Results for 'Mathematics'

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  1.  8
    Minimal Degrees of Unsolvability and the Full Approximation Construction.American Mathematical Society, Donald I. Cartwright, John Williford Duskin & Richard L. Epstein - 1975 - American Mathematical Soc..
    For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.
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  2.  55
    Foundations of Logic and Mathematics.Rudolf Carnap - 1937 - Chicago, IL, USA: U. Of Chicago P.
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  3.  74
    Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil.Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999 - American Mathematical Soc..
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...)
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  4. Does mathematics need new axioms.Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel - 1999 - Bulletin of Symbolic Logic 6 (4):401-446.
    Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, (...)
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  5. Professor, Water Science and Civil Engineering University of California Davis, California.A. Mathematical Model - 1968 - In Peter Koestenbaum (ed.), Proceedings. [San Jose? Calif.,: [San Jose? Calif.. pp. 31.
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  6. A Lattice of Chapters of Mathematics.Jan Mycielski, Pavel Pudlák, Alan S. Stern & American Mathematical Society - 1990 - American Mathematical Society.
     
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  7. Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
    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 (...)
  8.  33
    Kurt Gdel: Collected Works: Volume Iv: Selected Correspondence, a-G.Kurt Gdel & Stanford Unviersity of Mathematics - 1986 - Oxford, England: Clarendon Press.
    Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.
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  9.  60
    Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
    The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.
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  10. Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.George Lakoff & Rafael E. Núñez - 2000
  11. Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl.Paolo Mancosu & T. A. Ryckman - 2002 - Philosophia Mathematica 10 (2):130-202.
    Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered (...)
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  12.  48
    Paradoxes and Inconsistent Mathematics.Zach Weber - 2021 - New York, NY: Cambridge University Press.
    Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber (...)
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  13. Visualization in Logic and Mathematics.Paolo Mancosu - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Springer. pp. 13-26.
    In the last two decades there has been renewed interest in visualization in logic and mathematics. Visualization is usually understood in different ways but for the purposes of this article I will take a rather broad conception of visualization to include both visualization by means of mental images as well as visualizations by means of computer generated images or images drawn on paper, e.g. diagrams etc. These different types of visualization can differ substantially but I am interested in offering (...)
     
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  14.  28
    Why is There Philosophy of Mathematics at All?Ian Hacking - 2014 - New York: Cambridge University Press.
    This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary (...)
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  15. Revolutions in mathematics.Donald Gillies (ed.) - 1992 - New York: Oxford University Press.
    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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  16. The Order and Connection of Things.Are They Constructed Mathematically—Deductively - forthcoming - Kant Studien.
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  17.  98
    The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
    This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. (...)
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  18. Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
    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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  19. Can Mathematics Explain Physical Phenomena?Otávio Bueno & Steven French - 2012 - British Journal for the Philosophy of Science 63 (1):85-113.
    Batterman raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan. Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within (...)
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  20.  16
    Classification Theory: Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985.J. T. Baldwin & U. Workshop on Model Theory in Mathematical Logic - 1987 - Springer.
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  21.  83
    Reverse Mathematics in Bishop’s Constructive Mathematics.Hajime Ishihara - 2006 - Philosophia Scientiae:43-59.
    We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.
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  22.  45
    The applicability of mathematics in science: indispensability and ontology.Sorin Bangu - 2012 - New York: Palgrave-Macmillan.
    Suppose we are asked to draw up a list of things we take to exist. Certain items seem unproblematic choices, while others (such as God) are likely to spark controversy. The book sets the grand theological theme aside and asks a less dramatic question: should mathematical objects (numbers, sets, functions, etc.) be on this list? In philosophical jargon this is the ‘ontological’ question for mathematics; it asks whether we ought to include mathematicalia in our ontology. The goal of this (...)
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  23. Experimental Mathematics.Alan Baker - 2008 - Erkenntnis 68 (3):331-344.
    The rise of the field of “ experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and (...)
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  24.  50
    The Philosophy of Mathematics Education.Paul Ernest - 1991 - Falmer Press.
    Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.
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  25. Philosophy of Mathematics.Christopher Pincock - 2011 - In Steven French & Juha Saatsi (eds.), Continuum Companion to the Philosophy of Science. Continuum. pp. 314-333.
    For many philosophers of science, mathematics lies closer to logic than it does to the ordinary sciences like physics, biology and economics. While this view may account for the relative neglect of the philosophy of mathematics by philosophers of science, it ignores at least two pressing questions about mathematics that philosophers of science need to be able to answer. First, do the similarities between mathematics and science support the view that mathematics is, after all, another (...)
     
