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  1. Symbolic Logic.Dale Jacquette - 2001
  2. Simple Logic.Daniel Bonevac - 1998 - Oup Usa.
    Simple Logic succeeds in conveying the standard topics in introductory logic with easy-to-understand explanations of rules and methods, whilst featuring a multitude of interesting and relevant examples drawn from both literary texts and contemporary culture.
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  3. Automated Deduction--Cade-19 19th International Conference on Automated Deduction, Miami Beach, Fl, Usa, July 28-August 2, 2003 : Proceedings. [REVIEW]Franz Baader - 2003
  4. A Structural Account of Mathematics.Charles S. Chihara - 2003 - Oxford University Press UK.
    Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented (...)
  5. Pappus of Alexandria and the Mathematics of Late Antiquity.Serafina Cuomo - 2000 - Cambridge University Press.
    This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. An important first chapter looks at the mathematicians of the period and how mathematics was perceived by people at large. The central chapters of the book analyse sections of the Collection, identifying features typical of Pappus's mathematical practice. The final chapter draws (...)
  6. The Philosophy of Mathematics.W. D. Hart (ed.) - 1996 - Oxford University Press.
    This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, (...)
  7. Degrees of Unsolvability: Local and Global Theory.M. Lerman - 1983 - Springer Verlag.
  8. Computer Science Logic.Dirk van Dalen & Marc Bezem (eds.) - 1997 - Springer.
  9. Converging Realities: Toward a Common Philosophy of Physics and Mathematics.Roland Omnès - 2004 - Princeton University Press.
    The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject.
  10. Non-Standard Logics for Automated Reasoning.Philippe Smets (ed.) - 1988 - Academic Press.
    Although there are a few books available that give brief surveys of a variety of nonstandard logics, there is a growing need for a critical presentation providing both a greater depth and breadth of insight into these logics. This book assembles a wider and deeper view of the many potentially applicable logics. Three appendixes provide short tutorials on classical logic and modal logics, and give a brief introduction to the existing literature on the logical aspects of probability theory. These tutorials (...)
  11. Proofs and Fundamentals: A First Course in Abstract Mathematics.Ethan D. Bloch - 2000 - Birkhäuser.
    The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
  12. Moderate Realism and its Logic.D. W. Mertz - 1996 - Yale University Press.
    Instance ontology, or particularism—the doctrine that asserts the individuality of properties and relations—has been a persistent topic in Western philosophy, discussed in works by Plato and Aristotle, by Muslim and Christian scholastics, and by philosophers of both realist and nominalist positions. This book by D. W. Mertz is the first sustained analysis that applies the rules and systems of mathematics and logic to instance ontology in order to argue for its validity and for its problem-solving capacities and to associate it (...)
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  13. Against the Realisms of the Age.B. H. Slater - 1998
  14. Methods of Logic.Willard Van Orman Quine - 1950 - Harvard University Press.
  15. An Introduction to Gödel's Theorems.Peter Smith - 2007 - Cambridge University Press.
    In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the (...)
  16. Mathematics, a Concise History and Philosophy.W. S. Anglin - 1994 - Springer.
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures (...)
  17. 100% Mathematical Proof.Rowan Garnier & John Taylor - 1996
  18. Logic.Paul Tomassi - 1999 - Routledge.
    Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, _Logic_ introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the (...)
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  19. The Laboratory of the Mind: Thought Experiments in the Natural Sciences.James Robert Brown - 1991 - Routledge.
    Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend (...)
  20. Meaning and Structure Structuralism of Analytic Philosophers.Jaroslav Peregrin - 2001
  21. Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume.Maria Zack & Dirk Schlimm (eds.) - 2020 - New York, USA: Springer Verlag.
    This volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era. -/- The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy (...)
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  22. Mathematics and Mind.Alexander George (ed.) - 1994 - Oxford University Press.
    Those inquiring into the nature of mind have long been interested in the foundations of mathematics, and conversely this branch of knowledge is distinctive in that our access to it is purely through thought. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. The link between conceptions of mind and of mathematics has been (...)
  23. How to Prove It: A Structured Approach.Daniel J. Velleman - 2006 - Cambridge University Press.
    Geared to preparing students to make the transition from solving problems to proving theorems, this text teachs them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition (...)
