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  • 1.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    Högskolan i Skövde, Institutionen för vård och natur.
    Philosophy and mathematics education2013Inngår i: Modus Tolland: En festskrift med anledning av Anders Tollands sextioårsdag / [ed] Filip Radovic & Susanna Radovic, Göteborg: Göteborgs universitet , 2013, s. 9-23Kapittel i bok, del av antologi (Annet (populærvitenskap, debatt, mm))
  • 2.
    Bennet, Christian
    et al.
    Göteborgs universitet.
    Sjögren, Jörgen
    Högskolan i Skövde, Institutionen för vård och natur. Högskolan i Skövde, Forskningsspecialiseringen Hälsa och Lärande.
    The Viability of Social Constructivism as a Philosophy of Mathematics2013Inngår i: Croatian Journal of Philosophy, ISSN 1333-1108, E-ISSN 1847-6139, Vol. XIII, nr 39, s. 341-355Artikkel i tidsskrift (Fagfellevurdert)
    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
    Högskolan i Skövde, Institutionen för vård och natur. Dept. of Philosophy, Linguistics, and Theory of Science, University of Göteborg.
    A Note on the Relation Between Formal and Informal Proof2010Inngår i: Acta Analytica, ISSN 0353-5150, E-ISSN 1874-6349, Vol. 25, nr 4, s. 447-458Artikkel i tidsskrift (Fagfellevurdert)
    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
    Högskolan i Skövde, Institutionen för vård och natur.
    Concept Formation in Mathematics2011Doktoravhandling, med artikler (Annet vitenskapelig)
    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
    Högskolan i Skövde, Institutionen för vård och natur. Department of Philosophy, Linquistics, Theory of Science, University of Gothenburg, Sweden.
    Holism and Indispensability2012Inngår i: Logique et Analyse, ISSN 0024-5836, E-ISSN 2295-5836, Vol. 55, nr 219, s. 463-476Artikkel i tidsskrift (Fagfellevurdert)
    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
    Högskolan i Skövde, Institutionen för vård och natur. University of Gothenburg.
    Indispensability, the Testing of Mathematical Theories, and Provisional Realism2011Inngår i: Polish Journal of Philosophy, ISSN 1897-1652, E-ISSN 2154-3747, Polish Journal of Philosophy, ISSN 1897-1652, Vol. 5, nr 2, s. 99-116Artikkel i tidsskrift (Fagfellevurdert)
    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
    Högskolan i Skövde, Institutionen för vård och natur.
    Measuring the Power of Arithmetical Theories2005Licentiatavhandling, monografi (Annet vitenskapelig)
    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
    Högskolan i Skövde, Institutionen för vård och natur.
    Om begreppsbildning i matematik2006Inngår i: Filosofisk Tidskrift, ISSN 0348-7482, Vol. 27, nr 1, s. 49-57Artikkel i tidsskrift (Fagfellevurdert)
  • 9.
    Sjögren, Jörgen
    Högskolan i Skövde, Institutionen för vård och natur. Department of Philosophy/Logic, University of Göteborg, Gothenburg, Sweden.
    On explicating the concept the power of an arithmetical theory2008Inngår i: Journal of Philosophical Logic, ISSN 0022-3611, E-ISSN 1573-0433, Vol. 37, nr 2, s. 183-202Artikkel i tidsskrift (Fagfellevurdert)
    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
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningsspecialiseringen Hälsa och Lärande.
    Philosophy of Mathematics and Mathematics Education: Some Reflections2014Inngår i: 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, s. 85-100Kapittel i bok, del av antologi (Fagfellevurdert)
  • 11.
    Sjögren, Jörgen
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningsspecialiseringen Hälsa och Lärande.
    Bennet, Christian
    Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Sweden.
    Concept Formation and Concept Grounding2014Inngår i: Philosophia (Ramat Gan), ISSN 0048-3893, E-ISSN 1574-9274, Vol. 42, nr 3, s. 827-839Artikkel i tidsskrift (Fagfellevurdert)
    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.

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