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  26. (1 other version)Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
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  27.  10
    Early writings in the philosophy of logic and mathematics.Edmund Husserl - 1993 - Boston: Kluwer Academic Publishers. Edited by Dallas Willard.
    This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...)
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  28. Mathematics without foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
  29. 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, (...)
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  30. Mathematics Intelligent Tutoring System.Nour N. AbuEloun & Samy S. Abu Naser - 2017 - International Journal of Advanced Scientific Research 2 (1):11-16.
    In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...)
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  31. The philosophy of mathematics: an introductory essay.Stephan Körner - 1960 - Mineola, N.Y.: Dover Publications.
    This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
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  32.  23
    Philosophy of mathematics.Stephen Francis Barker - 1964 - Englewood Cliffs, N.J.,: Prentice-Hall.
  33.  83
    Philosophy of Mathematics.Øystein Linnebo - 2017 - Princeton, NJ: Princeton University Press.
    Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of (...). Readers are introduced to all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. The book also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The exposition is always closely informed by ongoing research in the field and sometimes draws on the author’s own contributions to this research. This means that Gottlob Frege—a German mathematician and philosopher widely recognized as one of the founders of analytic philosophy—figures prominently in the book, both through his own views and his criticism of other thinkers. (shrink)
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  34.  95
    Mathematics has a front and a back.Reuben Hersh - 1991 - Synthese 88 (2):127 - 133.
    It is explained that, in the sense of the sociologist Erving Goffman, mathematics has a front and a back. Four pervasive myths about mathematics are stated. Acceptance of these myths is related to whether one is located in the front or the back.
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  35. Mathematics as a science of patterns: Ontology and reference.Michael Resnik - 1981 - Noûs 15 (4):529-550.
  36.  71
    Language, Logic, and Mathematics in Schopenhauer.Jens Lemanski (ed.) - 2020 - Basel, Schweiz: Birkhäuser.
    The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on (...)
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  37. Mathematics is megethology.David K. Lewis - 1993 - Philosophia Mathematica 1 (1):3-23.
    is the second-order theory of the part-whole relation. It can express such hypotheses about the size of Reality as that there are inaccessibly many atoms. Take a non-empty class to have exactly its non-empty subclasses as parts; hence, its singleton subclasses as atomic parts. Then standard set theory becomes the theory of the member-singleton function—better, the theory of all singleton functions—within the framework of megethology. Given inaccessibly many atoms and a specification of which atoms are urelements, a singleton function exists, (...)
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  38. Reverse Mathematics and Fully Ordered Groups.Reed Solomon - 1998 - Notre Dame Journal of Formal Logic 39 (2):157-189.
    We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).
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  39. Mathematics and indispensability.Elliott Sober - 1993 - Philosophical Review 102 (1):35-57.
    Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just (...)
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  40. Visualizing in Mathematics.Marcus Giaquinto - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 22-42.
    Visual thinking in mathematics is widespread; it also has diverse kinds and uses. Which of these uses is legitimate? What epistemic roles, if any, can visualization play in mathematics? These are the central philosophical questions in this area. In this introduction I aim to show that visual thinking does have epistemically significant uses. The discussion focuses mainly on visual thinking in proof and discovery and touches lightly on its role in understanding.
     
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  41. (1 other version)Philosophy of Mathematics and Natural Science.Hermann Weyl & Olaf Helmer - 1951 - British Journal for the Philosophy of Science 2 (7):257-260.
     
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  42. Explicit mathematics with the monotone fixed point principle. II: Models.Michael Rathjen - 1999 - Journal of Symbolic Logic 64 (2):517-550.
    This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications (Feferman's notion of set) possesses a least fixed point. To be more precise, the new (...)
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  43. Epistemology of mathematics: What are the questions? What count as answers?Stewart Shapiro - 2011 - Philosophical Quarterly 61 (242):130-150.
    A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietism. For this purpose the notion of (...)
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  44. Mathematics anxiety and mental arithmetic performance: An exploratory investigation.Mark H. Ashcraft & Michael W. Faust - 1994 - Cognition and Emotion 8 (2):97-125.
  45.  18
    When Grades Are High but Self-Efficacy Is Low: Unpacking the Confidence Gap Between Girls and Boys in Mathematics.Lysann Zander, Elisabeth Höhne, Sophie Harms, Maximilian Pfost & Matthew J. Hornsey - 2020 - Frontiers in Psychology 11:552355.
    Girls have much lower mathematics self-efficacy than boys, a likely contributor to the underrepresentation of women in STEM. To help explain this gender confidence gap, we examined predictors of mathematics self-efficacy in a sample of 1,007 9th graders aged 13–18 years (54.2% girls). Participants completed a standardized math test, after which they rated three indices of mastery: an affective component (state self-esteem), a meta-cognitive component (self-enhancement), and their prior math grade. Despite having similar grades, girls reported lower (...) self-efficacy and state self-esteem, and were less likely than boys to self-enhance in terms of performance. Multilevel multiple-group regression analyses showed that the affective mastery component explained girls’ self-efficacy while cognitive self-enhancement explained boys’. Yet, a chi-square test showed that both constructs were equally relevant in the prediction of girls’ and boys’ self-efficacy. Measures of interpersonal sources of self-efficacy were not predictive of self-efficacy after taking the other dimensions into account. Results suggest that boys are advantaged in their development of mathematics self-efficacy beliefs, partly due to more positive feelings and more cognitive self-enhancement following test situations. (shrink)
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  46. Plato's philosophy of mathematics.Paul Pritchard - 1995 - Sankt Augustin: Academia Verlag.
    Available from UMI in association with The British Library. ;Plato's philosophy of mathematics must be a philosophy of 4th century B.C. Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. The development of the post-Renaissance notion of number brought with it a different conception of what mathematics is, and (...)
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  47. Reflections on mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
    This paper contains answers to the following Five questions, posed by the editors are answered: (1) Why were you initially drawn to the foundations of mathematics and/or the philosophy of mathematics? (2) What example(s) from your work (or the work of others) illustrates the use of mathematics for philosophy? (3) What is the proper role of philosophy of mathematics in relation to logic, foundations of mathematics, the traditional core areas of mathematics, and science? (4) (...)
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  48.  86
    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 (...)
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  49.  74
    Logic and philosophy of mathematics in the early Husserl.Stefania Centrone - 2009 - New York: Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  50. How Mathematics Can Make a Difference.Sam Baron, Mark Colyvan & David Ripley - 2017 - Philosophers' Imprint 17.
    Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
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