Results for 'Mathematics'

999 found
Order:
  1. The Order and Connection of Things.Are They Constructed Mathematically—Deductively - forthcoming - Kant Studien.
    No categories
     
    Export citation  
     
    Bookmark  
  2. A Lattice of Chapters of Mathematics.Jan Mycielski, Pavel Pudlák, Alan S. Stern & American Mathematical Society - 1990 - American Mathematical Society.
     
    Export citation  
     
    Bookmark   7 citations  
  3.  1
    Minimal Degrees of Unsolvability and the Full Approximation Construction.American Mathematical Society, Donald I. Cartwright, John Williford Duskin & Richard L. Epstein - 1975 - American Mathematical Soc..
    For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  4. William S. Hatcher.I. Prologue on Mathematical Logic - 1973 - In Mario Augusto Bunge (ed.), Exact Philosophy; Problems, Tools, and Goals. Boston: D. Reidel. pp. 83.
     
    Export citation  
     
    Bookmark  
  5. Professor, Water Science and Civil Engineering University of California Davis, California.A. Mathematical Model - 1968 - In Peter Koestenbaum (ed.), Proceedings. [San Jose? Calif.. pp. 31.
    No categories
     
    Export citation  
     
    Bookmark  
  6. Izvlečki• abstracts.Mathematical Structuralism is A. Kind ofPlatonism - forthcoming - Filozofski Vestnik.
     
    Export citation  
     
    Bookmark  
  7.  7
    Kurt Gdel: Collected Works: Volume Iv: Selected Correspondence, a-G.Kurt Gdel & Stanford Unviersity of Mathematics - 1986 - Clarendon Press.
    Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.
    Direct download  
     
    Export citation  
     
    Bookmark  
  8.  61
    Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil.Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999 - American Mathematical Soc..
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society 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 leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  9.  2
    Classification Theory: Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985.J. T. Baldwin & U. Workshop on Model Theory in Mathematical Logic - 1987 - Springer.
    Direct download  
     
    Export citation  
     
    Bookmark  
  10.  2
    Logic and Combinatorics: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held August 4-10, 1985.Stephen G. Simpson, American Mathematical Society, Institute of Mathematical Statistics & Society for Industrial and Applied Mathematics - 1987 - American Mathematical Soc..
    In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  11.  65
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: Routledge.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   58 citations  
  12.  3
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  13.  1
    Mathematical Reasoning and Heuristics.Carlo Cellucci & Donald Gillies (eds.) - 2005 - College Publications.
    This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as (...)
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  14.  23
    Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - Oxford, GB: Oxford University Press UK.
    Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to (...)
    Direct download  
     
    Export citation  
     
    Bookmark   27 citations  
  15. Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of (...)--the view that mathematics is about things that really exist. (shrink)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   238 citations  
  16. Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
    INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   158 citations  
  17.  64
    Mathematics in Aristotle.Thomas Heath - 1949 - Routledge.
    Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature. Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of (...)
  18. A mathematical introduction to logic.Herbert Bruce Enderton - 1972 - New York,: Academic Press.
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   120 citations  
  19.  64
    Mathematical rigor and proof.Yacin Hamami - 2022 - Review of Symbolic Logic 15 (2):409-449.
    Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowl- edge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  20.  34
    Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
    On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.
  21.  43
    Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.
    This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at (...)
  22.  3
    Mathematics and the Image of Reason.Mary Tiles - 1991 - New York: Routledge.
    A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  23. Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
    Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition (...)
    Direct download  
     
    Export citation  
     
    Bookmark   93 citations  
  24.  24
    Applying Mathematics: Immersion, Inference, Interpretation.Otávio Bueno & Steven French - 2018 - Oxford, England: Oxford University Press. Edited by Steven French.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  25.  36
    Mathematics and plausible reasoning.George Polya - 1954 - Princeton, N.J.,: Princeton University Press.
    2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   72 citations  
  26.  84
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: London.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   86 citations  
  27. Mathematics, Morality, and Self‐Effacement.Jack Woods - 2016 - Noûs 52 (1):47-68.
    I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   26 citations  
  28. Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
  29. Mathematical logic.Stephen Cole Kleene - 1967 - Mineola, N.Y.: Dover Publications.
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   85 citations  
  30. Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
  31. Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
    Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   112 citations  
  32. Mathematical symbols as epistemic actions.Johan De Smedt & Helen De Cruz - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  33.  20
    Mathematics: The Loss of Certainty.Morris Kline - 1982 - New York, NY, USA: Oxford University Press USA.
    This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.
  34. The Mathematical Universe.Max Tegmark - 2007 - Foundations of Physics 38 (2):101-150.
    I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   102 citations  
  35. Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  36.  19
    The Mathematical Principles of Natural Philosophy.Isaac Newton - 2020 - Filozofski Vestnik 41 (3).
    The Mathematical Principles of Natural Philosophy.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   79 citations  
  37.  27
    The mathematical experience.Philip J. Davis - 1981 - Boston: Birkhäuser. Edited by Reuben Hersh & Elena Marchisotto.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
    Direct download  
     
    Export citation  
     
    Bookmark   144 citations  
  38. Mathematics Intelligent Tutoring System.Nour N. AbuEloun & Samy S. Abu Naser - 2017 - International Journal of Advanced Scientific Research 2 (1):11-16.
    In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  39.  22
    Mathematics in Philosophy: Selected Essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell Univ Pr.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
    Direct download  
     
    Export citation  
     
    Bookmark   50 citations  
  40. Mathematical Pluralism and Indispensability.Silvia Jonas - 2023 - Erkenntnis 1:1-25.
    Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  41. Mathematics, Models, and Modality: Selected Philosophical Essays.John P. Burgess - 2008 - Cambridge University Press.
    John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across (...)
     
    Export citation  
     
    Bookmark   7 citations  
  42.  4
    Mathematics for human flourishing.Francis Edward Su - 2020 - New Haven: Yale University Press. Edited by Christopher Jackson.
    An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and (...)
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  43. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  44.  15
    Principles of Mathematics.Bertrand Russell - 1903 - New York,: Routledge.
    First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.
    Direct download  
     
    Export citation  
     
    Bookmark   178 citations  
  45.  86
    Mathematics, science, and epistemology.Imre Lakatos - 1978 - New York: Cambridge University Press. Edited by Gregory Currie & John Worrall.
    Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.
    Direct download  
     
    Export citation  
     
    Bookmark   39 citations  
  46.  44
    Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
    8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.
  47. Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   163 citations  
  48.  12
    Principles of Mathematics.Bertrand Russell - 1937 - New York,: Routledge.
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   145 citations  
  49. Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford, England: Oxford University Press.
    Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   261 citations  
  50. Mathematics in philosophy: selected essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell University Press.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   32 citations  
1 — 50 / 999