Search results for 'Mathematics Foundations' (try it on Scholar)

1000+ found
Order:
  1. André Bazzoni (2015). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic 44 (5):507-516.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  2. William Bragg Ewald (ed.) (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press.
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated (...)
     
    Export citation  
     
    My bibliography   20 citations  
  3.  9
    Jean-Pierre Marquis (2013). Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics. Review of Symbolic Logic 6 (1):51-75.
    Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  4.  14
    O. Bradley Bassler (2005). Book Review: J. P. Mayberry. Foundations of Mathematics in the Theory of Sets. [REVIEW] Notre Dame Journal of Formal Logic 46 (1):107-125.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  5. Hans D. Sluga (ed.) (1993). Logic and Foundations of Mathematics in Frege's Philosophy. Garland Pub..
  6. Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
    THE FOUNDATIONS OF MATHEMATICS () PREFACE The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with..
    Direct download  
     
    Export citation  
     
    My bibliography   256 citations  
  7.  55
    Paolo Mancosu (ed.) (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these (...)
    Direct download  
     
    Export citation  
     
    My bibliography   27 citations  
  8.  31
    Frank Waaldijk (2005). On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10 (3):249-324.
    We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  9.  30
    Eric Livingston (1986). The Ethnomethodological Foundations of Mathematics. Routledge & K. Paul.
    A Non-Technical Introduction to Ethnomethodological Investigations of the Foundations of Mathematics through the Use of a Theorem of Euclidean Geometry* I ...
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   28 citations  
  10.  60
    M. Giaquinto (2002). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. Oxford University Press.
    Marcus Giaquinto tells the compelling story of one of the great intellectual adventures of the modern era: the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  11.  31
    Ludwig Wittgenstein (1978). Remarks on the Foundations of Mathematics. B. Blackwell.
  12.  7
    Sean O. Nuallain (2015). The Deathbed Conversion of a Scientific Saint: Review of "Foundations and Methods From Mathematics to Neuroscience: Essays Inspired by Patrick Suppes". [REVIEW] Cosmos and History: The Journal of Natural and Social Philosophy 11 (1):362-372.
    Review Artcile of an anthology of writings inspired by Patrick Suppes, "Foundations and Methods from Mathematics to Neuroscience" examined in the context of Suppes' life and philosophical development.
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  13.  44
    G. T. Kneebone (1963). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover.
    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.
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  14.  29
    Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
    Machine generated contents note: Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletabilty theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  15.  13
    Laura Crosilla & Peter Schuster (eds.) (2005). From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford University Press.
    This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope.
    Direct download  
     
    Export citation  
     
    My bibliography  
  16. Abraham Adolf Fraenkel & Yehoshua Bar-Hillel (eds.) (1966). Essays on the Foundations of Mathematics. Jerusalem, Magnes Press Hebrew University.
    Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...)
     
    Export citation  
     
    My bibliography  
  17.  25
    P. Cariani (2012). Infinity and the Observer: Radical Constructivism and the Foundations of Mathematics. Constructivist Foundations 7 (2):116-125.
    Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  18. Charles Parsons (1967). Mathematics, Foundations Of. In Paul Edwards (ed.), The Encyclopedia of Philosophy. New York, Macmillan 5--188.
     
    Export citation  
     
    My bibliography   1 citation  
  19. Alonzo Church (1975). Barker Stephen F.. Realism as a Philosophy of Mathematics. Foundations of Mathematics, Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel, Edited by Bulloff Jack J., Thomas C. Holyoke, and S. W. Hahn, Springer-Verlag, Berlin, Heidelberg, and New York, 1969, Pp. 1–9. [REVIEW] Journal of Symbolic Logic 40 (4):593.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  20. William Craig (1970). Parsons Charles. Mathematics, Foundations Of. The Encyclopedia of Philosophy, Edited by Edwards Paul, The Macmillan Company & The Free Press, New York, and Collier-Macmillan Limited, London, 1967, Vol. 5, Pp. 188–213. [REVIEW] Journal of Symbolic Logic 35 (2):300.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  21. Frederick W. Kroon (1986). Hatcher William S.. The Logical Foundations of Mathematics. Foundations and Philosophy of Science and Technology Series. Pergamon Press, Oxford Etc. 1982, X + 320 Pp.Hatcher William S.. Foundations of Mathematics. W. B. Saunders Company, Philadelphia, London, and Toronto, 1968, Xiii + 327 Pp. [REVIEW] Journal of Symbolic Logic 51 (2):467-470.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  22. Frederick W. Kroon, William S. Hatcher & William Hatcher'S. (1986). The Logical Foundations of Mathematics.Foundations of Mathematics.Logical Foundations of Mathematics. Journal of Symbolic Logic 51 (2):467.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  23.  88
    Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
    One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   8 citations  
  24.  20
    J. P. Mayberry (2000). The Foundations of Mathematics in the Theory of Sets. Cambridge University Press.
    This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
    Direct download  
     
