Results for 'Mathematics Philosophy'

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  1.  7
    The mathematical philosophy of Bertrand Russell: origins and development.Francisco A. Rodríguez-Consuegra - 1991 - Boston: Birkhäuser Verlag.
    Traces the development of British philosopher Russell's (1872-1970) ideas on mathematics from the 1890s to the publication of his Principles of mathematics in 1903. Draws from Russell's unpublished manuscripts, correspondence, and published works to point out the influence of Hegel, Cantor, Whitehead, Peano, and others. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
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  2.  5
    Mathematical philosophy.Charles Sanders Peirce - 1976 - The Hague: Humanities Press.
  3.  32
    Greek Mathematical Philosophy.Edward A. Maziarz - 1968 - New York: Ungar. Edited by Thomas Greenwood.
  4. The mathematical philosophy of Giuseppe peano.Hubert C. Kennedy - 1963 - Philosophy of Science 30 (3):262-266.
    Because Bertrand Russell adopted much of the logical symbolism of Peano, because Russell always had a high regard for the great Italian mathematician, and because Russell held the logicist thesis so strongly, many English-speaking mathematicians have been led to classify Peano as a logicist, or at least as a forerunner of the logicist school. An attempt is made here to deny this by showing that Peano's primary interest was in axiomatics, that he never used the mathematical logic developed by him (...)
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  5. Greek Mathematical Philosophy [by] Edward A. Maziarz [and] Thomas Greenwood.Edward A. Maziarz & Thomas Greenwood - 1968 - Ungar.
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  6.  18
    Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell.David DeVidi, Michael Hallett & Peter Clark (eds.) - 2011 - Dordrecht, Netherland: Springer.
    The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory (...)
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  7.  40
    Mathematics and Finance: Some Philosophical Remarks.Emiliano Ippoliti - 2021 - Topoi 40 (4):771-781.
    I examine the role that mathematics plays in understanding and modelling finance, especially stock markets, and how philosophy affects it. To this end, I explore how mathematics penetrates finance via physics, constructing a ‘financial physics’, and I outline the philosophical backgrounds of this process, in particular the ‘philosophy of equilibrium’ and that of critical points or ‘out-of-equilibrium’. I discuss the main characteristics and a few weaknesses of these mathematizations of financial systems, notably econometrics and econophysics, and (...)
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  8. Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
  9.  29
    Greek Mathematical Philosophy.Ian Mueller, Edward A. Maziarz & Thomas Greenwood - 1970 - Philosophical Review 79 (3):427.
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  10. Scientific Philosophy, Mathematical Philosophy, and All That.Hannes Leitgeb - 2013 - Metaphilosophy 44 (3):267-275.
    This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress.
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  11. The Mathematical Philosophy of Bertrand Russell: Origins and Development.Francisco A. Rodriguez-Consuegra - 1993 - Erkenntnis 39 (3):421-424.
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  12.  31
    Mathematical Category Theory and Mathematical Philosophy.F. William Lawvere - unknown
    Explicit concepts and sufficiently precise definitions are the basis for further advance of a science beyond a given level. To move toward a situation where the whole population has access to the authentic results of science (italics mine) requires making explicit some general philosophical principles which can help to guide the learning, development, and use of mathematics, a science which clearly plays a pivotal role regarding the learning, development and use of all the sciences. Such philosophical principles have not (...)
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  13.  17
    Mathematical Philosophy; a Study of Fate and Freedom.H. T. Costello - 1923 - Journal of Philosophy 20 (5):137-139.
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  14.  37
    Wittgenstein’s and Other Mathematical Philosophies.Hao Wang - 1984 - The Monist 67 (1):18-28.
    I construe mathematical philosophy not in the narrow sense of philosophy of mathematics but in a broad indefinite sense of different manners of giving mathematics a privileged place in the study of philosophy. For example, in one way or another, mathematics plays an important part in the philosophy of Plato, Descartes, Spinoza, Leibniz, and Kant. In contrast, history plays a central role in the philosophy of Vico, Hegel, and Marx. In more recent (...)
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  15. Introduction to mathematical philosophy.Bertrand Russell - 1920 - Revue de Métaphysique et de Morale 27 (2):4-5.
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  16.  10
    Greek Mathematical Philosophy. Edward A. Maziarz, Thomas Greenwood.H. Gericke - 1969 - Isis 60 (3):406-406.
