Related categories

139 found
Order:
1 — 50 / 139
  1. Commentary On: Begoña Carrascal's "The Practice of Arguing and the Arguments: Examples From Mathematics".Andrew Aberdein - 2013 - In Dima Mohammed & Marcin Lewinski (eds.), Virtues of argumentation: Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 22–25, 2013. OSSA.
  2. 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 (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  3. 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 mathematical practice. (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  4. The Dialectical Tier of Mathematical Proof.Andrew Aberdein - 2011 - In Frank Zenker (ed.), Argumentation: Cognition & Community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2011. OSSA.
    Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson’s account provides a compelling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to challenge. Hence much actual mathematical practice takes place in the dialectical tier.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  5. Observations on Sick Mathematics.Andrew Aberdein - 2010 - In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice. College Publications. pp. 269--300.
    This paper argues that new light may be shed on mathematical reasoning in its non-pathological forms by careful observation of its pathologies. The first section explores the application to mathematics of recent work on fallacy theory, specifically the concept of an ‘argumentation scheme’: a characteristic pattern under which many similar inferential steps may be subsumed. Fallacies may then be understood as argumentation schemes used inappropriately. The next section demonstrates how some specific mathematical fallacies may be characterized in terms of argumentation (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  6. Rationale of the Mathematical Joke.Andrew Aberdein - 2010 - In Alison Pease, Markus Guhe & Alan Smaill (eds.), Proceedings of AISB 2010 Symposium on Mathematical Practice and Cognition. AISB. pp. 1-6.
    A widely circulated list of spurious proof types may help to clarify our understanding of informal mathematical reasoning. An account in terms of argumentation schemes is proposed.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  7. Argumentation Schemes and Communities of Argumentational Practice.Andrew Aberdein - 2009 - In Juho Ritola (ed.), Argument Cultures: Proceedings of OSSA 2009. OSSA.
    Is it possible to distinguish communities of arguers by tracking the argumentation schemes they employ? There are many ways of relating schemes to communities, but not all are productive. Attention must be paid not only to the admissibility of schemes within a community of argumentational practice, but also to their comparative frequency. Two examples are discussed: informal mathematics, a convenient source of well-documented argumentational practice, and anthropological evidence of nonstandard reasoning.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  8. Mathematics and Argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.
    Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  9. Fallacies in Mathematics.Andrew Aberdein - 2007 - Proceedings of the British Society for Research Into Learning Mathematics 27 (3):1-6.
    This paper considers the application to mathematical fallacies of techniques drawn from informal logic, specifically the use of ”argument schemes’. One such scheme, for Appeal to Expert Opinion, is considered in some detail.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  10. Proofs and Rebuttals: Applying Stephen Toulmin's Layout of Arguments to Mathematical Proof.Andrew Aberdein - 2006 - In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005. Filosofia. pp. 11-23.
    This paper explores some of the benefits informal logic may have for the analysis of mathematical inference. It shows how Stephen Toulmin’s pioneering treatment of defeasible argumentation may be extended to cover the more complex structure of mathematical proof. Several common proof techniques are represented, including induction, proof by cases, and proof by contradiction. Affinities between the resulting system and Imre Lakatos’s discussion of mathematical proof are then explored.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  11. Introduction to the New Edition.Andrew Aberdein - 2006 - In The Elements: Books I-XIII by Euclid. Barnes & Noble.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  12. The Informal Logic of Mathematical Proof.Andrew Aberdein - 2006 - In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer Verlag. pp. 56-70.
    Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  13. Managing Informal Mathematical Knowledge: Techniques From Informal Logic.Andrew Aberdein - 2006 - Lecture Notes in Artificial Intelligence 4108:208--221.
    Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management of informal mathematical (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  14. The Uses of Argument in Mathematics.Andrew Aberdein - 2005 - Argumentation 19 (3):287-301.
    Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  15. The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Springer.
    Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  16. Advances in Experimental Philosophy of Logic and Mathematics.Andrew Aberdein & Matthew Inglis (eds.) - forthcoming - London: Bloomsbury Press.
  17. Editorial: Teaching and the Nature of Mathematics.Dennis Almeida & Paul Ernest - 1996 - Philosophy of Mathematics Education Journal 9.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  18. Jeremy Gray. Plato's Ghost: The Modernist Transformation of Mathematics. Princeton: Princeton University Press, 2008. Isbn 978-0-69113610-3. Pp. VIII + 515. [REVIEW]A. Arana - 2012 - Philosophia Mathematica 20 (2):252-255.
