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  1. added 2017-11-12
    Iter Italicum and Leibniz/Giordano Correspondence.Francesco Tampoia - manuscript
    Letters exchanged by scientists are a crucial source by which to trace the process that accompanies their scientific evolution. In this paper -accomplished through a historical approach- I aim to throw new light on Leibniz's continuing interest in classical geometry and to stress the significance of his correspondence with the Italian mathematician Vitale Giordano.
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  2. added 2017-07-12
    Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...)
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  3. added 2016-12-08
    Consequence Operations Based on Hypergraph Satisfiability.Kolany Adam - 1997 - Studia Logica 58 (2):261-272.
    Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.
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  4. added 2016-12-08
    Colloquium on the Foundations of Mathematics, Mathematical Machines and Their Applications. [REVIEW]J. M. P. - 1966 - Review of Metaphysics 19 (4):821-821.
  5. added 2016-04-04
    A Numerical Approach for Solving Classes of Linear and Nonlinear Volterra Integral Equations by Chebyshev Polynomial.Mohammad Husein Saleh, Doaa Mohammad Shokry & Saada A. Rahman Abu Shammala - manuscript
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  6. added 2016-03-23
    Countable Fusion Not yet Proven Guilty: It May Be the Whiteheadian Account of Space Whatdunnit.G. Oppy - 1997 - Analysis 57 (4):249-253.
    I criticise a paper by Peter Forrest in which he argues that a principle of unrestricted countable fusion has paradoxical consequences. I argue that the paradoxical consequences that he exhibits may be due to his Whiteheadean assumptions about the nature of spacetime rather than to the principle of unrestricted countable fusion.
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  7. added 2015-11-22
    Reconfiguring the Centre: The Structure of Scientific Exchanges Between Colonial India and Europe.Dhruv Raina - 1996 - Minerva 34 (2):161-176.
    The “centre-periphery” relationship historically structured scientific exchanges between metropolis and province, between the fount of empire and its outposts. But the exchange, if regarded merely as a one-way flow of scientific information, ignores both the politics of knowledge and the nature of its appropriation. Arguably, imperial structures do not entirely determine scientific practices and the exchange of knowledge. Several factors neutralise the over-determining influence of politics—and possibly also the normative values of science—on scientific practice.In examining these four examples of Indian (...)
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  8. added 2015-07-07
    Some Uses of Dilators in Combinatorial Problems.V. Michele Abrusci - 1989 - Archive for Mathematical Logic 29 (2):85-109.
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  9. added 2015-06-15
    Berkeleys Kritik Am Leibniz´Schen Calculus.Horst Struve, Eva Müller-Hill & Ingo Witzke - 2015 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 46 (1):63-82.
    One of the most famous critiques of the Leibnitian calculus is contained in the essay “The Analyst” written by George Berkeley in 1734. His key argument is those on compensating errors. In this article, we reconstruct Berkeley's argument from a systematical point of view showing that the argument is neither circular nor trivial, as some modern historians think. In spite of this well-founded argument, the critique of Berkeley is with respect to the calculus not a fundamental one. Nevertheless, it highlights (...)
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  10. added 2015-05-25
    Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (2):222-223.
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  11. added 2015-05-23
    Numbers and Proofs.R. B. J. T. Allenby - 1997 - Copublished in North, South, and Central America by John Wiley & Sons.
    'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any (...)
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  12. added 2015-03-18
    Unbiased Stereology.Vyvyan Howard - 2004 - Garland Science/Bios Scientific Publishers.
    The Advanced Methods series is intented for advanced undergraduates, postgraduates and established research scientists. Titles in the series are designed to cover current important areas of research in life sciences, and include both theoretical background and detailed protocols. The aim is to give researchers sufficient theory, supported by references, to take the given protocols and adapt them to their particular experimental systems. Unbiased Stereology , Second Edition expands the comprehensive practical first edition guide to 3-D measurements in microscopy using stereological (...)
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  13. added 2014-04-16
    Special Systems Theory.Kent Palmer - manuscript
    A new advanced systems theory concerning the emergent nature of the Social, Consciousness, and Life based on Mathematics and Physical Analogies is presented. This meta-theory concerns the distance between the emergent levels of these phenomena and their ultra-efficacious nature. The theory is based on the distinction between Systems and Meta-systems (organized Openscape environments). We first realize that we can understand the difference between the System and the Meta-system in terms of the relationship between a ‘Whole greater than the sum of (...)
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  14. added 2014-04-01
    Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.
