This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Siblings:
98 found
Search inside:
(import / add options)   Sort by:
1 — 50 / 98
  1. T. Achourioti & M. van Lambalgen (2011). A Formalization of Kant's Transcendental Logic. Review of Symbolic Logic 4 (2):254-289.
    Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely what (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  2. Alice Ambrose (1933). A Controversy in the Logic of Mathematics. Philosophical Review 42 (6):594-611.
  3. Michael A. Arbib (1990). A Piagetian Perspective on Mathematical Construction. Synthese 84 (1):43 - 58.
    In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The axiom set does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view truth not as something to be defined within (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  4. Jeremy Avigad & Jeffrey Helzner (2002). Transfer Principles in Nonstandard Intuitionistic Arithmetic. Archive for Mathematical Logic 41 (6):581-602.
    Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic. Internalizing the construction allows us to strengthen these results with additional transfer rules; we then show that even trivial transfer axioms or minor strengthenings of these rules destroy (...)
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  5. Steve Awodey (2013). Structuralism, Invariance, and Univalence. Philosophia Mathematica 22 (1):nkt030.
    The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy (...)
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  6. J. L. Bell (2013). Review of M. Van Atten, P. Boldini, M. Bourdeau, and G. Heinzmann (Eds.), _One Hundred Years of Intuitionism (1907–2007): The Cerisy Conference. [REVIEW] Philosophia Mathematica 21 (3):392-399.
    Remove from this list | Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  7. H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
    claims that constructive mathematics is inadequate for spacetime physics and hence that constructive mathematics cannot be considered as an alternative to classical mathematics. He also argues that the contructivist must be guilty of a form of a priorism unless she adopts a strong form of anti-realism for science. Here I want to dispute both claims. First, even if there are non-constructive results in physics this does not show that adequate constructive alternatives could not be formulated. Secondly, the constructivist adopts a (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  8. Helen Billinge (2003). Did Bishop Have a Philosophy of Mathematics? Philosophia Mathematica 11 (2):176-194.
    When Bishop published Foundations of Constructive Analysis he showed that it was possible to do ordinary analysis within a constructive framework. Bishop's reasons for doing his mathematics constructively are explicitly philosophical. In this paper, I will expound, examine, and amplify his philosophical arguments for constructivism in mathematics. In the end, however, I argue that Bishop's philosophical comments cannot be rounded out into an adequate philosophy of constructive mathematics.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  9. Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
    Friedrich Waismann, a little-known mathematician and onetime student of Wittgenstein's, provides answers to problems that vexed Wittgenstein in his attempt to explicate the foundations of mathematics through an analysis of its practice. Waismann argues in favor of mathematical intuition and the reality of infinity with a Wittgensteinian twist. Waismann's arguments lead toward an approach to the foundation of mathematics that takes into consideration the language and practice of experts.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  10. Michel J. Blais (1989). A Pragmatic Analysis of Mathematical Realism and Intuitionism. Philosophia Mathematica (1):61-85.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  11. D. S. Bridges (1987). Varieties of Constructive Mathematics. Cambridge University Press.
    This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  12. Douglas S. Bridges (1995). Constructive Mathematics and Unbounded Operators — a Reply to Hellman. Journal of Philosophical Logic 24 (5):549 - 561.
    It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  13. L. E. J. Brouwer (1981). Brouwer's Cambridge Lectures on Intuitionism. Cambridge University Press.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  14. James Robert Brown (2003). Science and Constructive Mathematics. Analysis 63 (1):48–51.
    Remove from this list | Direct download (10 more)  
     
    My bibliography  
     
    Export citation  
  15. 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 (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  16. 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.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  17. Dirk Van Dalen (1995). Hermann Weyl's Intuitionistic Mathematics. Bulletin of Symbolic Logic 1 (2):145 - 169.
  18. E. B. Davies (2005). A Defence of Mathematical Pluralism. Philosophia Mathematica 13 (3):252-276.
    We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  19. Michael de (2013). Empirical Negation. Acta Analytica 28 (1):49-69.
    An extension of intuitionism to empirical discourse, a project most seriously taken up by Dummett and Tennant, requires an empirical negation whose strength lies somewhere between classical negation (‘It is unwarranted that. . . ’) and intuitionistic negation (‘It is refutable that. . . ’). I put forward one plausible candidate that compares favorably to some others that have been propounded in the literature. A tableau calculus is presented and shown to be strongly complete.
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  20. David Dedivi (2004). Choice Principles and Constructive Logics. Philosophia Mathematica 12 (3):222-243.
    to constructive systems is significant for contemporary metaphysics. However, many are surprised by these results, having learned that the Axiom of Choice (AC) is constructively valid. Indeed, even among specialists there were, until recently, reasons for puzzlement-rival versions of Intuitionistic Type Theory, one where (AC) is valid, another where it implies classical logic. This paper accessibly explains the situation, puts the issues in a broader setting by considering other choice principles, and draws philosophical morals for the understanding of quantification, choice (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  21. M. Detlefsen (1998). Walter van Stigt. Brouwer's Intuitionism. Amsterdam: North-Holland Publishing Co., 1990. Pp. Xxvi + 530. ISBN 0-444-88384-3 (Cloth). [REVIEW] Philosophia Mathematica 6 (2):235-241.
  22. Michael Detlefsen (1995). Review of J. Folina, Poincare and the Philosophy of Mathematics. [REVIEW] Philosophia Mathematica 3 (2):208-218.
