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John Bell [57]John L. Bell [48]John F. Bell [6]John S. Bell [3]
John Fred Bell [1]John Stewart Bell [1]
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John Bell
University Of Glasgow
  1. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy.John Stewart Bell - 2004 - Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
     
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  2. How to Teach Special Relativity.John S. Bell - 1976 - Progress in Scientific Culture 1.
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  3. Set Theory: Boolean-Valued Models and Independence Proofs.John L. Bell - 2011 - Oxford University Press.
    This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.
     
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  4. The Continuous and the Infinitesimal in Mathematics and Philosophy.John L. Bell - 2007 - Bulletin of Symbolic Logic 13 (3):361-363.
     
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  5.  72
    Continuity and Infinitesimals.John L. Bell - unknown
    The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity —a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz's famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century (...)
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  6.  45
    An Exchange on Local Beables.John S. Bell, J. Clauser, M. Horne & A. Shimony - 1985 - Dialectica 39 (2):85-96.
    Summarya) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space‐time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory.b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible with quantum (...)
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  7. The Axiom of Choice.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.
    The principle of set theory known as the Axiom of Choice 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” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of (...)
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  8. Hermann Weyl on Intuition and the Continuum.John L. Bell - 2000 - Philosophia Mathematica 8 (3):259-273.
    Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.
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  9. Whole and Part in Mathematics.John L. Bell - 2004 - Axiomathes 14 (4):285-294.
    The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.
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  10. The Development of Categorical Logic.John L. Bell - unknown
    5.5. Every topos is linguistic: the equivalence theorem.
     
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  11. Logical Reflections On the Kochen-Specker Theorem.John L. Bell - unknown
    IN THEIR WELL-KNOWN PAPER, Kochen and Specker (1967) introduce the concept of partial Boolean algebra (pBa) and show that certain (finitely generated) partial Boolean algebras arising in quantum theory fail to possess morphisms to any Boolean algebra (we call such pBa's intractable in the sequel). In this note we begin by discussing partial..
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  12.  26
    Hermann Weyl.John L. Bell - 2010 - Revue Philosophique de la France Et de l'Etranger.
  13.  26
    Subject and Object.John S. Bell - 1973 - In Jagdish Mehra (ed.), The Physicist's Conception of Nature. Boston: Reidel. pp. 687--690.
  14. Types, Sets and Categories.John L. Bell - unknown
    This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard to the latter) with any pretensions to completeness within the space of a comparatively short article, (...)
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  15.  32
    Hilbert’s Varepsilon -Operator in Intuitionistic Type Theories.John L. Bell - 1993 - Mathematical Logic Quarterly 39 (1):323--337.
    We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.
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  16.  76
    Infinitary Logic.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.
    Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called (...)
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  17. Observations on Category Theory.John L. Bell - 2001 - Axiomathes 12 (1-2):151-155.
    is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea (...)
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  18. Hermann Weyl's Later Philosophical Views: His Divergence From Husserl.John Bell - manuscript
    In what seems to have been his last paper, Insight and Reflection (1954), Hermann Weyl provides an illuminating sketch of his intellectual development, and describes the principal influences—scientific and philosophical—exerted on him in the course of his career as a mathematician. Of the latter the most important in the earlier stages was Husserl’s phenomenology. In Weyl’s work of 1918-22 we find much evidence of the great influence Husserl’s ideas had on Weyl’s philosophical outlook—one need merely glance through the pages of (...)
     
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  19. Frege's Theorem in a Constructive Setting.John L. Bell - 1999 - Journal of Symbolic Logic 64 (2):486-488.
    then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map ν be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., (...)
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  20. Logic, Quantum Logic and Empiricism.John Bell & Michael Hallett - 1982 - Philosophy of Science 49 (3):355-379.
    This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation crucially does not. (...)
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  21. The Continuum in Smooth Infinitesimal Analysis.John Bell - manuscript
    The relation ≤ on R is defined by a ≤ b ⇔ ¬b < a. The open interval (a, b) and closed interval [a, b] are defined as usual, viz. (a, b) = {x: a < x < b} and [a, b] = {x: a ≤ x ≤ b}; similarly for half-open, half-closed, and unbounded intervals.
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  22. Cohesiveness.John L. Bell - unknown
    ABSTRACT: It is characteristic of a continuum that it be “all of one piece”, in the sense of being inseparable into two (or more) disjoint nonempty parts. By taking “part” to mean open (or closed) subset of the space, one obtains the usual topological concept of connectedness . Thus a space S is defined to be connected if it cannot be partitioned into two disjoint nonempty open (or closed) subsets – or equivalently, given any partition of S into two open (...)
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  23. Continuity and the Logic of Perception.John L. Bell - 2000 - Transcendent Philosophy 1 (2):1-7.
    If we imagine a chess-board with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided into four smaller squares also alternating between these two colours. If, however, we were to continue with such divisions until we had exceeded the boundary of noticeability for the individual small squares which result, then (...)
     
