Search results for 'conventionalism in mathematics' (try it on Scholar)

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  1. P. Garavaso (2013). Hilary Putnam's Consistency Objection Against Wittgenstein's Conventionalism in Mathematics. Philosophia Mathematica 21 (3):279-296.score: 531.0
    Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can (...)
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  2. Pieranna Garavaso (1988). Wittgenstein's Philosophy of Mathematics: A Reply to Two Objections. Southern Journal of Philosophy 26 (2):179-191.score: 306.0
    This paper has two main purposes: first to compare Wittgenstein's views to the more traditional views in the philosophy of mathematics; second, to provide a general outline for a Wittgensteinian reply to two objections against Wittgenstein's account of mathematics: the objectivity objection and the consistency objections, respectively. Two fundamental thesmes of Wittgenstein's account of mathematics title the first two sections: mathematical propositions are rules and not descritpions and mathematics is employed within a form of life. Under (...)
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  3. E. Slowik (2003). Conventionalism in Reid's 'Geometry of Visibles'. Studies in History and Philosophy of Science Part A 34 (3):467-489.score: 218.0
    The subject of this investigation is the role of conventions in the formulation of Thomas Reid's theory of the geometry of vision, which he calls the 'geometry of visibles'. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid's 'geometry of visibles' and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the (...)
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  4. Peter Mittelstaedt (1977). Conventionalism in Special Relativity. Foundations of Physics 7 (7-8):573-583.score: 211.0
    Reichenbach, Grünbaum, and others have argued that special relativity is based on arbitrary conventions concerning clock synchronizations. Here we present a mathematical framework which shows that this conventionality is almost equivalent to the arbitrariness in the choice of coordinates in an inertial system. Since preferred systems of coordinates can uniquely be defined by means of the Lorentz invariance of physical laws irrespective of the properties of light signals, a special clock synchronization—Einstein's standard synchrony—is selected by this principle. No further restrictions (...)
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  5. Barry Smith (1976). Historicity, Value and Mathematics. In. In A. T. Tymieniecka (ed.), Ingardeniana. 219--239.score: 200.0
    At the beginning of the present century, a series of paradoxes were discovered within mathematics which suggested a fundamental unclarity in traditional mathemati­cal methods. These methods rested on the assumption of a realm of mathematical idealities existing independently of our thinking activity, and in order to arrive at a firmly grounded mathematics different attempts were made to formulate a conception of mathematical objects as purely human constructions. It was, however, realised that such formulations necessarily result in a (...) which lacks the richness and power of the old ‘platonistic’ methods, and the latter are still defended, in various modified forms, as embodying truths about self-existent mathematical entities. Thus there is an idealism-realism dispute in the philosophy of mathematics in some respects parallel to the controversy over the existence of the experiential world to the settle­ment of which lngarden devoted his life. The present paper is an attempt to apply Ingarden’s methods to the sphere of mathematical existence. This exercise will reveal new modes of being applicable to non-real objects, and we shall put forward arguments to suggest that these modes of being have an importance outside mathematics, especially in the areas of value theory and the ontology of art. (shrink)
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  6. Emily Grosholz (2007). Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford University Press.score: 188.0
    Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous.
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  7. Penelope Maddy (1997). Naturalism in Mathematics. Oxford University Press.score: 180.0
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both (...)
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  8. M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.score: 180.0
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual (...)
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  9. Michael Detlefsen (ed.) (1992). Proof and Knowledge in Mathematics. Routledge.score: 180.0
    Proof and Knowledge in Mathematics tackles the main problem that arises when considering an epistemology for mathematics, the nature and sources of mathematical justification. Focusing both on particular and general issues, these essays from leading philosophers of mathematics raise important issues for our current understanding of mathematics. Is mathematical justification a priori or a posteriori? What role, if any, does logic play in mathematical reasoning or inference? And how epistemologically important is the formalizability of proof? Michael (...)
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  10. Donald Gillies (ed.) (1992). Revolutions in Mathematics. Oxford University Press.score: 180.0
    Social revolutions--that is critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. But can the idea of revolutionary upheaval be extended to the world of ideas and theoretical debate? The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began in the United States in the mid-1970's as to whether the concept of revolution could (...)
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  11. Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.score: 176.0
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version (...)