    Given a classical theory T, a Kripke model K for the language L of T is called T-normal or locally PA just in case the classical L-structure attached to each node of K is a classical model of T. Van Dalen, Mulder, Krabbe, and Visser showed that Kripke models of Heyting Arithmetic (HA) over finite frames are locally PA, and that Kripke models of HA over frames ordered like the natural numbers contain infinitely many PA-nodes. We show that Kripke models (...)
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  15. added 2014-03-29
    The Gödel Hierarchy and Reverse Mathematics.Stephen G. Simpson - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
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  16. added 2014-03-29
    Proceedings of International Conference on Challenges and Applications of Mathematics in Science and Technology: Camist, January 11-13, 2010. [REVIEW]Snehashish Chakraverty (ed.) - 2010 - Macmillan Publishers India.
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  17. added 2014-03-28
    Introduction to Proof in Abstract Mathematics.Andrew Wohlgemuth - 1990 - Dover Publications.
    Originally published: Philadelphia: Saunders College Pub., c1990.
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  18. added 2014-03-28
    A Bridge to Advanced Mathematics.Dennis Sentilles - 1975 - Baltimore: Williams & Wilkins.
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  19. added 2014-03-26
    Theory of Computation.George J. Tourlakis - 2012 - Wiley.
    In addition, this book contains tools that, in principle, can search a set of algorithms to see whether a problem is solvable, or more specifically, if it can be solved by an algorithm whose computations are efficient.
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  20. added 2014-03-26
    Introduction to Mathematical Logic.Michał Walicki - 2012 - World Scientific.
    A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness and (...)
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  21. added 2014-03-26
    Basic Stereology for Biologists and Neuroscientists.Mark J. West - 2012 - Cold Spring Harbor, New York.
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  22. added 2014-03-26
    Reason's Nearest Kin: Philosophies of Arithmetic From Kant to Carnap.Michael Potter - 2000 - Oxford University Press.
    This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.
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  23. added 2014-03-23
    Cohomology for Anyone.David A. Rabson, John F. Huesman & Benji N. Fisher - 2003 - Foundations of Physics 33 (12):1769-1796.
    Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods borrowed from algebraic topology. We now show what topology, which studies global properties of manifolds, has to do with crystallography. No mathematics is assumed beyond what the typical physics or crystallography student will have seen of group theory; in particular, the reader need not have (...)
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  24. added 2014-03-20
    Induction and Inductive Definitions in Fragments of Second Order Arithmetic.Klaus Aehlig - 2005 - Journal of Symbolic Logic 70 (4):1087 - 1107.
    A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way, that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on arithmetical formulae only affects the arithmetical consequences of these theories, whereas adding induction for arbitrary formulae (...)
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  25. added 2014-03-16
    Mathematical Contributions of Sir Asutosh Mookerjee: Contemporaneity and Relevance.Asutosh Mookerjee - 2009 - Jijnasa Pub. House.
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  26. added 2014-03-16
    Mathematical Analysis and Proof.David S. G. Stirling - 2009 - Horwood.
    This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have (...)
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  27. added 2014-03-16
    Computable Models.Raymond Turner - 2009 - Springer.
    Raymond Turner first provides a logical framework for specification and the design of specification languages, then uses this framework to introduce and study ...
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  28. added 2014-03-09
    Whole and Part in Mathematics.John L. Bell - 2004 - Axiomathes 14 (4):285-294.
    The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.
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  29. added 2014-03-08
    The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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  30. added 2014-03-01
    Reasoning About Truth in First-Order Logic.Claes Strannegård, Fredrik Engström, Abdul Rahim Nizamani & Lance Rips - 2013 - Journal of Logic, Language and Information 22 (1):115-137.
    First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when (...)
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  31. added 2013-12-27
    Quantitative Stereology.Ervin E. Underwood - 1970 - Reading, Mass., Addison-Wesley Pub. Co..
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  32. added 2013-12-09
    Solving Ordinary Differential Equations by Working with Infinitesimals Numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.
    There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...)
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  33. added 2013-12-02
    Q.Burkard Polster - 2004 - Walker & Co..
    Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras’s theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes’ method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and (...)
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  34. added 2013-10-30
    Review of N. Wildberger, Divine Proportions: Rational Trigonometry to Universal[REVIEW]James Franklin - 2006 - Mathematical Intelligencer 28 (3):73-74.
    Reviews Wildberger's account of his rational trigonometry project, which argues for a simpler way of doing trigonometry that avoids irrationals.
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  35. added 2013-10-30
    Review of D. Aeheson, 1089 and All That[REVIEW]John Mighton - 2004 - Mathematical Intelligencer 26 (2):70.