    Remove from this list   Direct download (9 more)  
     
    Export citation  
     
    My bibliography  
  19. The Changing Practices of Proof in Mathematics.Andrew Arana - forthcoming - Metascience:1-5.
  20. On the Depth of Szemerédi's Theorem.Andrew Arana - 2015 - Philosophia Mathematica 23 (2):163-176.
    Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case on which (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  21. L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.
    Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...)
    Remove from this list  
    Translate
      Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  22. Proof Theory in Philosophy of Mathematics.Andrew Arana - 2010 - Philosophy Compass 5 (4):336-347.
    A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel's incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  23. On Formally Measuring and Eliminating Extraneous Notions in Proofs.Andrew Arana - 2008 - Philosophia Mathematica 17 (2):208–219.
    Many mathematicians and philosophers of mathematics believe some proofs contain elements extraneous to what is being proved. In this paper I discuss extraneousness generally, and then consider a specific proposal for measuring extraneousness syntactically. This specific proposal uses Gentzen’s cut-elimination theorem. I argue that the proposal fails, and that we should be skeptical about the usefulness of syntactic extraneousness measures.
    Remove from this list   Direct download (9 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  24. Review of D. Corfield, Toward a Philosophy of Real Mathematics[REVIEW]Andrew Arana - 2007 - Mathematical Intelligencer 29 (2).
    Remove from this list  
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  25. The Interplay Between Mathematical Practices and Results.Mélissa Arneton, Amirouche Moktefi & Catherine Allamel-Raffin - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science after the Practice Turn in the Philosophy, History, and Social Studies of Science. New York - London: Routledge. pp. 269-276.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  26. Foundational Instances and Attention to Practices in the Philosophy of Contemporary Mathematics.Tatiana Arrigoni - 2003 - Rivista di Filosofia Neo-Scolastica 95 (2):199-232.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  27. The Relationship of Derivations in Artificial Languages to Ordinary Rigorous Mathematical Proof.J. Azzouni - 2013 - Philosophia Mathematica 21 (2):247-254.
    The relationship is explored between formal derivations, which occur in artificial languages, and mathematical proof, which occurs in natural languages. The suggestion that ordinary mathematical proofs are abbreviations or sketches of formal derivations is presumed false. The alternative suggestion that the existence of appropriate derivations in formal logical languages is a norm for ordinary rigorous mathematical proof is explored and rejected.
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  28. Review: Stewart Shapiro, Thinking About Mathematics. The Philosophy of Mathematics. [REVIEW]Mark Balaguer - 2002 - Bulletin of Symbolic Logic 8 (1):89-91.
  29. Do Mathematics Constitute a Scientific Continent?Aristides Baltas - 1995 - Neusis 3:97-108.
  30. Empiricism as a Historical Phenomenon of Philosophy of Mathematics.A. Barabashev - 1988 - Revue Internationale de Philosophie 42 (167):509-517.
  31. On the Impact of the World Outlook on Mathematical Creativity.A. G. Barabashev - 1988 - Philosophia Mathematica (1):1-20.
  32. Regularities and Modern Tendencies of the Development of Mathematics.A. G. Barabashev, S. S. Demidov & M. I. Panov - 1987 - Philosophia Mathematica (1):32-47.
  33. The Philosophy of Mathematics in U.S.S.R.Alexei G. Barabashev - 1986 - Philosophia Mathematica (1-2):15-25.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  34. Mathematical Jujitsu: Some Informal Thoughts About G�Del and Physics.John D. Barrow - 2000 - Complexity 5 (5):28-34.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  35. Review of David Corfield, Towards a Philosophy of Real Mathematics[REVIEW]Timothy Bays - 2004 - Notre Dame Philosophical Reviews 2004 (1).
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  36. The Philosophy of Mathematical Practice.JC Beall - 2010 - Australasian Journal of Philosophy 88 (2):376-376.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  37. Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-Nineteenth Century.Kajsa Bråting - 2012 - Foundations of Science 17 (4):301-320.
    In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. One example is (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  38. The Philosophy of Mathematical Practice.James Robert Brown - 2010 - International Journal of Philosophical Studies 18 (1):111 – 115.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  39. Review of D. Mac Kenzie, Mechanizing Proof: Computing, Risk, and Trust.Otávio Bueno & Jody Azzouni - 2005 - Philosophia Mathematica 13 (3):319-325.
