Results for 'Mathematical Logic and Foundations'

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  1. Mathematical Logic and the Foundations of Mathematics: An Introductory Survey.G. T. Kneebone - 1963 - Dover Publications.
    Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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  2. Mathematical Logic and Foundations of Set Theory Proceedings of an International Colloquium Under the Auspices of the Israel Academy of Sciences and Humanities, Jerusalem, 11-14 November 1968. [REVIEW]Yehoshua Bar-Hillel, Akademyah Ha-le Umit Ha-Yi Sre Elit le-Mada Im, Einstein Institute of Mathematics & International Mathematical Union - 1970
     
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  3. Mathematical Logic and Foundations of Set Theory. Y. Bar-Hillel - 1972 - Synthese 23 (4):491-493.
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  4.  50
    Mathematical Logic and Foundations of Set Theory.Yehoshua Bar-Hillel (ed.) - 1970 - Amsterdam: North-Holland Pub. Co..
    LN , so f lies in the elementary submodel M'. Clearly co 9 M' . It follows that 6 = {f(n): n em} is included in M'. Hence the ordinals of M' form an initial ...
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  5. Second-Order Logic and Foundations of Mathematics.Jouko Väänänen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
    We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order (...) are not radically different: the latter is a major fragment of the former. (shrink)
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  6.  6
    Logic and Foundations of Mathematics in Frege's Philosophy.Hans D. Sluga (ed.) - 1993 - Garland.
    The four volumes of this collection bring together some of the major contributions to the literature on Gottlob Frege (1848-1925), one of the most formative influences on the course of philosophy during the last hundred years. The first volume provided general assessments of Frege's work and examined its historical context. The present volume deals with Frege's contributions to logic and the foundations of mathematics. The essays are arranged in order of their first publication, providing insight into the historical (...)
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  7.  13
    Mathematical Logic and the Foundations of Mathematics.E. J. Cogan - 1964 - British Journal for the Philosophy of Science 15 (59):268-270.
  8.  51
    Lesniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  9. Logic and Foundations of Mathematics: Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.Andrea Cantini, Ettore Casari & Pierluigi Minari - 1999 - Springer.
    The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a (...)
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  10. Logic and Foundations of Mathematics.D. van Dalen, J. G. Dijkman, A. Heyting, Stephen Cole Kleene & A. S. Troelstra - 1968 - Wolters-Noordhoff.
  11.  8
    Mathematical Logic and the Foundations of Mathematics.R. L. Goodstein - 1963 - Philosophical Books 4 (2):8-9.
  12.  8
    Foundations of Logic and Mathematics.Rudolf Carnap - 1937 - U. Of Chicago P.
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  13.  35
    Foundations of Logic and Mathematics.E. N. - 1939 - Journal of Philosophy 36 (23):636-637.
  14.  64
    IF Logic and the Foundations of Mathematics.Gabriel Sandu & Tapani Hyttinen - 2001 - Synthese 126 (1):37-47.
  15.  38
    Kenneth Kunen, The Foundations of Mathematics, Studies in Logic, Mathematical Logic and Foundations, Vol. 19. College Publications, London, 2009, Vii + 251 Pp. [REVIEW]Steffen Lempp - 2016 - Bulletin of Symbolic Logic 22 (2):287-288.
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  16.  12
    Rabin Michael O.. Weakly Definable Relations and Special Automata. Mathematical Logic and Foundations of Set Theory, Proceedings of an International Colloquium Held Under the Auspices of the Israel Academy of Sciences and Humanities, Jerusalem, 11-14 November 1968, Edited by Bar-Hillel Yehoshua, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam and London 1970, Pp. 1–23. [REVIEW]Dirk Siefkes - 1975 - Journal of Symbolic Logic 40 (4):622-623.
  17.  9
    Contemporary Philosophy . Volume I, Logic and Foundations of Mathematics. [REVIEW]H. K. R. - 1970 - Review of Metaphysics 23 (3):570-571.
    This is the first of a number of volumes designed to review the philosophical work which has been done in various areas of philosophy between the years 1956 and 1966. It succeeds an earlier three volume publication entitled Philosophy in the Mid-Century which covered the period from 1949 to 1955. This first volume in the series covers the fields of logic, philosophical logic, foundations and philosophy of mathematics. For anyone interested in these fields, the book is an (...)
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  18. Foundations of Logic and Mathematics.Rudolf Carnap - 1939 - In Otto Neurath, Rudolf Carnap & Charles Morris (eds.), International Encyclopedia of Unified Science. University of Chicago Press. pp. 139--213.