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  24.  42
    Logical Options: An Introduction to Classical and Alternative Logics.John L. Bell, David DeVidi & Graham Solomon - 2001 - Broadview Press.
    Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...)
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  25. Sets and Classes as Many.John L. Bell - 2000 - Journal of Philosophical Logic 29 (6):585-601.
    In this paper the view is developed that classes should not be understood as individuals, but, rather, as "classes as many" of individuals. To correlate classes with individuals "labelling" and "colabelling" functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.
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  26. The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories.John L. Bell - 2008 - Mathematical Logic Quarterly 54 (2):194-201.
    A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.
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  27.  80
    Elementary Propositions and Independence.John L. Bell & William Demopoulos - 1996 - Notre Dame Journal of Formal Logic 37 (1):112-124.
    This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.
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  28.  11
    Fregean Extensions of First‐Order Theories.John L. Bell - 1994 - Mathematical Logic Quarterly 40 (1):27-30.
    It is shown by Parsons [2] that the first-order fragment of Frege's logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first-order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.
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  29.  51
    Finite Sets and Frege Structures.John L. Bell - 1999 - Journal of Symbolic Logic 64 (4):1552-1556.
    Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.
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  30.  53
    The Infinite Past Regained: A Reply to Whitrow.John Bell - 1979 - British Journal for the Philosophy of Science 30 (2):161-165.
    I show the inadequacy of whitrow's recent argument ("british journal for the philosophy of science", Volume 29, Pages 39-45) against the possibility of an infinite past. I argue that it is impossible to prove "a priori" the non-Existence of an infinite past or future.
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  31.  24
    Emotional Intelligence and Academic Attainment of British Secondary School Children: A Cross-Sectional Survey.Carmen L. Vidal Rodeiro, Joanne L. Emery & John F. Bell - 2012 - Educational Studies 38 (5):521-539.
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  32.  18
    Emotional Intelligence and Academic Attainment of British Secondary School Children: A Cross-Sectional Survey.Carmen L. Vidal Rodeiro, Joanne L. Emery & John F. Bell - 2012 - Educational Studies 38 (5):521-539.
    Trait emotional intelligence (trait EI) covers a wide range of self-perceived skills and personality dispositions such as motivation, confidence, optimism, peer relations and coping with stress. In the last few years, there has been a growing awareness that social and emotional factors play an important part in students? academic success and it has been claimed that those with high scores on a trait EI measure perform better. This research investigated whether scores on a questionnaire measure of trait EI were related (...)
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  33. Infinitesimals and the Continuum.John Bell - manuscript
    The opposed concepts of continuity and discreteness have figured prominently in the development of mathematics, and have also commanded the attention of philosophers. Continuous entities may be characterized by the fact that they can be divided indefinitely without altering their essential nature. So, for instance, the water in a bucket may be indefinitely halved and yet remain water. (For the purposes of illustration I ignore the atomic nature of matter which has been established by modern physics.) Discrete entities, on the (...)
     
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  34.  27
    Boolean Algebras and Distributive Lattices Treated Constructively.John L. Bell - 1999 - Mathematical Logic Quarterly 45 (1):135-143.
    Some aspects of the theory of Boolean algebras and distributive lattices–in particular, the Stone Representation Theorems and the properties of filters and ideals–are analyzed in a constructive setting.
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  35. Divergent Conceptions of the Continuum in 19th and Early 20th Century Mathematics and Philosophy.John L. Bell - 2005 - Axiomathes 15 (1):63-84.
  36.  13
    A Comparison of Science Performance and Uptake by Fifteen‐Year‐Old Boys and Girls in Co‐Educational and Single‐Sex Schools—APU Survey Findings.John F. Bell - 1989 - Educational Studies 15 (2):193-203.
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  37. Choice Principles in Intuitionistic Set Theory.John L. Bell - 2006 - In David DeVidi, Graham Solomon & Tim Kenyon (eds.), ¸ Itedevidikenyon2006. Springer Verlag.
    subsets X of A for which ∃x (x ∈ A). The set of functions from A to B is denoted by BA.
     