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  17. Logic–MathematicsPhilosophy.Pavel Materna - 2010 - In Jaroslav Peregrin (ed.), Foundations of logic. Prague: Charles University in Prague/Karolinum Press.
  18.  93
    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 (...)
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  19. Mathematical Philosophy?Leon Horsten - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 73--86.
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  20. What is Mathematics, Really?Reuben Hersh - 1997 - New York: Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will (...)
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  21.  18
    Husserl and Mathematics.Mirja Hartimo - 2021 - New York, NY: Cambridge University Press.
    Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, (...)
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  22. Philosophical Papers: Volume 1, Mathematics, Matter and Method.Hilary Putnam (ed.) - 1979 - New York: Cambridge University Press.
    Professor Hilary Putnam has been one of the most influential and sharply original of recent American philosophers in a whole range of fields. His most important published work is collected here, together with several new and substantial studies, in two volumes. The first deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry; the second deals with the philosophy of language and mind. Volume one is now issued in a new (...)
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  23. 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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  24. Deleuze and the Mathematical Philosophy of Albert Lautman.Simon B. Duffy - 2009 - In Jon Roffe & Graham Jones (eds.), Deleuze’s Philosophical Lineage. Edinburgh University Press.
    In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon (...)
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  25. Visual thinking in mathematics: an epistemological study.Marcus Giaquinto - 2007 - New York: Oxford University Press.
    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 (...)
  26. Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
    This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.
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  27.  50
    Three views of logic: Mathematics, Philosophy, Computer Science.Donald W. Loveland, Richard E. Hodel & Susan G. Sterrett - 2014 - Princeton, New Jersey: Princeton University Press. Edited by Richard E. Hodel & Susan G. Sterrett.
    Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and (...)
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  28.  73
    Between Mathematics and Physics.Michael D. Resnik - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:369 - 378.
    Nothing has been more central to philosophy of mathematics than the distinction between mathematical and physical objects. Yet consideration of quantum particles shows the inadequacy of the popular spacetime and causal characterizations of the distinction. It also raises problems for an assumption used recently by Field, Hellman and Horgan, namely, that the mathematical realm is metaphysically independent of the physical one.
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  29.  11
    The Relevance of Mathematical Philosophy to the Teaching of Mathematics.Max Black - 1938 - S.N.
  30.  60
    Pluralism in Mathematics: A New Position in Philosophy of Mathematics.Michèle Friend - 2013 - Dordrecht, Netherland: Springer.
    The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. (...)
  31.  17
    Feferman on Foundations: Logic, Mathematics, Philosophy.Gerhard Jäger & Wilfried Sieg (eds.) - 2017 - Cham: Springer.
    This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic, but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With (...)
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  32.  20
    Concepts of Proof in Mathematics, Philosophy, and Computer Science.Peter Schuster & Dieter Probst (eds.) - 2016 - Boston: De Gruyter.
  33.  18
    Remarks on the foundations of mathematics.Ludwig Wittgenstein, G. E. M. Anscombe, Rush Rhees & G. H. von Wright - 1956 - Oxford,: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
    Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
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  34.  15
    Founding Mathematics on Semantic Conventions.Casper Storm Hansen - 2021 - Springer Verlag.
    This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops (...)
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  35. Kant’s Philosophy of Mathematics and the Greek Mathematical Tradition.Daniel Sutherland - 2004 - Philosophical Review 113 (2):157-201.
    The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...)
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  36. The Paradoxism in Mathematics, Philosophy, and Poetry.Florentin Smarandache - 2022 - Bulletin of Pure and Applied Sciences 41 (1):46-48.
    This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion (...)
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  37.  21
    Mathematics and the body: material entanglements in the classroom.Elizabeth De Freitas - 2014 - New York NY: Cambridge University Press. Edited by Nathalie Sinclair.
    This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.
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  38.  96
    What is dialectical philosophy of mathematics?Brendan Larvor - 2001 - Philosophia Mathematica 9 (2):212-229.
    The late Imre Lakatos once hoped to found a school of dialectical philosophy of mathematics. The aim of this paper is to ask what that might possibly mean. But Lakatos's philosophy has serious shortcomings. The paper elaborates a conception of dialectical philosophy of mathematics that repairs these defects and considers the work of three philosophers who in some measure fit the description: Yehuda Rav, Mary Leng and David Corfield.