  24. The Elements of Deductive Logic.Thomas Fowler - 1867
  25. What is a Number?: Mathematical Concepts and Their Origins.Robert Tubbs - 2008 - Johns Hopkins University Press.
    Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of topics (...)
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  26. The Principles of Mathematics.Bertrand Russell - 1903 - Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
  27. What is Mathematics, Really?Reuben Hersh - 1997 - 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 continue to exist (...)
  28. Introduction to the Foundations of Mathematics.Raymond Louis Wilder - 1952 - R. E. Krieger Pub. Co..
  29. Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education.Sal Restivo, Jean Paul Van Bendegem & Roland Fischer (eds.) - 1993 - State University of New York Press.
    An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...)
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  30. Introduction to Axiomatic Set Theory.Gaisi Takeuti - 1971 - New York: Springer Verlag.
    In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in (...)
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  31. Godel's Theorem in Focus.S. G. Shanker (ed.) - 1990 - Routledge.
    A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
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  32. To Infinity and Beyond: A Cultural History of the Infinite.Eli Maor - 1987 - Princeton University Press.
    Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes (...)
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  33. Meta-Logics and Logic Programming.Krzysztof R. Apt & Franco Turini - 1995
  34. Trees: National Champions.Barbara Bosworth & Roger Conover - 2005 - MIT Press.
  35. Deductive Logic in Natural Language.Douglas Cannon - 2002 - Broadview Press.
    This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
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  36. Euclid in the Rainforest: Discovering Universal Truth in Logic and Math.Joseph Mazur - 2005 - Pi Press.
    Euclid in the Rainforest combines the literary with the mathematical to explore logic--the one indispensable tool in man's quest to understand the world. Mazur argues that logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.
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  37. Descartes' Dream: The World According to Mathematics.Philip J. Davis - 1986 - Dover Publications.
    Philosopher Rene Descartes visualized a world unified by mathematics, in which all intellectual issues could be resolved rationally by local computation. This series of provocative essays takes a modern look at the seventeenth-century thinker’s dream, examining the physical and intellectual influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the effectiveness of these applications; and how applied mathematics constrain lives and transform perceptions of reality. Highly suitable for (...)
  38. How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics.William Byers - 2010 - Princeton University Press.
    "--David Ruelle, author of "Chance and Chaos" "This is an important book, one that should cause an epoch-making change in the way we think about mathematics.
  39. Ce este matematica: Ghidul şcolar al înţelegerii conceptuale a matematicii.Catalin Barboianu - 2020 - Targu Jiu: PhilScience Press.
    Aceasta nu este o carte de matematică, ci una despre matematică, care se adresează elevului sau studentului, dar şi dascălului său, cu un scop cât se poate de practic, anume acela de a iniţia şi netezi calea către înţelegerea completă a matematicii predate în şcoală. Tradiţia predării matematicii într-o abordare preponderent procedural-formală a avut ca efect o viziune deformată a elevilor asupra matematicii, ca fiind ceva strict formal, instrumental şi calculatoriu. Pierzând contactul cu baza conceptuală a matematicii, elevii dezvoltă pe (...)
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  40. Non-Standard Analysis.A. Robinson - 1961 - North-Holland Publishing Co..
  41. Logic Programming and Non-Monotonic Reasoning Proceedings of the Second International Workshop.Luís Moniz Pereira & Anil Nerode - 1993
  42. A Bridge to Advanced Mathematics.Dennis Sentilles - 1975 - Baltimore: Williams & Wilkins.
  43. Introduction to Proof in Abstract Mathematics.Andrew Wohlgemuth - 1990 - Dover Publications.
    Originally published: Philadelphia: Saunders College Pub., c1990.
  44. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu - 1996 - Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...)
  45. Set Theory, Logic and Their Limitations.Moshe Machover - 1996 - Cambridge University Press.
    This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations.
  46. Realism in Mathematics.Penelope MADDY - 1990 - 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 of mathematical realism. (...)
  47. The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
    This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...
  48. The Magic of Numbers.Eric Temple Bell - 1946 - London: Mcgraw-Hill Book Company.
    It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how "number magic" has influenced religion, philosophy, science, and mathematics.
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  49. Proof and Other Dilemmas: Mathematics and Philosophy.Bonnie Gold & Roger A. Simons (eds.) - 2008 - Mathematical Association of America.
    This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to ...
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  50. Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Oxford University Press.
    In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...)
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