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  1. Matrix models and poetic verses of the human mind.Matthew He - 2023 - New Jersey: World Scientific Publishing Co. Pte..
    In this multidisciplinary book, mathematician Matthew He provides integrative perspectives of algebraic biology, cognitive informatics, and poetic expressions of the human mind. Using classical Pythagorean Theorem and contemporary Category Theory, the proposed matrix models of the human mind connect three domains of the physical space of objective matters, mental space of subjective meanings, and emotional space of bijective modes; draws the connections between neural sparks and idea points, between synapses and idea lines, and between action potentials and frequency curves.
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  2. Artistic Mediation in Mathematized Phenomenology.Robert Prentner & Shanna Dobson - manuscript
    Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at the same time, well-defined, (...)
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  3. Advances in Experimental Philosophy of Logic and Mathematics: A. Aberdein and M. Inglis, editors, London: Bloomsbury Academic, 2019. 291 pp. $28.76. ISBN 978-1-3500-3902-5.Yuri Sato - 2021 - History and Philosophy of Logic 43 (3):305-307.
    This book is a collection of articles on research that attempts to connect logic and mathematics with empirical and cognition. There have been various such a...
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  4. Salvatore Florio* and Øystein Linnebo**. The Many and the One. A Philosophical Study of Plural Logic.Francesca Boccuni - 2022 - Philosophia Mathematica 30 (3):369-381.
    1. OverviewSeveral natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages can contain singular forms of reference and quantification, as in, e.g., ‘Cecilia is Italian’ and ‘There is a basket of apples on the counter’. But they can contain also plural forms of reference and quantification, as in, e.g., ‘Cecilia and Francesca met in Cathedral Square’ and ‘There are some apples on the counter’. Famously, some sentences in natural language containing (...)
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  5. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
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  6. El Programa original de David Hilbert y el Problema de la Decibilidad.Franklin Galindo & Ricardo Da Silva - 2017 - Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 37 (1):1-23.
    En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...)
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  7. Critical Studies/Book Reviews.Juliette Kennedy - forthcoming - Philosophia Mathematica.
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  8. Critical Studies/Book Reviews.Chris Scambler - forthcoming - Philosophia Mathematica.
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  9. The Curious Neglect of Geometry in Modern Philosophies of Mathematics.Siavash Shahshahani - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and Their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 379-389.
    From ancient times to 19th century geometryGeometry symbolized the essence of mathematical thinking and method, but modern philosophy of mathematics seems to have marginalized the philosophical status of geometryGeometry. The roots of this transformation will be sought in the ascendance of logical foundations in place of intuitive primacy as the cornerstone of mathematical certainty in the late 19th century. Nevertheless, geometry and geometrical thinking, in multiple manifestations, have continued to occupy a central place in the practice of mathematics proper. We (...)
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  10. Applying Mathematics: Immersion, Inference, Interpretation.Otávio Bueno & Steven French - 2018 - Oxford, England: Oxford University Press.
    How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made (...)
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  11. Counting Composites.Jonathan D. Payton - 2022 - Australasian Journal of Philosophy 100 (4):695-710.
    I defend the thesis that Composition Entails Identity (CEI): that is, a whole is identical to all of its parts, taken together. CEI seems to be inconsistent, since it seems to require that the parts of a whole possess incompatible number properties (for instance, being one thing and being many things). I show that these number properties are, in fact, compatible.
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  12. Philosophische Notizbücher, Band 2: Zeiteinteilung (Maximen) I und II / Philosophical Notebooks, Volume 2: Time Management (Maxims) I and II, edited by Eva-Maria Engelen, translated by Merlin Carl, Berlin (De Gruyter) 2020.Kurt Gödel (ed.) - 2020 - Berlin: De Gruyter.
    Volume 2 contains both notebooks of "Time Management (Max) I and II" and thereby Gödel’s applied individual ethics, which he received among others through his teacher Heinrich Gomperz. Gödel thus incorporates the ethical ideal of self-perfection into his opus. The volume is prefaced by an introduction to relevant considerations from the ethics of the Stoics as well as ancient dietetics, which provide the philosophical background to understand Gödel’s approach. In addition, editor Eva-Maria Engelen presents how this fits into the context (...)
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  13. Hilbert's Metamathematical Problems and Their Solutions.Besim Karakadilar - 2008 - Dissertation, Boston University
    This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily (...)
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  14. Review of Andrew Aberdein and Matthew Inglis (eds), Advances in Experimental Philosophy of Logic and Mathematics: New York: Bloomsbury Academic Publishers, 2019, 296 pages, $114. [REVIEW]Mark Zelcer - 2020 - Philosophia 48 (3):1283-1287.
