This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Subcategories:
464 found
Search inside:
(import / add options)   Sort by:
1 — 50 / 464
Material to categorize
  1. Toshiyasu Arai (2003). Avigad Jeremy. Update Procedures and the 1-Consistency of Arithmetic. Mathematical Logic Quarterly, Vol. 48 (2002), Pp. 3–13. [REVIEW] Bulletin of Symbolic Logic 9 (1):45-47.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  2. Josef Berger & Douglas Bridges (2008). The Anti-Specker Property, a Heine–Borel Property, and Uniform Continuity. Archive for Mathematical Logic 46 (7-8):583-592.
    Working within Bishop’s constructive framework, we examine the connection between a weak version of the Heine–Borel property, a property antithetical to that in Specker’s theorem in recursive analysis, and the uniform continuity theorem for integer-valued functions. The paper is a contribution to the ongoing programme of constructive reverse mathematics.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  3. Josef Berger & Hajime Ishihara (2005). Brouwer's Fan Theorem and Unique Existence in Constructive Analysis. Mathematical Logic Quarterly 51 (4):360-364.
    Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  4. Ross T. Brady (2012). The Consistency of Arithmetic, Based on a Logic of Meaning Containment. Logique Et Analyse 55 (219).
  5. D. S. Bridges (2004). Constructive Complements of Unions of Two Closed Sets. Mathematical Logic Quarterly 50 (3):293.
    It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  6. Douglas S. Bridges (2008). Product a-Frames and Proximity. Mathematical Logic Quarterly 54 (1):12-26.
    Continuing the study of apartness in lattices, begun in [8], this paper deals with axioms for a product a-frame and with their consequences. This leads to a reasonable notion of proximity in an a-frame, abstracted from its counterpart in the theory of set-set apartness.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  7. Douglas Bridges & Hannes Diener (2006). A Constructive Treatment of Urysohn's Lemma in an Apartness Space. Mathematical Logic Quarterly 52 (5):464-469.
    This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant constructive version (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  8. Douglas Bridges & Steeve Reeves (1999). Constructive Mathematics in Theory and Programming Practice. Philosophia Mathematica 7 (1):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  9. John P. Burgess (2012). Frege’s Theorem by Richard G. Heck, Jr. Journal of Philosophy 109 (12):728-732.
  10. John P. Burgess (2012). Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW] Journal of Philosophy 109 (12):728-733.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  11. J. Posy Carl (1998). Brouwer Versus Hilbert: 1907–1928. Science in Context 11 (2):291.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  12. Abel Casanave (2004). Chateaubriand's Logicism. Manuscrito 27 (1):13-20.
    In his doctoral dissertation, O. Chateaubriand favored Dedekind’s analysis of the notion of number; whereas in Logical Forms, he favors a fregean approach to the topic. My aim in this paper is to examine the kind of logicism he defends. Three aspects will be considered: the concept of analysis; the universality of arithmetical properties and their definability; the irreducibility of arithmetical objects.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  13. Brian Coffey (1952). The Foundations of Arithmetic. Modern Schoolman 29 (2):157-157.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  14. Thierry Coquand (2004). About Brouwer's Fan Theorem. Revue Internationale de Philosophie 230:483-489.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  15. James X. Corgan (1968). Fossils and Evolution General Palaeontology A. Brouwer R. H. Kaye. BioScience 18 (3):250-250.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  16. Z. Damnjanovic (2012). Truth Through Proof: A Formalist Foundation for Mathematics * by Alan Weir. Analysis 72 (2):415-418.
    Remove from this list | Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  17. Oswald Demuth (1969). Lebesgue Integral in Constructive Analysis. In A. O. Slisenko (ed.), Studies in Constructive Mathematics and Mathematical Logic. New York, Consultants Bureau. 9--14.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  18. Solomon Feferman, Challenges to Predicative Foundations of Arithmetic.