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  12. Tomasz Bigaj (2003). The Indispensability Argument – a New Chance for Empiricism in Mathematics? Foundations of Science 8 (2):173-200.score: 176.0
    In recent years, the so-calledindispensability argument has been given a lotof attention by philosophers of mathematics.This argument for the existence of mathematicalobjects makes use of the fact, neglected inclassical schools of philosophy of mathematics,that mathematics is part of our best scientifictheories, and therefore should receive similarsupport to these theories. However, thisobservation raises the question about the exactnature of the alleged connection betweenexperience and mathematics (for example: is itpossible to falsify empirically anymathematical theorems?). In my paper I (...)
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  13. Larry Krasnoff (2012). Voluntarism and Conventionalism in Hobbes and Kant. Hobbes Studies 25 (1):43-65.score: 176.0
    Kant's relation to Hobbesian voluntarism has recently become a source of controversy for the interpretation of Kant's practical philosophy. Realist interpreters, most prominently Karl Ameriks, have attacked the genealogies of Kantian autonomy suggested by J. B. Schneewind and Christine Korsgaard as misleadingly voluntarist and unacceptably anti-realist. In this debate, however, there has been no real discussion of Kant's own views about Hobbes. By examining the relation of Hobbes' voluntarism to a kind of conventionalism, and through a reading of Kant's (...)
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  14. Jean Paul van Bendegem (2014). Inconsistency in Mathematics and the Mathematics of Inconsistency. Synthese 191 (13):3063-3078.score: 176.0
    No one will dispute, looking at the history of mathematics, that there are plenty of moments where mathematics is “in trouble”, when paradoxes and inconsistencies crop up and anomalies multiply. This need not lead, however, to the view that mathematics is intrinsically inconsistent, as it is compatible with the view that these are just transient moments. Once the problems are resolved, consistency (in some sense or other) is restored. Even when one accepts this view, what remains is (...)
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  15. B. Pourciau (2000). Intuitionism as a (Failed) Kuhnian Revolution in Mathematics. Studies in History and Philosophy of Science Part A 31 (2):297-329.score: 174.0
    In this paper it is argued, firstly, that Kuhnian revolutions in mathematics are logically possible, in the sense of not being inconsistent with the nature of mathematics; and, secondly, that Kuhnian revolutions are actually possible, in the sense that a Kuhnian paradigm for mathematics can be exhibited which would, if accepted by the mathematical community, produce a full Kuhnian revolution. These two arguments depend on first proving that a shift from a classical conception of mathematics to (...)
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  16. Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.score: 174.0
    In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations (...)
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  17. Dieter Lohmar (2012). Non-Language Thinking in Mathematics. Axiomathes 22 (1):109-120.score: 172.0
    After a brief outline of the topic of non-language thinking in mathematics the central phenomenological tool in this concern is established, i.e. the eidetic method. The special form of eidetic method in mathematical proving is implicit variation and this procedure entails three rules that are established in a simple geometrical example. Then the difficulties and the merits of analogical thinking in mathematics are discussed in different aspects. On the background of a new phenomenological understanding of the performance of (...)
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  18. Justin Clarke-Doane (forthcoming). Justification and Explanation in Mathematics and Morality. In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics. Oxford University Press.score: 170.0
    In an influential book, Harman writes, "In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles [1977, 9 – 10]." What is the epistemological relevance of this contrast? In this article, I argue that ethicists and philosophers of mathematics have misunderstood it. They have confused what I shall call the justificatory challenge for realism about an area, D (...)
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  19. Elijah Chudnoff (forthcoming). Intuition in Mathematics. In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.score: 169.3
    The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the main problem (...)
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  20. S. Awodey (1996). Structure in Mathematics and Logic: A Categorical Perspective. Philosophia Mathematica 4 (3):209-237.score: 168.0
    A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with (...)
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  21. Kenny Easwaran (2008). The Role of Axioms in Mathematics. Erkenntnis 68 (3):381 - 391.score: 168.0
    To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements that are used to guarantee the truth of theorems proved from them. However, this may neither be possible nor necessary, and it doesn’t seem to fit the historical facts. Instead, I argue that the role of axioms is to systematize uncontroversial facts that mathematicians can accept from (...)
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  22. Alexander Paseau (2005). Naturalism in Mathematics and the Authority of Philosophy. British Journal for the Philosophy of Science 56 (2):377-396.score: 168.0
    Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two (...)
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  23. Kajsa Bråting & Johanna Pejlare (2008). Visualizations in Mathematics. Erkenntnis 68 (3):345 - 358.score: 168.0
    In this paper we discuss visualizations in mathematics from a historical and didactical perspective. We consider historical debates from the 17th and 19th centuries regarding the role of intuition and visualizations in mathematics. We also consider the problem of what a visualization in mathematical learning can achieve. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. We emphasize that a visualization in mathematics should always be considered in its (...)