  15. The Language Essence of Rational Cognition with some Philosophical Consequences.Boris Culina - 2021 - Tesis (Lima) 14 (19):631-656.
    The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.
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  16. Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  17. Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Marcus Rossberg & Philip A. Ebert (eds.), Abstractionism.
  18. Demostraciones «tópicamente puras» en la práctica matemática: un abordaje elucidatorio.Guillermo Nigro Puente - 2020 - Dissertation, Universidad de la República Uruguay
  19. গণিত দর্শন Gonit Dorshon.Avijit Lahiri - manuscript
    This article, written in Bengali ('Gonit Dorshon' means `philosophy of mathematics' ), briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in (...)
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  20. Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  21. Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium.Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.) - 2019 - Berlin, Boston: De Gruyter.
    The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea of an assertion sign. The contributions (...)
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  22. 关于在柴廷、维特根斯坦、霍夫施塔特、沃尔珀特、多里亚、达科斯塔、戈德尔、西尔、罗迪赫、贝托、弗洛伊德、贝托、弗洛伊德、莫亚尔-沙罗克和亚诺夫斯基.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    人们普遍认为,不可能性、不完整性、不一致性、不可度、随机性、可预见性、悖论、不确定性和理性极限是完全不同的科学物理或数学问题,在常见。我认为,它们主要是标准的哲学问题(即语言游戏),这些问题大多在80 多年前由维特根斯坦解决。 -/- "在这种情况下,我们'想说'当然不是哲学,而是它的原材料。因此,例如,数学家倾向于对数学事实的客观性和现实性说的,不是数学哲学,而是哲学处理的东西。维特根斯坦 PI 234 -/- "哲学家们经常看到科学的方法,他们不可抗拒地试图以科学的方式提问和回答问题。这种倾向是形而上学的真正源泉,将哲学家带入完全的黑暗之中。 维特根斯坦 -/- 我简要地总结了现代两位最杰出的学生路德维希·维特根斯坦和约翰·西尔关于故意的逻辑结构(思想、语言、行为)的一些主要发现,作为我的起点Wittgenstein 的基本发现——所有真正的"哲学"问题都是相同的——关于在特定上下文中如何使用语言的困惑,因此所有解决方案都是一样的——研究如何在相关上下文中使用语言,使其真实性条件(满意度或 COS 条件)是明确的。基本问题是,人们可以说什么,但一个人不能意味着(状态明确COS)任何任意的话语和意义只有在非常具体的上下文中才可能。 -/- 在两种思想体系的现代视角(被推广为"思维快,思维慢")的框架内,我从维特根斯坦人的角度剖析了一些主要评论员关于这些问题的一些著作,并采用了一个新的表意向性和新的双系统命名法。 我表明,这是一个强大的启发式描述这些假定的科学,物理或数学问题的真实性质,这是真正最好的处理作为标准哲学问题,如何使用语言(语言游戏在维特根斯坦的术语)。 -/- 我的论点是,这里突出特征的意向表(理性、思想、思想、语言、个性等)或多或少地准确地描述了,或者至少作为启发式,我们思考和行为的方式,所以它包含不只是哲学和心理学,但其他一切(历史,文学,数学,政治等) 。特别要注意,我(以及西尔、维特根斯坦和其他人)认为,故意和理性包括有意识的审议语言系统2和无意识的自动预语言系统1行为或反射。 .
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  23. Kurt Vogel: Kleinere Schriften zur Geschichte der Mathematik (ed. Menso Folkerts). (Boethius, Texte und Abhandlungen zur Geschichte der exakten Wissenschaften, 20.) Pp. xlvii + 413; vii + 414–884; illustrations. Stuttgart: Franz Steiner, 1988. Paper, DM 150. [REVIEW]Ivor Bulmer-Thomas - 1990 - The Classical Review 40 (1):190-190.
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  24. James Robert Brown. Philosophy of mathematics, an introduction to the world of proofs and pictures. Routledge, 1999, vii + 215 pp. [REVIEW]Janet Folina - 2003 - Bulletin of Symbolic Logic 9 (4):504-506.
  25. Visualization, Explanation and Reasoning Styles in Mathematics.Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.) - 2005 - Springer.
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  26. Concept and Formalization of Constellatory Self-Unfolding: A Novel Perspective on the Relation between Quantum and Relativistic Physics.Albrecht von Müller & Elias Zafiris - 2018 - Cham: Springer.
    This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time functions (...)
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  27. Deleuze and the conceptualizable character of mathematical theories.Simon B. Duffy - 2017 - In Nathalie Sinclair & Alf Coles Elizabeth de Freitas (ed.), What is a Mathematical Concept? Cambridge University Press.