  23. Michael Detlefsen (1995). Wright on the Non-Mechanizability of Intuitionist Reasoning. Philosophia Mathematica 3 (1):103-119.
    Crispin Wright joins the ranks of those who have sought to refute mechanist theories of mind by invoking Gödel's Incompleteness Theorems. His predecessors include Gödel himself, J. R. Lucas and, most recently, Roger Penrose. The aim of this essay is to show that, like his predecessors, Wright, too, fails to make his case, and that, indeed, he fails to do so even when judged by standards of success which he himself lays down.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  24. Michael Dummett (1998). Truth From the Constructive Standpoint. Theoria 64 (2-3):122-138.
  25. Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
    This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  26. Michael A. E. Dummett (1974). Intuitionistic Mathematics and Logic. Mathematical Institute.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  27. William J. Edgar (1973). Is Intuitionism the Epistemically Serious Foundation for Mathematics? Philosophia Mathematica (2):113-133.
  28. Solomon Feferman (2008). Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on Finitism, Constructivity and Hilbert's Program. Dialectica 62 (2: Table of Contents"/> Select):179–203.
  29. Eduardo L. Fermé & Sven Ove Hansson (1999). Selective Revision. Studia Logica 63 (3):331-342.
    We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision.
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  30. Peter Fletcher (2002). A Constructivist Perspective on Physics. Philosophia Mathematica 10 (1):26-42.
    This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible space-time continuum. I argue (contrary to Hellman) that these do not. (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  31. Miriam Franchella (2008). Mark Van Atten. Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Philosophia Mathematica 16 (2):276-281.
  32. Yvon Gauthier, Constructive Truth and Certainty in Logic and Mathematics.
    The theme « Truth and Certainty » is reminiscent of Hegel’s dialectic of prominent in the Phänomenologie des Geistes, but I want to treat it from a different angle in the perspective of the constructivist stance in the foundations of logic and mathematics. Although constructivism stands in opposition to mathematical realism, it is not to be considered as an idealist alternative in the philosophy of mathematics. It is true that Brouwer’s intuitionism, as a variety of constructivism, (...)
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  33. D. A. Gillies (1980). Brouwer's Philosophy of Mathematics: Review of L. E. J. Brouwer (A. Heyting and H. Freudenthal Eds.), Collected Works. [REVIEW] Erkenntnis 15 (1):105 - 126.
  34. Johan Georg Granström (2011). Treatise on Intuitionistic Type Theory. Springer.
    Prolegomena It is fitting to begin this book on intuitionistic type theory by putting the subject matter into perspective. The purpose of this chapter is to ...
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  35. R. G. Heck (2013). Sir Michael Anthony Eardley Dummett, 1925-2011. Philosophia Mathematica 21 (1):1-8.
    A remembrance of Dummett's work on philosophy of mathematcis.
    Remove from this list | Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  36. Gerhard Heinzmann & Giuseppina Ronzitti (eds.) (2006). Constructivism: Mathematics, Logic, Philosophy and Linguistics.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  37. Geoffrey Hellman (2006). Pluralism and the Foundations of Mathematics. In ¸ Itekellersetal:Sp. 65--79.
    A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises issues of (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  38. Geoffrey Hellman (1998). Mathematical Constructivism in Spacetime. British Journal for the Philosophy of Science 49 (3):425-450.
    To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it (...)
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  39. Jan Heylen (2013). Modal-Epistemic Arithmetic and the Problem of Quantifying In. Synthese 190 (1):89-111.
    The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of logical (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  40. A. Heyting (1971). Intuitionism. Amsterdam,North-Holland Pub. Co..
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  41. A. Heyting (1955). G. F. C. Griss and His Negationless Intuitionistic Mathematics. Synthese 9 (1):91 - 96.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  42. Arend Heyting (1974). Intuitionistic Views on the Nature of Mathematics. Synthese 27 (1-2):79 - 91.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  43. B. Kerkhove & J. P. Bendegem (2012). The Many Faces of Mathematical Constructivism. Constructivist Foundations 7 (2):97-103.
    Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  44. Charles F. Kielkopf (1995). ‘Surveyablity’ Should Not Be Formalized. Philosophia Mathematica 3 (2):175-178.
    There is a review of how Mark Addis has made a case that it would require great effort for scant philosophical profit to formalize a notion of surveyability as a metamathematical predicate demarcating strict finitistic mathematics. It is then suggested how the notion of surveyability is useful in informal philosophizing about mathematics.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  45. Charles F. Kielkopf (1970). Strict Finitism. The Hague,Mouton.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  46. Stephen Cole Kleene (1965). The Foundations of Intuitionistic Mathematics. Amsterdam, North-Holland Pub. Co..
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  47. Hugh Lehman (1983). Intuitionism and Platonism on Infinite Totalities. Idealistic Studies 13 (3):190-198.
  48. M. Lievers (2004). Critical Studies / Book Reviews. [REVIEW] Philosophia Mathematica 12 (2):176-186.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  49. Sten Lindström & Erik Palmgren (2009). Introduction: The Three Foundational Programmes. In Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.), Logicism, Intuitionism and Formalism: What has become of them? Springer.
  50. Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.) (2009). Logicism, Intuitionism, and Formalism - What has Become of Them? Springer.
    These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics.A special section is concerned with constructive ...
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 98