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  • 1.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences.
    Philosophy and mathematics education2013In: Modus Tolland: En festskrift med anledning av Anders Tollands sextioårsdag / [ed] Filip Radovic & Susanna Radovic, Göteborg: Göteborgs universitet , 2013, p. 9-23Chapter in book (Other (popular science, discussion, etc.))
  • 2.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. University of Skövde, Health and Education.
    The Viability of Social Constructivism as a Philosophy of Mathematics2013In: Croatian Journal of Philosophy, ISSN 1333-1108, E-ISSN 1847-6139, Vol. XIII, no 39, p. 341-355Article in journal (Refereed)
    Abstract [en]

    Attempts have been made to analyse features in mathematics within a social constructivist context. In this paper we critically examine some of those attempts recently made with focus on problems of the objectivity, ontology, necessity, and atemporality of mathematics. Our conclusion is that these attempts fare no better than traditional alternatives, and that they, furthermore, create new problems of their own.

  • 3.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. Dept. of Philosophy, Linguistics, and Theory of Science, University of Göteborg.
    A Note on the Relation Between Formal and Informal Proof2010In: Acta Analytica, ISSN 0353-5150, E-ISSN 1874-6349, Vol. 25, no 4, p. 447-458Article in journal (Refereed)
    Abstract [en]

    Using Carnap’s concept explication, we propose a theory of concept formation in mathematics. This theory is then applied to the problem of how to understand the relation between the concepts formal proof (deduction) and informal, mathematical proof.

  • 4.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences.
    Concept Formation in Mathematics2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of three overlapping parts, where the first one centers around the possibility of defining a measure of the power of arithmetical theories. In this part a partial measure of the power of arithmetical theories is constructed, where “power” is understood as capability to prove theorems. It is also shown that other suggestions in the literature for such a measure do not satisfy natural conditions on a measure. In the second part a theory of concept formation in mathematics is developed. This is inspired by Aristotle’s conception of mathematical objects as abstractions, and it uses Carnap’s method of explication as a means to formulate these abstractions in an ontologically neutral way. Finally, in the third part some problems of philosophy of mathematics are discussed. In the light of this idea of concept formation it is discussed how the relation between formal and informal proof can be understood, how mathematical theories are tested, how to characterize mathematics, and some questions about realism and indispensability.

  • 5.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. Department of Philosophy, Linquistics, Theory of Science, University of Gothenburg, Sweden.
    Holism and Indispensability2012In: Logique et Analyse, ISSN 0024-5836, E-ISSN 2295-5836, Vol. 55, no 219, p. 463-476Article in journal (Refereed)
    Abstract [en]

    One questioned premiss in the indispensability argument of Quine and Putnam is confirmational holism. In this paper I argue for a weakened form of holism, and thus a strengthened version of the indispensability argument. The argument is based on an idea of concept formation in mathematics. Mathematical concepts are arrived at via a sequence of explications, in Carnap's sense, of non-clear, originally empirical, concepts. I identify a deductive and an empirical component in mathematical concepts. In a test situation the use of the empirical component, but not of the deductive one, is corroborated or falsified together with the scientific theory.

  • 6.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. University of Gothenburg.
    Indispensability, the Testing of Mathematical Theories, and Provisional Realism2011In: Polish Journal of Philosophy, ISSN 1897-1652, E-ISSN 2154-3747, Polish Journal of Philosophy, ISSN 1897-1652, Vol. 5, no 2, p. 99-116Article in journal (Refereed)
    Abstract [en]

    Mathematical concepts are explications, in Carnap's sense, of vague or otherwise unclear concepts; mathematical theories have an empirical and a deductive component. From this perspective, I argue that the empirical component of a mathematical theory may be tested together with the fruitfulness of its explications. Using these ideas, I furthermore give an argument for mathematical realism, based on the indispensability argument combined with a weakened version of confirmational holism

  • 7.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences.
    Measuring the Power of Arithmetical Theories2005Licentiate thesis, monograph (Other scientific)
    Abstract [en]

    This thesis discusses the possibility to measure the power of extentions of Peano Aritmetic, P A. It consists of three parts, an introduction and two separately written papers. In the introduction we present the problem and briefly give an account of van Lambalgen's and raatikainen's criticism of gnenralization of two versions of Chaitin's incompleteness theorem, and reinforces the above mentioned criticism. The second paper is the main paper of the thesis, and here, using the modal logic GL, we design a measure of the power, in terms of the capacity to prove theorems, of an important set of extentions of P A.

  • 8.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences.
    Om begreppsbildning i matematik2006In: Filosofisk Tidskrift, ISSN 0348-7482, Vol. 27, no 1, p. 49-57Article in journal (Refereed)
  • 9.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. Department of Philosophy/Logic, University of Göteborg, Gothenburg, Sweden.
    On explicating the concept the power of an arithmetical theory2008In: Journal of Philosophical Logic, ISSN 0022-3611, E-ISSN 1573-0433, Vol. 37, no 2, p. 183-202Article in journal (Refereed)
    Abstract [en]

    In this paper I discuss possible ways of measuring the power of arithmetical theories, and the possiblity of making an explication in Carnap’s sense of this concept. Chaitin formulates several suggestions how to construct measures, and these suggestions are reviewed together with some new and old critical arguments. I also briefly review a measure I have designed together with some shortcomings of this measure. The conclusion of the paper is that it is not possible to formulate an explication of the concept.

  • 10.
    Sjögren, Jörgen
    University of Skövde, School of Engineering Science. University of Skövde, Health and Education.
    Philosophy of Mathematics and Mathematics Education: Some Reflections2014In: IDÉES FIXES: A festschrift dedicated to Christian Bennet on the occasion of his 60th birthday / [ed] Martin Kaså, Göteborg: Department of Philosophy, Linguistics and Theory of Science , 2014, p. 85-100Chapter in book (Refereed)
  • 11.
    Sjögren, Jörgen
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, Health and Education.
    Bennet, Christian
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Sweden.
    Concept Formation and Concept Grounding2014In: Philosophia (Ramat Gan), ISSN 0048-3893, E-ISSN 1574-9274, Vol. 42, no 3, p. 827-839Article in journal (Refereed)
    Abstract [en]

    Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.

1 - 11 of 11
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