    To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...)
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  28. Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective.Lawrence Sklar & Jan von Plato - 1994 - Journal of Philosophy 91 (11):622.
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  29. The Modern Aspect of Mathematics. Lucienne Félix, Julius H. Hlavaty, Francille H. Hlavaty. [REVIEW]Karl Menger - 1962 - Philosophy of Science 29 (1):95-96.
  30. The Rainbow, from Myth to Mathematics. Carl B. Boyer. [REVIEW]Oystein Ore - 1960 - Philosophy of Science 27 (2):207-208.
  31. Essay Review: Islamic Mathematics: The Muslim Contribution to Mathematics.David A. King - 1979 - History of Science 17 (4):295-296.
  32. Revisiting the reliability of published mathematical proofs: where do we go next?Joachim Frans & Laszlo Kosolosky - 2014 - Theoria 29 (3):345-360.
    Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several (...)
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  33. Jiri Hudecek, Reviving Ancient Chinese Mathematics: Mathematics, History and Politics in the Work of Wu Wen-Tsun. New York: Routledge, 2014. Pp. xii + 210. ISBN 978-0-4157-0296-6. £90.00. [REVIEW]Ubiratan D'Ambrosio - 2016 - British Journal for the History of Science 49 (1):143-144.
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  34. The Mathematical Intelligencer Flunks the Olympics.Alexander E. Gutman, Mikhail G. Katz, Taras S. Kudryk & Semen S. Kutateladze - 2017 - Foundations of Science 22 (3):539-555.
    The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and (...)
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  35. Counting on Strong Composition as Identity to Settle the Special Composition Question.Joshua Spencer - 2017 - Erkenntnis 82 (4):857-872.
    Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...)
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  36. Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  37. Category Theory and Indefinite Extensibility.Hasen Khudairi - manuscript
    This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in the category of sets is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of (...)
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  38. A process oriented definition of number.Rolfe David - manuscript
    In this paper Russell’s definition of number is criticized. Russell’s assertion that a number is a particular kind of set implies that number has the properties of a set. It is argued that this would imply that a number contains elements and that this does not conform to our intuitive notion of number. An alternative definition is presented in which number is not seen as an object, but rather as a process and is related to the act of counting and (...)
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  39. The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly finite world (...)
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  40. The Physicalization of Mathematics.Peter Milne - 1994 - British Journal for the Philosophy of Science 45 (1):305-340.
  41. Review article. Ontology, logic, and mathematics.J. Folina - 2000 - British Journal for the Philosophy of Science 51 (2):319-332.
  42. Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures James Robert Brown. [REVIEW]Thomas Hofweber - 2001 - British Journal for the Philosophy of Science 52 (2):413-416.
  43. The Fourth Dimension. [REVIEW]C. H. Hinton - 1905 - Ancient Philosophy (Misc) 15:310.
  44. La mathématique. Philosophie-enseignement. [REVIEW]C. A. Laisant - 1899 - Ancient Philosophy (Misc) 9:158.
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  45. Die Mathematik die Fackelträgerin einer neuen Zeit. [REVIEW]C. Dillmann - 1890 - Ancient Philosophy (Misc) 1:617.
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  46. ermann von Helmholtz's Untersuchungen über die Grundlagen der Mathematik und Mechanik. [REVIEW]Leo Koenigsberger - 1895 - Ancient Philosophy (Misc) 6:608.
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  47. A Budget of Paradoxes. [REVIEW]Augustus De Morgan - 1915 - Ancient Philosophy (Misc) 25:319.
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  48. The Philosophy of Mathematics.Auguste Comte - 1851 - Harper.
    This collection of literature attempts to compile many of the classic works that have stood the test of time and offer them at a reduced, affordable price, in an attractive volume so that everyone can enjoy them.
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  49. The Common Sense of the Exact Sciences. Edited, and with a Pref. By Karl Pearson; Newly Edited and with an Introd. By James R. Newman; Pref. By Bertrand Russell.William Kingdon Clifford, James Roy Newman & Karl Pearson - 1946 - Knopf.
  50. The Common Sense of the Exact Sciences.William Kingdon Clifford, Karl Pearson & Richard Charles Rowe - 1885 - Kegan, Paul, Trench.
    "Clifford was famous for his public lectures on physics and math and ethics because he explained complex things with easily understood, concrete examples. As you read through his clear, simple explanations of the true bases of number, algebra and geometry you will find yourself getting angry and saying "Why the hell wasn't I taught math this way?" and "Do math ed professors know so little mathematics that they have never heard of Clifford.?" Clifford was destined to be England's Einstein until (...)
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1 — 50 / 3885