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1 — 50 / 54
  1. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  2. added 2018-03-21
    A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  3. added 2018-01-28
    On the Chow Ring of a Flag.Christian Wenzel - 1997 - Mathematische Nachrichten 188:293-310.
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  4. added 2018-01-28
    On the Structure of Non-Reduced Parabolic Subgroup-Schemes.Christian Wenzel - 1994 - Proceedings of Symposia in Pure Mathematics 56 (1):291-297.
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  5. added 2018-01-28
    Rationality of G/P for a Non-Reduced Parabolic Subgroup Scheme P.Christian Wenzel - 1993 - Proceedings of the American Mathematical Society 117 (4):899-904.
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  6. added 2018-01-28
    Classification of All Parabolic Subgroup Schemes of a Reductive Linear Algebraic Group Over an Algebraically Closed Field.Christian Wenzel - 1993 - Transactions of the American Mathematical Society 337 (1):211-218.
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  7. added 2017-11-01
    Inequivalent Representations of Geometric Relation Algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
    It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...)
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  8. added 2017-10-10
    The Structure of Field Space.Dominic G. B. Edelen - 1962 - Berkeley: University of California Press.
  9. added 2017-10-06
    Automorphisms of Supermaximal Subspaces.R. G. Downey & G. R. Hird - 1985 - Journal of Symbolic Logic 50 (1):1-9.
  10. added 2017-09-23
    Linear and Geometric Algebra.Alan Macdonald - 2012 - North Charleston, SC: CreateSpace.
    This textbook for the second year undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. -/- Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much (...)
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  11. added 2017-08-23
    ‘Chasing’ The Diagram - The Use of Visualizations in Algebraic Reasoning.Silvia De Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  12. added 2017-04-06
    Finite Methods in Mathematical Practice.Peter Schuster & Laura Crosilla - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 351-410.
    In the present contribution we look at the legacy of Hilbert's programme in some recent developments in mathematics. Hilbert's ideas have seen new life in generalised and relativised forms by the hands of proof theorists and have been a source of motivation for the so--called reverse mathematics programme initiated by H. Friedman and S. Simpson. More recently Hilbert's programme has inspired T. Coquand and H. Lombardi to undertake a new approach to constructive algebra in which strong emphasis is laid on (...)
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  13. added 2016-12-08
    On Abstraction and the Importance of Asking the Right Research Questions: Could Jordan Have Proved the Jordan-Hölder Theorem?Dirk Schlimm - 2008 - Erkenntnis 68 (3):409-420.
    In 1870 Jordan proved that the composition factors of two composition series of a group are the same. Almost 20 years later Hölder (1889) was able to extend this result by showing that the factor groups, which are quotient groups corresponding to the composition factors, are isomorphic. This result, nowadays called the Jordan-Hölder Theorem, is one of the fundamental theorems in the theory of groups. The fact that Jordan, who was working in the framework of substitution groups, was able to (...)
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  14. added 2016-12-08
    The Architecture of Modern Mathematics.Gray Jeremy & Ferreiros Jose (eds.) - 2006 - Oxford University Press.
    This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.
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  15. added 2016-12-08
    On Free Annotated Algebras.Renato A. Lewin, Irene F. Mikenberg & Marı́a G. Schwarze - 2001 - Annals of Pure and Applied Logic 108 (1-3):249-259.
    In Lewin et al. 359–386) the authors proved that certain systems of annotated logics are algebraizable in the sense of Block and Rigozzi 396). Later in Lewin et al. the study of the associated quasi-varieties of annotated algebras is initiated. In this paper we continue the study of the these classes of algebras, in particular, we report some recent results about the free annotated algebras.
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  16. added 2016-12-08
    Théorie Métamathématique des Idéaux. [REVIEW]R. A. A. - 1956 - Review of Metaphysics 9 (4):709-709.