  40. Accessibility of Reformulated Mathematical Content.Stefan Buijsman - forthcoming - Synthese:1-18.
    I challenge a claim that seems to be made when nominalists offer reformulations of the content of mathematical beliefs, namely that these reformulations are accessible to everyone. By doing so, I argue that these theories cannot account for the mathematical knowledge that ordinary people have. In the first part of the paper I look at reformulations that employ the concept of proof, such as those of Mary Leng and Ottavio Bueno. I argue that ordinary people don’t have many beliefs about (...)
    No categories
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  41. Mathematical Practice and Human Cognition.Bernd Buldt - unknown
    Frank Quinn of Jaffe-Quinn fame worked out the basics of his own account of how mathematical practice should be described and analyzed, partly by historical comparisons with 19th century mathematics, partly by an analysis of contemporary mathematics and its pedagogy. Despite his claim that for this task, "professional philosophers seem as irrelevant as Aristotle is to modern physics," this philosophy talk will provide a critical summary of his main observations and arguments. The goal is to inject some of Quinns remarks (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  42. Is Mathematics Problem Solving or Theorem Proving?Carlo Cellucci - 2017 - Foundations of Science 22 (1):183-199.
    The question that is the subject of this article is not intended to be a sociological or statistical question about the practice of today’s mathematicians, but a philosophical question about the nature of mathematics, and specifically the method of mathematics. Since antiquity, saying that mathematics is problem solving has been an expression of the view that the method of mathematics is the analytic method, while saying that mathematics is theorem proving has been an expression of the view that the method (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  43. Proofs, Mathematical Practice and Argumentation.Begoña Carrascal - 2015 - Argumentation 29 (3):305-324.
    In argumentation studies, almost all theoretical proposals are applied, in general, to the analysis and evaluation of argumentative products, but little attention has been paid to the creative process of arguing. Mathematics can be used as a clear example to illustrate some significant theoretical differences between mathematical practice and the products of it, to differentiate the distinct components of the arguments, and to emphasize the need to address the different types of argumentative discourse and argumentative situation in the practice. I (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  44. The Practice of Arguing and the Arguments: Examples From Mathematics.Begoῆa Carrascal - unknown
    In argumentation studies, almost all theoretical proposals are applied, in general, to the analysis and evaluation of written argumentative texts. I will consider mathematics to illustrate some differences between argumentative practice and the products of it, to emphasize the need to address the different types of argumentative discourse and argumentative situation. Argumentative practice should be encouraged when teaching technical subjects to convey a better understanding and to improve thought and creativity.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  45. Mathematics Dealing with 'Hypothetical States of Things'.Jessica Carter - 2014 - Philosophia Mathematica 22 (2):209-230.
    This paper takes as a starting point certain notions from Peirce's writings and uses them to propose a picture of the part of mathematical practice that consists of hypothesis formation. In particular, three processes of hypothesis formation are considered: abstraction, generalisation, and an abductive-like inference. In addition Peirce's pragmatic conception of truth and existence in terms of higher-order concepts are used in order to obtain a kind of pragmatic realist picture of mathematics.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  46. Artificial Languages in the Mathematics of Ancient China.Karine Chemla - 2006 - Journal of Indian Philosophy 34 (1-2):31-56.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  47. Patricia A. Blanchette. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 (Hbk). Pp. Xv + 256. [REVIEW]Roy T. Cook - 2013 - Philosophia Mathematica (1):nkt029.
  48. Corcoran Reviews Boute’s 2013 Paper “How to Calculate Proofs”.John Corcoran - 2014 - MATHEMATICAL REVIEWS 14:444-555.
    Corcoran reviews Boute’s 2013 paper “How to calculate proofs”. -/- There are tricky aspects to classifying occurrences of variables: is an occurrence of ‘x’ free as in ‘x + 1’, is it bound as in ‘{x: x = 1}’, or is it orthographic as in ‘extra’? The trickiness is compounded failure to employ conventions to separate use of expressions from their mention. The variable occurrence is free in the term ‘x + 1’ but it is orthographic in that term’s quotes (...)
    No categories
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  49. What Mathematical Cognition Could Tell Us About the Actual World.Sorin Costreie - 2012 - In Elsevier (ed.), Procedia Social and Behavioral Science 33. pp. 138-142.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  50. Arithmetic, Set Theory, Reduction and Explanation.William D'Alessandro - forthcoming - Synthese:1-31.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
1 — 50 / 139