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  38. Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime Physics.John Bell - manuscript
    In the present paper the concept of a covering is presented and developed. The relationship between cover schemes, frames (complete Heyting algebras), Kripke models, and frame-valued set theory is discussed. Finally cover schemes and framevalued set theory are applied in the context of Markopoulou’s account of discrete spacetime as sets “evolving” over a causal set. We observe that Markopoulou’s proposal may be effectively realized by working within an appropriate frame-valued model of set theory. We go on to show that, within (...)
     
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  39.  22
    The Perspective of the Ordinary Citizen on Law.John Bell - 2004 - Res Publica 10 (3):311-317.
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  40.  38
    Oxford Essays in Jurisprudence.John Eekelaar & John Bell (eds.) - 1987 - Oxford University Press.
    This third book in the Oxford Essays in Jurisprudence series continues the established format and includes contributions from distinguished scholars in the field, each attempting to relate legal theory to specific areas of the law. Among the eminent contributors are Andrew Ashworth, Peter Cane, Hugh Collins, Anne de Moor, Jim Harris, Simon Lee, Bernard Rudden, and Christopher McCrudden.
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  41.  12
    Polymodal Lattices and Polymodal Logic.John L. Bell - 1996 - Mathematical Logic Quarterly 42 (1):219-233.
    A polymodal lattice is a distributive lattice carrying an n-place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and completeness theorems.
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  42.  10
    Precovers, Modalities and Universal Closure Operators in a Topos.John L. Bell & Silvia Gebellato - 1996 - Mathematical Logic Quarterly 42 (1):289-299.
    In this paper we develop the notion of formal precover in a topos by defining a relation between elements and sets in a local set theory. We show that such relations are equivalent to modalities and to universal closure operators. Finally we prove that these relations are well characterized by a convenient restriction to a particular set.
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  43.  2
    Incompleteness in a General Setting.John L. Bell - 2007 - Bulletin of Symbolic Logic 13 (1):21-30.
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  44.  11
    Patterns of Subject Uptake and Examination Entry 1984–1997.John F. Bell - 2001 - Educational Studies 27 (2):201-219.
    In 1984, the APU science survey collected information on the courses followed by Year 11 pupils. In this paper, the APU survey will be compared with recent GCSE examination level data and will describe the impact of the National Curriculum on the sexes and on pupils of differing ability. In 1984, there were considerable differences in uptake by the sexes and by ability. In 1997, pupils were taking more examinations than were pupils in 1984. Also, girls were taking more GCSEs (...)
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  45.  5
    Frege's Theorem in a Constructive Setting.John Bell - 1999 - Journal of Symbolic Logic 64 (2):486-488.
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  46.  3
    Studying Statute Law.John Bell - 1993 - Oxford Journal of Legal Studies 13 (1):130-141.
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  47. Algorithmicity and Consciousness.John L. Bell - manuscript
    Why should one believe that conscious awareness is solely the result of organizational complexity? What is the connection between consciousness and combinatorics: transformation of quantity into quality? The claim that the former is reducible to the other seems unconvincing—as unlike as chalk and cheese! In his book1 Penrose is at least attempting to compare like with like: the enigma of consciousness with the progress of physics.
     
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  48.  2
    A French Lesson in Judicial Review.John Bell - 1982 - Oxford Journal of Legal Studies 2 (1):142-146.
  49. An Invitation to Smooth Infinitesimal Analysis.John Bell - manuscript
    where f ′ (x) is the derivative of f(x) and A is a quantity whose value depends on both x and δx. Now if it were possible to take δx so small (but not demonstrably identical with 0) that (δx)2 = 0 then (1) would assume the simple form..
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  50.  11
    A Lifetime's Acquaintance with Shakespeare.John Bell - forthcoming - Australian Humanist, The 123:2.
    Bell, John I've been invited to share with you my experiences of a lifetime's acquaintance with Shakespeare, and how that acquaintance has led to what might be loosely termed a humanist philosophy.
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