  17. added 2016-11-04
    Fictionalism and Mathematical Objectivity.Iulian D. Toader - 2012 - In Metaphysics and Science. Festschrift for Professor Ilie Pârvu. University of Bucharest Press. pp. 137-158.
  18. added 2016-04-02
    Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
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  19. added 2015-11-22
    Reconfiguring the Centre: The Structure of Scientific Exchanges Between Colonial India and Europe.Dhruv Raina - 1996 - Minerva 34 (2):161-176.
    The “centre-periphery” relationship historically structured scientific exchanges between metropolis and province, between the fount of empire and its outposts. But the exchange, if regarded merely as a one-way flow of scientific information, ignores both the politics of knowledge and the nature of its appropriation. Arguably, imperial structures do not entirely determine scientific practices and the exchange of knowledge. Several factors neutralise the over-determining influence of politics—and possibly also the normative values of science—on scientific practice.In examining these four examples of Indian (...)
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  20. added 2015-11-22
    Aspects of Universal Algebra in Combinatory Logic.Beatrice Amrhein - 1995 - In Erwin Engeler (ed.), The Combinatory Programme. Birkhäuser. pp. 31--45.
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  21. added 2015-11-22
    Mathematical Foundations of a Cultural Project or Ramchandra's Treatise “Through the Unsentimentalised Light of Mathematics”.Dhruv Raina - 1992 - Historia Mathematica 19 (4).
    The nineteenth century witnessed a number of projects of cultural rapprochement between the knowledge traditions of the East and West. This paper discusses the attempt to render elementary calculus amenable to an Indian audience in the indigenous mathematical idiom, undertaken by an Indian polymath, Ramchandra. The exercise is specifically located in his book A Treatise on the Problems of Maxima and Minima. The paper goes on to discuss the “vocation of failure” of the book within the context of encounter and (...)
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  22. added 2015-11-22
    Quasi Equational Logic Of Partial Algebras.Hajnal Andreka, Peter Burmeister & Istvan Nemeti - 1980 - Bulletin of the Section of Logic 9 (4):193-197.
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  23. added 2015-07-21
    Computability of Boolean Algebras and Their Extensions.Donald A. Alton & E. W. Madison - 1973 - Annals of Mathematical Logic 6 (2):95-128.
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  24. added 2015-07-20
    A Simple Construction of Representable Relation Algebras with Non‐Representable Completions.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):237-244.
    We give a simple new construction of representable relation algebras with non-representable completions. Using variations on our construction, we show that the elementary closure of the class of completely representable relation algebras is not finitely axiomatizable.
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  25. added 2015-07-20
    Classes of Representable Algebras with the Amalgamation Property.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (2):115-121.
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  26. added 2015-07-20
    Amalgamation for Reducts of Polyadic Equality Algebras, a Negative Result.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (1):37-50.
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  27. added 2015-07-20
    Elementary Constructive Theory of Henselian Local Rings.María E. Alonso, Henri Lombardi & Hervé Perdry - 2008 - Mathematical Logic Quarterly 54 (3):253-271.
    We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.
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  28. added 2015-07-20
    Normal Subgroups of Nonstandard Symmetric and Alternating Groups.John Allsup & Richard Kaye - 2007 - Archive for Mathematical Logic 46 (2):107-121.
    Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement if (...)
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  29. added 2015-07-20
    Polyadic and Cylindric Algebras of Sentences.Mohamed Amer & Tarek Sayed Ahmed - 2006 - Mathematical Logic Quarterly 52 (5):444-449.
    In this note we give an interpretation of cylindric algebras as algebras of sentences of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof.
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  30. added 2015-07-07
    Zariski‐Type Topology for Implication Algebras.Manuel Abad, Diego Castaño & José P. Díaz Varela - 2010 - Mathematical Logic Quarterly 56 (3):299-309.
    In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof.
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  31. added 2015-07-07
    Boolean Algebras With A Distinguished Automorphism.M. Abad, J. P. D.\'{\I.}az Varela & M. Zander - 2003 - Reports on Mathematical Logic:101-112.
