science 25 (3):255 - 278.
    This article outlines a philosophy of science in practice that focuses on the engineering sciences. A methodological issue is that these practices seem to be divided by two different styles of scientific reasoning, namely, causal-mechanistic and mathematical reasoning. These styles are philosophically characterized by what Kuhn called ?disciplinary matrices?. Due to distinct metaphysical background pictures and/or distinct ideas of what counts as intelligible, they entail distinct ideas of the character of phenomena and what counts as a scientific (...)
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  25.  90
    Method of Analysis: A Paradigm of Mathematical Reasoning?Jaakko Hintikka - 2012 - History and Philosophy of Logic 33 (1):49 - 67.
    The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are typically allowed only (...)
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  26.  70
    Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,.John Corcoran - 1971 - Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of the second kind--they (...)
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  27.  35
    Physical-Mathematical Reasoning: Galileo on the Extruding Power of Terrestrial Rotation.Maurice A. Finocchiaro - 2003 - Synthese 134 (1-2):217 - 244.
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    Don't Take Me Half the Way: On Berkeley on Mathematical Reasoning.David Sherry - 1993 - Studies in History and Philosophy of Science Part A 24 (2):207-225.
  29.  63
    Mathematical Reasoning Vs. Abductive Reasoning: A Structural Approach.Atocha Aliseda - 2003 - Synthese 134 (1-2):25 - 44.
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  30.  13
    Editorial: The Role of Reasoning in Mathematical Thinking.Kinga Morsanyi, Jérôme Prado & Lindsey E. Richland - 2018 - Thinking and Reasoning 24 (2):129-137.
    Research into mathematics often focuses on basic numerical and spatial intuitions, and one key property of numbers: their magnitude. The fact that mathematics is a system of complex relationships that invokes reasoning usually receives less attention. The purpose of this special issue is to highlight the intricate connections between reasoning and mathematics, and to use insights from the reasoning literature to obtain a more complete understanding of the processes that underlie mathematical cognition. The topics that are (...)
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  31.  11
    Paradoxes of Randomness and the Limitations of Mathematical Reasoning.Gregory Chaitin - 2002 - Complexity 7 (5):14-21.
  32. Sex Differences in Mathematical Reasoning Ability in Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes.C. Persson - 1988 - Behavioral and Brain Sciences 11:169-183.
     
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  33. Reasoning with Images in Mathematical Activity.Grayson H. Wheatley - 1997 - In Lyn D. English (ed.), Mathematical Reasoning: Analogies, Metaphors, and Images. L. Erlbaum Associates. pp. 281--297.
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    How to Run Algorithmic Information Theory on a Computer:Studying the Limits of Mathematical Reasoning.Gregory J. Chaitin - 1996 - Complexity 2 (1):15-21.
  35.  17
    Mathematical Reasoning with Higher-Order Anti-Unifcation.Markus Guhe, Alison Pease, Alan Smaill, Martin Schmidt, Helmar Gust, Kai-Uwe Kühnberger & Ulf Krumnack - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
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  36. Mathematical Reasoning and External Symbolic Systems.Catarina Dutilh Novaes - 2013 - Logique Et Analyse 56 (221):45-65.
  37.  12
    Advanced Mathematical Reasoning Ability: A Behavioral Genetic Perspective.Thomas J. Bouchard & Nancy L. Segal - 1990 - Behavioral and Brain Sciences 13 (1):191-192.
  38.  11
    Bundy Alan, Basin David, Hutter Dieter and Ireland Andrew. Rippling: Meta-Level Guidance for Mathematical Reasoning. Cambridge Tracts in Theoretical Computer Science, Vol. 56. Cambridge University Press, 2005, Xiv+ 202 Pp. [REVIEW]Joe Hurd - 2006 - Bulletin of Symbolic Logic 12 (3):498-499.
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  39.  9
    Sex Differences in Mathematical Reasoning Ability Among the Intellectually Talented: Further Thoughts.Camilla Persson Benbow - 1990 - Behavioral and Brain Sciences 13 (1):196-198.
  40.  10
    Preaxiomatic Mathematical Reasoning : An Algebraic Approach.Mary Leng - unknown
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  41.  9
    Mathematical Reasoning and Pragmatism in Peirce.Gerhard Heinzmann - 1994 - In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer Academic Publishers. pp. 297--310.
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  42.  5
    Development of Abstract Mathematical Reasoning: The Case of Algebra.Ana Susac, Andreja Bubic, Andrija Vrbanc & Maja Planinic - 2014 - Frontiers in Human Neuroscience 8.
  43.  6
    Genetic Influences on Sex Differences in Outstanding Mathematical Reasoning Ability.Ada H. Zohar - 1996 - Behavioral and Brain Sciences 19 (2):266-267.
  44.  6
    Spatial Visualization and Mathematical Reasoning Abilities.Sarah A. Burnett - 1988 - Behavioral and Brain Sciences 11 (2):187-188.
  45.  3
    Commentary on Camilla Persson Benbow (1988) Sex Differences in Mathematical Reasoning Ability in Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes. BBS 11: 169—232. [REVIEW]Hirnrinde Deserwachsenen Menschen - 1990 - Behavioral and Brain Sciences 13:1.
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  46.  6
    Space and Mathematical Reasoning.Leonard J. Russell - 1908 - Mind 17 (67):321-349.
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  47.  2
    A History of the Circle: Mathematical Reasoning and the Physical Universe. Ernest Zebrowski, Jr.Paul J. Nahin - 2001 - Isis 92 (1):130-130.
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  48.  3
    Review: Alan Bundy, The Computer Modelling of Mathematical Reasoning[REVIEW]Vladimir Lifschitz - 1987 - Journal of Symbolic Logic 52 (2):555-557.
  49.  3
    Neuropsychological Factors and Mathematical Reasoning Ability.Alan Searleman - 1988 - Behavioral and Brain Sciences 11 (2):209-210.
  50.  2
    Sex Differences in Mathematical Reasoning Ability: Let Me Count the Ways.Diane F. Halpern - 1988 - Behavioral and Brain Sciences 11 (2):191-192.
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