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  19.  97
    Foundations of Mathematical Logic.Haskell B. Curry - 1963 - Dover Publications.
    Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.
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  20. The Theory of Probability: An Inquiry Into the Logical and Mathematical Foundations of the Calculus of Probability.Hans Reichenbach - 1949 - Berkeley: University of California Press.
    We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...
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  21.  14
    Philosophical Observations on Mathematical Logic and on Investigations Into the Foundations of Mathematics.Wilhelm Ackermann - 1958 - Journal of Symbolic Logic 23 (3):342-343.
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  22.  60
    Computability: Computable Functions, Logic, and the Foundations of Mathematics.Richard L. Epstein - 1989
    This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents (...)
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  23.  11
    The Trend of Logic and Foundation of Mathematics in Japan in 1991 to 1996.Yuzuru Kakuda, Kanji Namba & Nobuyoshi Motohashi - 1997 - Annals of the Japan Association for Philosophy of Science 9 (2):95-110.
  24.  8
    Bibliography of Soviet Work in the Field of Mathematical Logic and the Foundations of Mathematics, From 1917--1957.Guido Küng - 1962 - Notre Dame Journal of Formal Logic 3 (1):1-40.
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  25.  7
    Contemporary Philosophy: Vol. I: Logic and Foundations of Mathematics.N. G. E. Harris & Raymond Klibansky - 1970 - Philosophical Quarterly 20 (79):183.
  26.  19
    Selected Papers in Logic and Foundations, Didactics, Economics.Michael Hallett & Karl Menger - 1981 - Philosophical Quarterly 31 (122):92.
  27.  13
    Computability. Computable Functions, Logic, and the Foundations of Mathematics.Richard L. Epstein & Walter A. Carnielli - 2002 - Bulletin of Symbolic Logic 8 (1):101-104.
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  28.  3
    Feferman S. And Kreisel G.. Persistent and Invariant Formulas Relative to Theories of Higher Order. Bulletin of the American Mathematical Society, Vol. 72 , Pp. 480–485.Feferman Solomon. Persistent and Invariant Formulas for Outer Extensions. Logic and Foundations of Mathematics, Dedicated to Prof. A. Heyting on His 70th Birthday, Wolters-Noordhoff Publishing, Groningen 1968, Pp. 29–52; Also Compositio Mathematica, Vol. 20 , P. 29–52. [REVIEW]K. Jon Barwise - 1972 - Journal of Symbolic Logic 37 (4):764-765.
  29. Logic and Foundations of Science.Jean-Louis Destouches, Evert Willem Beth & Institut Henri Poincaré (eds.) - 1968 - Dordrecht: D. Reidel.
  30.  23
    Operators in Nature, Science, Technology, and Society: Mathematical, Logical, and Philosophical Issues.Mark Burgin & Joseph Brenner - 2017 - Philosophies 2 (3):21.
    The concept of an operator is used in a variety of practical and theoretical areas. Operators, as both conceptual and physical entities, are found throughout the world as subsystems in nature, the human mind, and the manmade world. Operators, and what they operate, i.e., their substrates, targets, or operands, have a wide variety of forms, functions, and properties. Operators have explicit philosophical significance. On the one hand, they represent important ontological issues of reality. On the other hand, epistemological operators form (...)
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  31.  3
    Mathematical Logic and Natural Language: Life at the Border.Benedikt Lowe & Thoralf Rasch Malzkorn - 2003 - In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer Academic Publishers.
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  32.  12
    Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics.Markus Pantsar - 2021 - Minds and Machines 31 (1):75-98.
    In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...)
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  33.  28
    On the Mathematical and Foundational Significance of the Uncountable.Dag Normann & Sam Sanders - 2019 - Journal of Mathematical Logic 19 (1):1950001.
    We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] (...)
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  34.  17
    Contemporary Philosophy (La Philosophie Contemporaine). Volume I, Logic and Foundations of Mathematics.R. H. K. - 1970 - Review of Metaphysics 23 (3):570-571.
    This is the first of a number of volumes designed to review the philosophical work which has been done in various areas of philosophy between the years 1956 and 1966. It succeeds an earlier three volume publication entitled Philosophy in the Mid-Century which covered the period from 1949 to 1955. This first volume in the series covers the fields of logic, philosophical logic, foundations and philosophy of mathematics. For anyone interested in these fields, the book is an (...)