    In this paper we investigate a subvariety $\BA$ of tense algebras, which we call Boolean algebras with a distinguished automorphism. This variety provides a unifying framework for the algebras studied by Monteiro in [4] and by Moisil in [5,6]. Among others we prove that $\BA$ is generated by its finite members and we characterize the locally finite subvarieties of $\BA$.
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  32. added 2015-07-07
    Free Boolean Correlations Lattices.Manuel Abad, Alicia Fernandez & Nelli Meske - 1996 - Reports on Mathematical Logic:2-11.
    In this paper we study some algebraic properties of the variety of Boolean correlation lattices. We give a characterization of congruences and simple algebras of the variety and we describe the algebra with a finite set of free generators.
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  33. added 2014-04-02
    Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten de Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61-78.
    For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. (...)
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  34. added 2014-04-01
    Distributive Lattices with an Operator.Alejandro Petrovich - 1996 - Studia Logica 56 (1-2):205 - 224.
    It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...)
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  35. added 2014-03-31
    Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator.Burghard Herrmann - 1997 - Studia Logica 58 (2):305-323.
    In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, (...)
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  36. added 2014-03-25
    Abstract Mathematical Tools and Machines for Mathematics.Jean-pierre Marquis - 1997 - Philosophia Mathematica 5 (3):250-272.
    In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...)
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  37. added 2014-03-22
    The Distance Function in Commutative ℓ-Semigroups and the Equivalence in Łukasiewicz Logic.Andrzej Wroński - 2004 - Studia Logica 77 (2):241 - 253.
    The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.
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  38. added 2014-03-21
    Dividing in the Algebra of Compact Operators.Alexander Berenstein - 2004 - Journal of Symbolic Logic 69 (3):817-829.
    We interpret the algebra of finite rank operators as imaginaries inside a Hilbert space. We prove that the Hilbert space enlarged with these imaginaries has built-in canonical bases.
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  39. added 2014-03-13
    Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920).Robert K. Meyer - 2008 - Journal of Philosophical Logic 37 (2):169 - 181.
    C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...)
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  40. added 2014-03-06
    The History of Algebra and the Development of the Form of its Language.Ladislav Kvasz - 2006 - Philosophia Mathematica 14 (3):287-317.
    This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwrizm, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form of the symbolic language of algebra. Thus the paper develops further the (...)
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  41. added 2013-02-11
    Notes on Groups and Geometry, 1978-1986.Steven H. Cullinane - 2012 - Internet Archive.
    Typewritten notes on groups and geometry.
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  42. added 2013-01-06
    Laws of Form.G. Spencer-Brown - 1972 - New York: Julian Press.
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  43. added 2012-12-25
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
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  44. added 2012-12-25
    An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  45. added 2012-12-25
    The Lattice of Distributive Closure Operators Over an Algebra.Josep M. Font & Ventura Verdú - 1993 - Studia Logica 52 (1):1 - 13.
    In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...)
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  46. added 2012-12-25
    The Representation of Takeuti's *20c ||_ -Operator.Roger M. Cooke & Michiel Lambalgen - 1983 - Studia Logica 42 (4):407 - 415.
    Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}(L)\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $(A)(A\subseteq L)$ corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L.
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  47. added 2012-12-25
    Distributive Lattices with a Dual Homomorphic Operation.Alasdair Urquhart - 1979 - Studia Logica 38 (2):201 - 209.
    The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
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  48. added 2012-12-16
    Newton and Hamilton: In Defense of Truth in Algebra.Janet Folina - 2012 - Southern Journal of Philosophy 50 (3):504-527.
    Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, (...)
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  49. added 2012-07-20
    Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - Synthese 190 (12):2141-2164.
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...)
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  50. added 2012-03-16
    Algebraic Logic with Generalized Quantifiers.Charles C. Pinter - 1975 - Notre Dame Journal of Formal Logic 16 (4):511-516.
1 — 50 / 54