    This is a sequel to our article “Predicative foundations of arithmetic” (1995), referred to in the following as [PFA]; here we review and clarify what was accomplished in [PFA], present some improvements and extensions, and respond to several challenges. The classic challenge to a program of the sort exemplified by [PFA] was issued by Charles Parsons in a 1983 paper, subsequently revised and expanded as Parsons (1992). Another critique is due to Daniel Isaacson (1987). Most recently, Alexander George and Daniel (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  19. I. Grattan-Guinness (2003). Mathematics in and Behind Russell's Logicism and its Reception'. In Nicholas Griffin (ed.), The Cambridge Companion to Bertrand Russell. Cambridge University Press. 51.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  20. Matthew Hendtlass (2012). The Intermediate Value Theorem in Constructive Mathematics Without Choice. Annals of Pure and Applied Logic 163 (8):1050-1056.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  21. U. Kohlenbach (2002). On Weak Markov's Principle. Mathematical Logic Quarterly 48 (S1):59-65.
    We show that the so-called weak Markov's principle which states that every pseudo-positive real number is positive is underivable in [MATHEMATICAL SCRIPT CAPITAL T]ω ≔ E-HAω + AC. Since [MATHEMATICAL SCRIPT CAPITAL T]ω allows one to formalize Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within the framework of Bishop-style mathematics . The underivability even holds if the ine.ective schema of full comprehension for negated formulas is added, which allows one to derive the law of excluded (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  22. V. A. Lifshits (1969). On Constructive Groups. In A. O. Slisenko (ed.), Studies in Constructive Mathematics and Mathematical Logic. New York, Consultants Bureau. 32--35.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  23. Rod McBeth (1980). Fundamental Sequences for Exponential Polynomials. Mathematical Logic Quarterly 26 (7‐9):115-122.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  24. Charles Mccarty (2013). Brouwer's Weak Counterexamples and Testability: Further Remarks. Review of Symbolic Logic 6 (3):513-523.
    Straightforwardly and strictly intuitionistic inferences show that the BrouwerKolmogorov (BHK) interpretation, in the presence of a formulation of the recognition principle, entails the validity of the Law of Testability: that the form s original weak counterexample reasoning was fallacious. The results of the present article extend and refine those of McCarty, C. (2012). Antirealism and Constructivism: Brouwer’s Weak Counterexamples. The Review of Symbolic Logic. First View. Cambridge University Press.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  25. Joan Rand Moschovakis (2010). Unavoidable Sequences in Constructive Analysis. Mathematical Logic Quarterly 56 (2):205-215.
    Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π11 formula is unavoidable and that no sequence can fail to be classically Δ11. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  26. Satyadev Nandakumar (2009). A Characterization of Constructive Dimension. Mlq 55 (2):185-200.
    In the context of Kolmogorov's algorithmic approach to the foundations of probability, Martin-Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibility. We prove a direct conversion of a constructive martingale into a measure of impossibility and vice versa such that their success sets, for a suitably defined class of computable probability measures, are equal. The direct conversion is then generalized to give a (...)
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  27. Andrzej Orlicki (1987). Constructive and Locally Constructive Endofunctors on the Category of Enumerated Sets. Mathematical Logic Quarterly 33 (4):371-384.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  28. J. M. P. (1965). The Foundations of Intuitionistic Mathematics. [REVIEW] Review of Metaphysics 19 (1):154-155.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  29. Diederick Raven (2001). Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer. Volume 1: The Dawning Revolution. [REVIEW] British Journal for the History of Science 34 (1):97-124.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  30. Edoardo Rivello (forthcoming). Cofinally Invariant Sequences and Revision. Studia Logica:1-24.
    Revision sequences are a kind of transfinite sequences which were introduced by Herzberger and Gupta in 1982 (independently) as the main mathematical tool for developing their respective revision theories of truth. We generalise revision sequences to the notion of cofinally invariant sequences, showing that several known facts about Herzberger’s and Gupta’s theories also hold for this more abstract kind of sequences and providing new and more informative proofs of the old results.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  31. Matthias Schirn (2010). Consistency, Models, and Soundness. Axiomathes 20 (2-3):153-207.