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  35.  27
    Mathematical Logic.Heinz-Dieter Ebbinghaus - 1996 - Springer.
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. (...)
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  36.  57
    Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW]Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paulo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from (...)
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  37. Thirty Years of Foundational Studies Lectures on the Development of Mathematical Logic and the Study of the Foundations of Mathematics in 1930-1964.Andrzej Mostowski - 1965 - Blackwell.
  38.  12
    Mathematical Logic of Notions and Concepts.J. L. Usó-Doménech & J. A. Nescolarde-Selva - 2019 - Foundations of Science 24 (4):641-655.
    In this paper the authors develop a logic of concepts within a mathematical linguistic theory. In the set of concepts defined in a belief system, the order relationship and Boolean algebra of the concepts are considered. This study is designed to obtain a tool, which is the metatheoretical base of this type of theory.
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  39. Hans Sluga (Ed.), The Philosophy of Frege. A Four-Volume Collection of Scholarly Articles on All Aspects of Frege's Philosophy, Vol.1: General Assessments and Historical Accounts of Frege's Philosophy, Vol.2: Logic and Foundations of Mathematics in Frege's Philosophy, Vol.3: Meaning and Ontology in Frege's Philosophy, Vol.4: Sense and Reference in Frege's Philosophy. [REVIEW]Jan Wolenński - 1997 - Erkenntnis 46 (3):407-410.
  40. The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - Routledge & Kegan Paul.
  41.  29
    Jensen R. B.. Concrete Models of Set Theory. Sets, Models and Recursion Theory, Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, Edited by Crossley John N., Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, Pp. 44–74. [REVIEW]Frank R. Drake - 1970 - Journal of Symbolic Logic 35 (3):472-473.
  42.  19
    Contemporary Philosophy: La Philosophie Contemporaine; Vol. I, Logic and Foundations of Mathematics. Edited by Raymond Klibansky. Florence: La Nuova Italia Editrice; Montreal: Mario Casalini Ltd. Pp. Xi, 387. $9.80. [REVIEW]Alex C. Michalos - 1969 - Dialogue 8 (2):326-328.
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  43.  24
    Karp Carol. A Proof of the Relative Consistency of the Continuum Hypothesis. Sets, Models and Recursion Theory, Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, Edited by Crossley John N., Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, Pp. 1–32. [REVIEW]Leslie H. Tharp - 1970 - Journal of Symbolic Logic 35 (2):344-345.
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  44.  12
    C. E. M. Yates. Recursively Enumerable Degrees and the Degrees Less Than 0. Sets, Models and Recursion Theory, Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, Edited by John N. Crossley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, Pp. 264–271. [REVIEW]S. K. Thomason - 1970 - Journal of Symbolic Logic 35 (4):589-589.
  45.  28
    J. C. E. Dekker. Regressive Isols. Sets, Models and Recursion Theory. Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, Edited by John N. Crossley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, Pp. 272–296. [REVIEW]C. E. Bredlau - 1969 - Journal of Symbolic Logic 34 (3):519-519.
  46. Logic and the Foundations of Mathematics.Danielle Macbeth - 2008 - In Cheryl Misak (ed.), The Oxford Handbook of American Philosophy. Oxford University Press.
  47.  46
    A Course in Mathematical Logic.J. L. Bell - 1977 - Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..
    A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.
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  48.  33
    Rafał Urbaniak. Leśniewski’s Systems of Logic and Foundations of Mathematics.Rafał Urbaniak & Peter Simons - forthcoming - Philosophia Mathematica:nkw031.
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  49.  19
    Ackermann Wilhelm. Philosophische Bemerkungen Zur Mathematischen Logik Und Zur Mathematischen Grundlagenforschung. Ratio , Vol. 1 No. 1 , Pp. 1–20.Ackermann Wilhelm. Philosophical Observations on Mathematical Logic and on Investigations Into the Foundations of Mathematics. English Translation. Ratio , Vol. 1 No. 1 , Pp. 1–23. [REVIEW]John van Heijenoort - 1958 - Journal of Symbolic Logic 23 (3):342-343.
  50.  16
    John Myhill. The Formalization of Intuitionism. Contemporary Philosophy, A Survey, I, Logic and Foundations of Mathematics , Edited by Raymond Klibansky, La Nuova Italia Editrice, Florence 1968, Pp. 324–341. [REVIEW]Joan Rand Moschovakis - 1975 - Journal of Symbolic Logic 40 (4):625.
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