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  24. Markus Pantsar (2009). Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics. Dissertation, University of Helsinkiscore: 168.0
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established (...)
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  25. John Mumma & Marco Panza (2012). Diagrams in Mathematics: History and Philosophy. Synthese 186 (1):1-5.score: 168.0
    Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.
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  26. Andrew Arana (2009). Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW] Analysis 69:401-403.score: 168.0
    Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this “crisis” (...)
     
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  27. Charlotte Werndl (2009). Justifying Definitions in Mathematics—Going Beyond Lakatos. Philosophia Mathematica 17 (3):313-340.score: 168.0
    This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world justification, condition justification, and redundancy justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show how various kinds of (...)
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  28. W. W. Tait (2001). Beyond the Axioms: The Question of Objectivity in Mathematics. Philosophia Mathematica 9 (1):21-36.score: 168.0
    This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. (...)
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  29. John L. Bell (2004). Whole and Part in Mathematics. Axiomathes 14 (4):285-294.score: 168.0
    The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.
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  30. Jairo José Da Silva (2000). Husserl's Two Notions of Completeness: Husserl and Hilbert on Completeness and Imaginary Elements in Mathematics. Synthese 125 (3):417 - 438.score: 168.0
    In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures he gave in Göttingen in 1901 and other related texts of the same period, a problem that had occupied Husserl since the beginning of 1890, when he was planning a never published sequel to "Philosophie der Arithmetik" (1891). In order to solve the problem of imaginary entities Husserl introduced, independently of Hilbert, two notions of completeness (definiteness (...)
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  31. Angela Breitenbach (2013). Beauty in Proofs: Kant on Aesthetics in Mathematics. European Journal of Philosophy 22 (2).score: 168.0
    It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the (...)
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  32. Andrew Aberdein (2005). The Uses of Argument in Mathematics. Argumentation 19 (3):287-301.score: 168.0
    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 (...)
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  33. John P. Burgess (1992). How Foundational Work in Mathematics Can Be Relevant to Philosophy of Science. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:433 - 441.score: 168.0
    Foundational work in mathematics by some of the other participants in the symposium helps towards answering the question whether a heterodox mathematics could in principle be used as successfully as is orthodox mathematics in scientific applications. This question is turn, it will be argued, is relevant to the question how far current science is the way it is because the world is the way it is, and how far because we are the way we are, which is (...)
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  34. James Franklin (1996). Proof in Mathematics. Quakers Hill Press.score: 168.0
    A textbook on proof in mathematics, inspired by an Aristotelian point of view on mathematics and proof. It explains how to prove statements in mathematics, from evident premises. It deals with the proof of "all" statements, "some" statements, multiple quantifiers and mathematical induction.
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  35. Mary Leng (2011). Creation and Discovery in Mathematics. In John Polkinghorne (ed.), Meaning in Mathematics. Oup Oxford.score: 168.0
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  36. Pierre Cassou-Nogués (2006). Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics. Theoria 21 (1):89-104.score: 168.0
    This paper is concerned with Cavaillès’ account of “intuition” in mathematics. Cavaillès starts from Kant’s theory of constructions in intuition and then relies on various remarks by Hilbert to apply it to modern mathematics. In this context, “intuition” includes the drawing of geometrical figures, the use of algebraic or logical signs and the generation of numbers as, for example, described by Brouwer. Cavaillès argues that mathematical practice can indeed be described as “constructions in intuition” but that these constructions (...)
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  37. Joachim Frans & Erik Weber (2014). Mechanistic Explanation and Explanatory Proofs in Mathematics. Philosophia Mathematica 22 (2):231-248.score: 168.0
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does (...)
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  38. Adam Rieger (2003). Naturalism in Mathematics. [REVIEW] Philosophical Review 112 (3):425-427.score: 168.0
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both (...)
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  39. Neil Tennant (2000). What is Naturalism in Mathematics, Really?: A Critical Study of P. Maddy, Naturalism in Mathematics. [REVIEW] Philosophia Mathematica 8 (3):316-338.score: 168.0
    Review of PENELOPE MADDY. Naturalism in Mathematics. Oxford: Clarendon Press, 1997.
