8 found
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  1.  47
    A Note on the Relation Between Formal and Informal Proof.Jörgen Sjögren - 2010 - Acta Analytica 25 (4):447-458.
    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 and informal, mathematical proof.
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  2.  14
    Concept Formation and Concept Grounding.Jörgen Sjögren & Christian Bennet - 2014 - Philosophia 42 (3):827-839.
    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. (...)
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  3.  27
    Indispensability, the Testing of Mathematical Theories, and Provisional Realism.Jörgen Sjögren - 2011 - Polish Journal of Philosophy 5 (2):99-116.
    Mathematical concepts are explications, in Carnap's sense, of vague or otherwise non-clear 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.
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  4.  18
    On Explicating the Concept the Power of an Arithmetical Theory.Jörgen Sjögren - 2008 - Journal of Philosophical Logic 37 (2):183 - 202.
    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 (...)
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  5. Om begreppsbildning i matematik.Jörgen Sjögren - 2006 - Norsk Filosofisk Tidsskrift 1.
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  6.  10
    Holism and Indispensability.Jörgen Sjögren - 2012 - Logique Et Analyse 55 (219):463-476.
    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 ind ..
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  7.  5
    The Viability of Social Constructivism as a Philosophy of Mathematics.Jörgen Sjögren & Christian Bennet - 2013 - Croatian Journal of Philosophy 13 (3):341-355.
    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.
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  8.  3
    Measuring the Power of Arithmetical Theories.Jörgen Sjögren - unknown
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