    This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  32. Harvey Siegel (2010). Penelope MaddySecond Philosophy: A Naturalistic Method. British Journal for the Philosophy of Science 61 (4):897-903.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  33. Jakob G. Simonsen (2006). On Local Non‐Compactness in Recursive Mathematics. Mathematical Logic Quarterly 52 (4):323-330.
    A metric space is said to be locally non-compact if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non-compact iff it is without isolated points.The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence (...)
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  34. Mark Steiner (1991). Hilbert's Program: An Essay on Mathematical Instrumentalism by Michael Detlefsen. Journal of Philosophy 88 (6):331-336.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  35. N. Tennant (2000). Penelope Maddy, Naturalism in Mathematics. Philosophia Mathematica 8 (3):316-338.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  36. Silvio Valentini (2005). The Problem of the Formalization of Constructive Topology. Archive for Mathematical Logic 44 (1):115-129.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  37. Mark van Atten (2004). Hesseling Dennis E.. Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s. Science Networks. Historical Studies, Vol. 28. Birkhäuser, Boston, 2003, Xxiii+ 447 Pp. [REVIEW] Bulletin of Symbolic Logic 10 (3):423-427.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  38. Jaap Van Oosten (2006). From Sets and Types to Topology and Analysis—Towards Practicable Foundations for Constructive Mathematics, Edited by Crosilla Laura and Schuster Peter, Oxford Logic Guides, Vol. 48. Clarendon Press, 2005, Xix+ 450 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (4):611-612.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  39. Alan Weir (1998). Dummett on Impredicativity. Grazer Philosophische Studien 55:65-101.
    Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
Logicism in Mathematics
  1. Bird Alexander (1997). The Logic in Logicism. Dialogue 36:341�60.
    Frege's logicism consists of two theses: (1) the truths of arithmetic are truths of logic; (2) the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G are (...)
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  2. Alice Ambrose (1933). A Controversy in the Logic of Mathematics. Philosophical Review 42 (6):594-611.
  3. Irving H. Anellis (1987). Russell and Engels: Two Approaches to a Hegelian Philosophy of Mathematics. Philosophia Mathematica (2):151-179.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  4. Irving H. Anellis (1987). Russell's Earliest Interpretation of Cantorian Set Theory, 1896–1900. Philosophia Mathematica (1):1-31.
  5. G. A. Antonelli (2010). Notions of Invariance for Abstraction Principles. Philosophia Mathematica 18 (3):276-292.
    The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance (...)
    Remove from this list | Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  6. Timothy Bays (2000). The Fruits of Logicism. Notre Dame Journal of Formal Logic 41 (4):415-421.
    You’ll be pleased to know that I don’t intend to use these remarks to comment on all of the papers presented at this conference. I won’t try to show that one paper was right about this topic, that another was wrong was about that topic, or that several of our conference participants were talking past one another. Nor will I try to adjudicate any of the discussions which took place in between our sessions. Instead, I’ll use these remarks to make (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  7. Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.
    Frege's logicism consists of two theses: (1) the truths of arithmetic are truths of logic; (2) the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G are (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  8. Kenneth Blackwell, Nicholas Griffin & Bernard Linsky (eds.) (2011). Principia Mathematica at 100. Bertrand Russell Research Centre.
  9. George Boolos (1990). The Standard of Equality of Numbers. In , Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge University Press. 261--77.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  10. George S. Boolos (ed.) (1990). Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge University Press.
    This volume is a report on the state of philosophy in a number of significant areas.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  11. Andrew Boucher, Who Needs (to Assume) Hume's Principle?
    Neo-logicism uses definitions and Hume's Principle to derive arithmetic in second-order logic. This paper investigates how much arithmetic can be derived using definitions alone, without any additional principle such as Hume's.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
1 — 50 / 464