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  40. Ferdinando Arzarello, Valeria Andriano, Federica Olivero & Ornella Robutti (1998). Abduction and Conjecturing in Mathematics. Philosophica 61 (1):77-94.score: 168.0
    The logic of discovering and that of justifying have been a permanent source of debate in mathematics, because of their different and apparently contradictory features within the processes of production of mathematical sentences. In fact, a fundamental unity appears as soon as one investigates deeply the phenomenology of conjecturing and proving using concrete examples. In this paper it is shown that abduction, in the sense of Peirce, is an essential unifying activity, ruling such phenomena. Abduction is the major ingredient (...)
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  41. Abbas Edalat (1997). Domains for Computation in Mathematics, Physics and Exact Real Arithmetic. Bulletin of Symbolic Logic 3 (4):401-452.score: 168.0
    We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on (...)
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  42. Wataru Asanuma, A Defense of Platonic Realism In Mathematics: Problems About The Axiom Of Choice.score: 168.0
    The conflict between Platonic realism and Constructivism marks a watershed in philosophy of mathematics. Among other things, the controversy over the Axiom of Choice is typical of the conflict. Platonists accept the Axiom of Choice, which allows a set consisting of the members resulting from infinitely many arbitrary choices, while Constructivists reject the Axiom of Choice and confine themselves to sets consisting of effectively specifiable members. Indeed there are seemingly unpleasant consequences of the Axiom of Choice. The non-constructive nature (...)
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  43. Julie Davies (1998). Counting the Cost‐‐Monitoring Standards in Mathematics in Year 6: An Eight‐Year Cross‐Sectional Study. Educational Studies 24 (1):61-67.score: 168.0
    Summary The National Curriculum was introduced into British primary schools in 1989 to raise standards of attainment, especially in the basic skills of English and mathematics. Has this expensive innovation succeeded? This paper analyses the mathematics standards of eight cohorts of Year 6 children from five randomly selected primary schools within one Local Education Authority (n=1503) who had all done Mathematics 11 from 1989 to 1996. Examination of the means of the standardised mathematics scores for each (...)
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  44. Cody S. Ding, Kim Song & Lloyd I. Richardson (2006). Do Mathematical Gender Differences Continue? A Longitudinal Study of Gender Difference and Excellence in Mathematics Performance in the U.S. Educational Studies 40 (3):279-295.score: 168.0
    A persistent belief in American culture is that males both outperform and have a higher inherent aptitude for mathematics than females. Using data from two school districts in two different states in the United States, this study used longitudinal multilevel modeling to examine whether overall performance on standardized as well as classroom tests reveals a gender difference in mathematics performance. The results suggest that both male and female students demonstrated the same growth trend in mathematics performance (as (...)
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  45. Marcus Giaquinto (2011). Visual Thinking in Mathematics. OUP Oxford.score: 168.0
    Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual (...)
     
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  46. Mathieu Vidal (2014). The Defective Conditional in Mathematics. 24 (1-2):169-179.score: 168.0
    (2014). The defective conditional in mathematics. Journal of Applied Non-Classical Logics: Vol. 24, Three-Valued Logics and their Applications, pp. 169-179. doi: 10.1080/11663081.2014.911540.
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  47. Marcel Danesi (2013). A Semiotic Note on Accuracy and Precision in Mathematics. American Journal of Semiotics 28 (3/4):169 - 173.score: 168.0
    The concept of accuracy in mathematics is something that is rarely discussed. It is taken for granted, mainly because the various symbolic tools of the discipline, such as the digits and its equations, are meant to have a precise interpretation within the primary referential field. Yet, mathematics is full of inaccuracies and imprecise notions and techniques. The science of limits or the calculus, for example, is the science of imprecision, since it is based on the notions of “approximation”. (...)
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  48. Caroline Dunmore (1992). Meta-Level Revolutions in Mathematics. In Donald Gillies (ed.), Revolutions in Mathematics. Oxford University Press. 209--225.score: 168.0
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  49. C. Ulrich (2014). Issues Around Reflective Abstraction in Mathematics Education. Constructivist Foundations 9 (3):370-371.score: 168.0
    Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Cifarelli and Sevim’s analysis of Marie’s problem solving activity raises two questions for me. The first regards what Marie is reflectively abstracting: the use of the generic phrase her solution activity finesses a largely unarticulated disagreement in the mathematics education community about what the nature of actions are in (...)
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  50. Yuxin Zheng (1992). Non-Euclidean Geometry and Revolutions in Mathematics. In Donald Gillies (ed.), Revolutions in Mathematics. Oxford University Press. 169--182.score: 168.0
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