    Export citation  
     
    My bibliography   8 citations  
  25. Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
    The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  26. Frode Kjosavik (2009). Kant on Geometrical Intuition and the Foundations of Mathematics. Kant-Studien 100 (1):1-27.
    It is argued that geometrical intuition, as conceived in Kant, is still crucial to the epistemological foundations of mathematics. For this purpose, I have chosen to target one of the most sympathetic interpreters of Kant's philosophy of mathematics – Michael Friedman – because he has formulated the possible historical limitations of Kant's views most sharply. I claim that there are important insights in Kant's theory that have survived the developments of modern mathematics, and thus, that they (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  27.  17
    Fraser MacBride (2004). Introduction to Foundations of Logic & Mathematics, Special Issue. Philosophical Quarterly 54 (214):1 - 15.
    Frege attempted to provide arithmetic with a foundation in logic. But his attempt to do so was confounded by Russell's discovery of paradox at the heart of Frege's system. The papers collected in this special issue contribute to the on-going investigation into the foundations of mathematics and logic. After sketching the historical background, this introduction provides an overview of the papers collected here, tracing some of the themes that connect them.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  28.  19
    Alexander James, On the Idea of an Investigation Into the Foundations of Mathematics or Psychology in Wittgenstein.
    Wittgenstein said of Kierkegaard that he was the “single most profound philosopher of the 19th century”; but what accounts for Wittgenstein’s estimation of Kierkegaard’s work? I argue that Kierkegaard, who was a student of ancient philosophy, synthesized Socratic and Aristotelian concepts into a conception of philosophical inquiry that provided the basis for a Socratic-style engagement with what Kierkegaard calls “the present age”. This allows Kierkegaard to engage Socratically with the present age’s assumptions, but with a kind of categorial sophistication that (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  29.  58
    Solomon Feferman, The Development of Programs for the Foundations of Mathematics in the First Third of the 20th Century.
    The most prominent “schools” or programs for the foundations of mathematics that took shape in the first third of the 20th century emerged directly from, or in response to, developments in mathematics and logic in the latter part of the 19th century. The first of these programs, so-called logicism, had as its aim the reduction of mathematics to purely logical principles. In order to understand properly its achievements and resulting problems, it is necessary to review the (...)
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  30. John Bell, The Axiom of Choice in the Foundations of Mathematics.
    The principle of set theory known as the Axiom of Choice (AC) has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago”1 It has been employed in countless mathematical papers, a number of monographs have been exclusively devoted to it, and it has long played a prominently role in discussions on the (...) of mathematics. (shrink)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  31.  2
    Richard L. Epstein & Walter A. Carnielli (1989). Computability Computable Functions, Logic, and the Foundations of Mathematics. Monograph Collection (Matt - Pseudo).
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   4 citations  
  32.  32
    Paolo Mancosu (1999). Between Russell and Hilbert: Behmann on the Foundations of Mathematics. Bulletin of Symbolic Logic 5 (3):303-330.
    After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  33.  13
    Lawrence Neff Stout (2005). Upsetting the Foundations for Mathematics. Philosophia Scientiae 9 (2):5-21.
    Starting with a review of the kinds of questions a foundation for mathematics should address, this paper provides a critique of set theoretical foundations, a proposal that multiple interconnected categorical foundations would be an improvement, and a way of recovering set theory within a categorical approach.RésuméCommençant par une revue sommaire des types de questions qu’une fondation des mathématiques devrait poser, cet article présente premièrement une critique des fondements basés sur la théorie des ensembles, puis propose l’idée que (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  34. Mathieu Marion (2008). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press Uk.
    Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking from the 1920s through to the 1950s, in the context of the mathematical and philosophical work of the times, to make coherent (...)
    No categories
     
    Export citation  
     
    My bibliography   1 citation  
  35.  5
    Sean O. Nuallain (2015). The Deathbed Conversion of a Scientific Saint: Review of "Foundations and Methods From Mathematics to Neuroscience: Essays Inspired by Patrick Suppes". [REVIEW] Cosmos and History: The Journal of Natural and Social Philosophy 11.
    Review Artcile of an anthology of writings inspired by Patrick Suppes, "Foundations and Methods from Mathematics to Neuroscience" examined in the context of Suppes' life and philosophical development.
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  36.  3
    Cora Diamond (1977). Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939. Philosophy and Phenomenological Research 37 (4):584-586.
    For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many (...)
    Direct download  
     