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  36. added 2013-04-20
    Review of G. Pólya, Mathematics and Plausible Reasoning, Vols. I and II.D. Dantzig - 1959 - Synthese 11 (4):353-358.
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  37. added 2013-01-11
    On the Roles of Types in Mathematics.N. G. de Bruijn - 1995 - In Philippe De Groote (ed.), The Curry-Howard Isomorphism. Academia. pp. 27-54.
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  38. added 2013-01-06
    A New Proof of the NP-Completeness of Visual Match.Ronald Rensink - manuscript
    A new proof is presented of Tsotsos' result that the VISUAL MATCH problem is NP-complete when no (high-level) constraints are imposed on the search space. Like the proof given by Tsotsos, it is based on the polynomial reduction of the NP-complete problem KNAPSACK to VISUAL MATCH. Tsotsos' proof, however, involves limited-precision real numbers, which introduces an extra degree of complexity to his treatment. The reduction of KNAPSACK to VISUAL MATCH presented here makes no use of limited-precision numbers, leading to a (...)
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  39. added 2013-01-06
    Twenty-Five Years of Constructive Type Theory: Proceedings of a Congress Held in Venice, October 1995.Giovanni Sambin & Jan M. Smith (eds.) - 1998 - Oxford University Press.
    This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Lof over the last twenty-five years.
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  40. added 2013-01-06
    Intentional Mathematics.Stewart Shapiro (ed.) - 1985 - Elsevier.
    Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
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  41. added 2013-01-06
    The Foundations of Mathematics.Ian Stewart & David Tall - 1977 - Oxford University Press.
    The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.
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  42. added 2013-01-06
    Five Papers on Logic and Foundations.G. S. Ceĭtin (ed.) - 1971 - Providence, R.I., American Mathematical Society.
    Markov, A. A. On constructive mathematics.--Ceĭtin, G. S. Mean value theorems in constructive analysis.--Zaslavskiĭ, I. D. and Ceĭtlin, G. S. On singular coverings and properties of constructive functions connected with them.--Maslov, S. Ju. Certain properties of E. L. Post's apparatus of canonical calculi.--Zaslavskiĭ, I. D. Graph schemes with memory.
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  43. added 2013-01-06
    An Introduction to Mathematical Thought.Edward Russell Stabler - 1953 - Cambridge: Mass., Addison-Wesley.
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  44. added 2013-01-06
    Fundamentals of Mathematics.Moses Richardson - 1941 - New York: Macmillan.
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  45. added 2013-01-06
    Number Relationships-2008 as an Algorithm or Relationship Between Numbers. A Number Relationship Discovered Similar to Pi, E, and 0.James Timothy Struck - unknown
    Number Relationship between Numbers identified Similar to Pi, E, and O. Could be called a new group such that the first number when raised to the number of units or places before the final digit equals the value of the final number.
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  46. added 2013-01-05
    Review of C. Mortensen, Inconsistent Mathematics[REVIEW]Jean Paul van Bendegem - 1999 - Philosophia Mathematica 7 (2):202-212.
  47. added 2013-01-03
    Representing Popov V Hayashi with Dimensions and Factors.T. J. M. Bench-Capon - 2012 - Artificial Intelligence and Law 20 (1):15-35.
    Modelling reasoning with legal cases has been a central concern of AI and Law since the 1980s. The approach which represents cases as factors and dimensions has been a central part of that work. In this paper I consider how several varieties of the approach can be applied to the interesting case of Popov v Hayashi. After briefly reviewing some of the key landmarks of the approach, the case is represented in terms of factors and dimensions, and further explored using (...)
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  48. added 2013-01-02
    Review of K. Devlin, Logic and Information[REVIEW]Neil Tennant - 1995 - Philosophia Mathematica 3 (2).
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  49. added 2013-01-02
    Review of S. Sternberg, Group Theory and Physics[REVIEW]Mark Steiner - 1995 - Philosophia Mathematica 3 (3):313-316.
  50. added 2013-01-01
    Practical Reasoning as Presumptive Argumentation Using Action-Based Alternating Transition Systems.Katie Atkinson & Trevor J. M. Bench-Capon - 2007 - Artificial Intelligence 171 (10-15):855-874.
    In this paper we describe an approach to practical reasoning, reasoning about what it is best for a particular agent to do in a given situation, based on presumptive justifications of action through the instantiation of an argument scheme, which is then subject to examination through a series of critical questions. We identify three particular aspects of practical reasoning which distinguish it from theoretical reasoning. We next provide an argument scheme and an associated set of critical questions which is able (...)
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