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  39.  46
    Mathematics, Models and Zeno's Paradoxes.Joseph S. Alper & Mark Bridger - 1997 - Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that (...)
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  40. Godel's legacy in mathematical philosophy.Harvey Friedman - manuscript
    Gödel's definitive results and his essays leave us with a rich legacy of philosophical programs that promise to be subject to mathematical treatment. After surveying some of these, we focus attention on the program of circumventing his demonstrated impossibility of a consistency proof for mathematics by means of extramathematical concepts.
     
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  41.  18
    Some Recent Writings in the Philosophy of Mathematics.Adolf Grünbaum - 1951 - Review of Metaphysics 5 (2):281 - 292.
    Maziarz proposes to offer "a solution that meets the requirements of recent developments in mathematics" as well as to chart "the course of its historical development." The leitmotiv of his entire treatment is the doctrine of abstraction. Says he: "...mathematics...in common with all sciences...arises through the mental action of abstraction from sense data," and again, "pure mathematics is a speculative science which originates from the mental action of formal abstraction from things." More specifically, we are told that (...)
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  42.  41
    IX. Naturalizing mathematics and naturalizing ethics.Fabrice Pataut - 2011 - In Petrov V. (ed.), Ontological Landscapes: Recent Thought on Conceptual Interfaces between Science and Philosophy. Ontos. pp. 183.
    I offer several reasons for rejecting naturalism as a philosophical viewpoint or program envisaged for two paradigm cases: the case of mathematics and the case of ethics. Semantical, epistemological and metaphysical similarities between the two are investigated and assessed. I then offer a sketch of a different way of understanding the nature of mathematical difficulties and that of ethical puzzles.
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  43.  8
    The Relevance of Mathematical Philosophy to the Teaching of Mathematics.Charles A. Baylis - 1938 - Journal of Symbolic Logic 3 (2):88-89.
  44.  55
    Mathematics: The Language of Science?Mary Tiles - 1984 - The Monist 67 (1):3-17.
    Science has become, as all nonspecialists know to their cost, increasingly mathematical; science textbooks and research papers, even popularising articles in Scientific American, are littered with graphs, numbers, mathematical symbols and equations. This has prompted the question “What exactly is the function of mathematics in science?” For example, could one understand a theory such as Einstein’s theory of special relativity without having knowledge of any sophisticated mathematics?
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  45.  18
    Mathematics, Arts and Literature.Ferdinando Casolaro & Giovanna Della Vecchia - 2018 - Science and Philosophy 6 (2):177-186.
    This work, in continuity with the article published by Ferdinando Casolaro and Giovanna Della Vecchia in Vol 5, 2017 of this series, in which we noted that in the centuries since the eight century B.C. at the 13th century A.D. the evolution of Astronomy and historical events have influenced the development of Mathematics, intends to demonstrate how the Architecture and Literature of the following centuries have further conditioned the development of the sciences in Italy and, in particular, of (...), identifying the affinities and, in some cases, the coincidences between the different forms of thought that invite us to make a serious reflection on the uniqueness of culture. (shrink)
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  46. Emergence in Science and Philosophy: Introduction; Part I Introduction: General Perspectives; Part II Introduction: Self, Agency and Free Will; Part III Introduction: Physics, Mathematics, and the Special Sciences.Antonella Corradini & O'connor Thimothy - unknown
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  47. Natorp's mathematical philosophy of science.Thomas Mormann - 2022 - Studia Kantiana 20 (2):65 - 82.
    This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that (...)
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  48. Understanding, formal verification, and the philosophy of mathematics.Jeremy Avigad - 2010 - Journal of the Indian Council of Philosophical Research 27:161-197.
    The philosophy of mathematics has long been concerned with deter- mining the means that are appropriate for justifying claims of mathemat- ical knowledge, and the metaphysical considerations that render them so. But, as of late, many philosophers have called attention to the fact that a much broader range of normative judgments arise in ordinary math- ematical practice; for example, questions can be interesting, theorems important, proofs explanatory, concepts powerful, and so on. The as- sociated values are often loosely (...)
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  49.  14
    Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective.Jan von Plato - 1997 - Philosophical Quarterly 47 (186):122-125.
  50.  30
    A metaphysical foundation for mathematical philosophy.Wójtowicz Krzysztof & Skowron Bartłomiej - 2022 - Synthese 200 (4):1-28.
    Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable (...)
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