    Export citation  
     
    My bibliography   5 citations  
  37.  29
    Vito F. Sinisi (1983). Leśniewski's Foundations of Mathematics. Topoi 2 (1):3-52.
    During 1927-1931 Leśniewski published a series of articles (169 pages) entitled 'O podstawach matematyki' [On the Foundations of Mathematics] in the journal Przeglad Filozoficzny [Philosophical Review], and an abridged English translation of this series is presented here. With the exception of this work, all of Leśniewski's publications appearing after the first World War were written in German, and hence accessible to scholars and logicians in the West. This work, however, since written in Polish, has heretofore not been accessible (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  38.  40
    Alex A. B. Aspeitia, Internalism and Externalism in the Foundations of Mathematics.
    Without a doubt, one of the main reasons Platonsim remains such a strong contender in the Foundations of Mathematics debate is because of the prima facie plausibility of the claim that objectivity needs objects. It seems like nothing else but the existence of external referents for the terms of our mathematical theories and calculations can guarantee the objectivity of our mathematical knowledge. The reason why Frege – and most Platonists ever since – could not adhere to the idea (...)
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  39. Marcus Giaquinto (2004). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. Oxford University Press Uk.
    Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of (...). The Search for Certainty focuses mainly on two major twentieth-century programmes: Russell's logicism and Hilbert's finitism. Giaquinto examines their philosophical underpinnings and their outcomes, asking how successful they were, and how successful they could be, in placing mathematics on a sound footing. He sets these questions in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all Gödel's underivability theorems.More than six decades after those discoveries Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response. (shrink)
    No categories
     
    Export citation  
     
    My bibliography   1 citation  
  40.  23
    I. Grattan-Guinness (1982). Psychology in the Foundations of Logic and Mathematics: The Cases of Boole, Cantor and Brouwer. History and Philosophy of Logic 3 (1):33-53.
    In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  41.  42
    Gianluigi Oliveri (2009). Stefano Donati. I Fondamenti Della Matematica Nel Logicismo di Bertrand Russell [the Foundations of Mathematics in the Logicism of Bertrand Russell]. Philosophia Mathematica 17 (1):109-113.
    Bertrand Russell's contributions to last century's philosophy and, in particular, to the philosophy of mathematics cannot be overestimated.Russell, besides being, with Frege and G.E. Moore, one of the founding fathers of analytical philosophy, played a major rôle in the development of logicism, one of the oldest and most resilient1 programmes in the foundations of mathematics.Among his many achievements, we need to mention the discovery of the paradox that bears his name and the identification of its logical nature; (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  42.  15
    Miriam Franchella (1994). Heyting's Contribution to the Change in Research Into the Foundations of Mathematics. History and Philosophy of Logic 15 (2):149-172.
    After the 1930s, the research into the foundations of mathematics changed.None of its main directions (logicism, formalism and intuitionism) had any longer the pretension to be the only true mathematics.Usually, the determining factor in the change is considered to be Gödel?s work, while Heyting?s role is neglected.In contrast, in this paper I first describe how Heyting directly suggested the abandonment of the big foundational questions and the putting forward of a new kind of foundational research consisting in (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  43.  6
    Elena Anne Marchisotto (1995). In the Shadow of Giants: The Work of Mario Pieri in the Foundations of Mathematics. History and Philosophy of Logic 16 (1):107-119.
    (1995). In the shadow of giants: The work of mario pieri in the foundations of mathematics. History and Philosophy of Logic: Vol. 16, No. 1, pp. 107-119.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  44.  7
    Colin Mclarty (2013). Foundations as Truths Which Organize Mathematics. Review of Symbolic Logic 6 (1):76-86.
    The article looks briefly at Fefermans own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  45. William Bragg Ewald (2005). From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics. Oxford University Press Uk.
    Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number theory, analysis, logic and set theory--with (...)
     
    Export citation  
     
    My bibliography  
  46.  13
    William Bragg Ewald (2005). From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics. OUP Oxford.
    This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.
    Direct download  
     
    Export citation  
     
    My bibliography  
  47. William Bragg Ewald (2005). From Kant to Hilbert Volume 2: A Source Book in the Foundations of Mathematics. Oxford University Press Uk.
    Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number theory, analysis, logic and set theory--with (...)
    No categories
     
    Export citation  
     
    My bibliography  
  48.  90
    Ian Stewart & David Tall (1977). The Foundations of Mathematics. 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.
    Direct download  
     
    Export citation  
     
    My bibliography  
  49. Gabriel Uzquiano (1999). Ontology and the Foundations of Mathematics. Dissertation, Massachusetts Institute of Technology
    "Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences place serious constraints on (...)
     
    Export citation  
     
    My bibliography  
  50.  33
    Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.
    This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   7 citations  
1 — 50 / 1000