his.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Sjögren, Jörgen
Publications (10 of 11) Show all publications
Sjögren, J. & Bennet, C. (2014). Concept Formation and Concept Grounding. Philosophia (Ramat Gan), 42(3), 827-839
Open this publication in new window or tab >>Concept Formation and Concept Grounding
2014 (English)In: Philosophia (Ramat Gan), ISSN 0048-3893, E-ISSN 1574-9274, Vol. 42, no 3, p. 827-839Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2014
Keywords
Epistemology, Mathematics, Knowledge of theorems, The role of proof, Empiricism, Concept grounding, Concept formation
National Category
Other Mathematics
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-9075 (URN)10.1007/s11406-014-9528-8 (DOI)000342167800019 ()2-s2.0-84901729733 (Scopus ID)
Available from: 2014-05-12 Created: 2014-05-12 Last updated: 2017-12-05Bibliographically approved
Sjögren, J. (2014). Philosophy of Mathematics and Mathematics Education: Some Reflections. In: Martin Kaså (Ed.), IDÉES FIXES: A festschrift dedicated to Christian Bennet on the occasion of his 60th birthday (pp. 85-100). Göteborg: Department of Philosophy, Linguistics and Theory of Science
Open this publication in new window or tab >>Philosophy of Mathematics and Mathematics Education: Some Reflections
2014 (English)In: 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)
Place, publisher, year, edition, pages
Göteborg: Department of Philosophy, Linguistics and Theory of Science, 2014
Series
Philosophical Communications. Web Series, ISSN 1652-0459 ; 61
National Category
Other Mathematics
Identifiers
urn:nbn:se:his:diva-10035 (URN)978-91-982100-0-2 (ISBN)
Available from: 2014-09-30 Created: 2014-09-30 Last updated: 2017-11-27Bibliographically approved
Bennet, C. & Sjögren, J. (2013). Philosophy and mathematics education. In: Filip Radovic & Susanna Radovic (Ed.), Modus Tolland: En festskrift med anledning av Anders Tollands sextioårsdag (pp. 9-23). Göteborg: Göteborgs universitet
Open this publication in new window or tab >>Philosophy and mathematics education
2013 (English)In: 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.))
Place, publisher, year, edition, pages
Göteborg: Göteborgs universitet, 2013
Series
Philosophical Communications. Web Series, ISSN 1652-0459 ; 59
National Category
Mathematics
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-8715 (URN)978-91-637-3384-0 (ISBN)
Available from: 2014-01-03 Created: 2014-01-03 Last updated: 2017-11-27Bibliographically approved
Bennet, C. & Sjögren, J. (2013). The Viability of Social Constructivism as a Philosophy of Mathematics. Croatian Journal of Philosophy, XIII(39), 341-355
Open this publication in new window or tab >>The Viability of Social Constructivism as a Philosophy of Mathematics
2013 (English)In: Croatian Journal of Philosophy, ISSN 1333-1108, E-ISSN 1847-6139, Vol. XIII, no 39, p. 341-355Article in journal (Refereed) Published
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.

Keywords
Social constructivism, mathematics, ontology, objectivity, necessity, atemporality
National Category
Other Mathematics
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-9074 (URN)000334817200001 ()
Available from: 2014-05-12 Created: 2014-05-12 Last updated: 2017-11-27Bibliographically approved
Sjögren, J. (2012). Holism and Indispensability. Logique et Analyse, 55(219), 463-476
Open this publication in new window or tab >>Holism and Indispensability
2012 (English)In: Logique et Analyse, ISSN 0024-5836, E-ISSN 2295-5836, Vol. 55, no 219, p. 463-476Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Centre national de recherches de Logique (Belgien), 2012
National Category
Mathematics
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-7149 (URN)000310114800005 ()2-s2.0-84867427823 (Scopus ID)
Available from: 2013-02-11 Created: 2013-02-07 Last updated: 2017-12-06Bibliographically approved
Sjögren, J. (2011). Concept Formation in Mathematics. (Doctoral dissertation). University of Gothenburg
Open this publication in new window or tab >>Concept Formation in Mathematics
2011 (English)Doctoral 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.

Place, publisher, year, edition, pages
University of Gothenburg, 2011. p. 63
Series
Acta Philosophica Gothoburgensia, ISSN 0283-2380 ; 27
Keywords
Explication, Power of arithmetical theories, Formal proof, Informal proof, Indispensability, Mathematical realism
National Category
Natural Sciences
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-5634 (URN)978-91-7346-705-6 (ISBN)
Note

I) Measuring the Power of Arithmetical Theories. Thesis for the Licentiate degree, Department of Philosophy, University of Göteborg, (2004) Philosophical Communications, Red Series number 39, ISSN: 0347 - 5794. Also available at: http://www.phil.gu.se/posters/jslic.pdf

II) On Explicating the Concept The Power of an Arithmetical Theory. Journal of Philosophical Logic, (2008) 37: 183-202. DOI: 10.1007/s10992-007-9077-8

III) A Note on the Relation Between Formal and Informal Proof. Acta Analytica, (2010) 25: 447-458. DOI 10.1007/s12136-009-0084-y

IV) Indispensability, The Testing of Mathematical Theories, and Provisional Realism. Re-submitted paper.

V) Mathematical Concepts as Unique Explications (with Christian Bennet). Submitted paper.

 

Available from: 2012-03-27 Created: 2012-03-26 Last updated: 2017-11-27Bibliographically approved
Sjögren, J. (2011). Indispensability, the Testing of Mathematical Theories, and Provisional Realism. Polish Journal of Philosophy, 5(2), 99-116
Open this publication in new window or tab >>Indispensability, the Testing of Mathematical Theories, and Provisional Realism
2011 (English)In: 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) Published
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

Place, publisher, year, edition, pages
Jagiellonian University Press, 2011
National Category
Natural Sciences
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-5918 (URN)10.5840/pjphil20115220 (DOI)
Available from: 2012-06-04 Created: 2012-06-04 Last updated: 2017-12-07Bibliographically approved
Sjögren, J. (2010). A Note on the Relation Between Formal and Informal Proof. Acta Analytica, 25(4), 447-458
Open this publication in new window or tab >>A Note on the Relation Between Formal and Informal Proof
2010 (English)In: Acta Analytica, ISSN 0353-5150, E-ISSN 1874-6349, Vol. 25, no 4, p. 447-458Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer Netherlands, 2010
Keywords
Concept formation in mathematics, Explication, Formal proof, Informal proof, Mathematization
National Category
Mathematics
Research subject
Natural sciences
Identifiers
urn:nbn:se:his:diva-4331 (URN)10.1007/s12136-009-0084-y (DOI)000284266900005 ()2-s2.0-78649317475 (Scopus ID)
Available from: 2010-08-26 Created: 2010-08-26 Last updated: 2017-12-12Bibliographically approved
Sjögren, J. (2008). On explicating the concept the power of an arithmetical theory. Journal of Philosophical Logic, 37(2), 183-202
Open this publication in new window or tab >>On explicating the concept the power of an arithmetical theory
2008 (English)In: Journal of Philosophical Logic, ISSN 0022-3611, E-ISSN 1573-0433, Vol. 37, no 2, p. 183-202Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2008
Keywords
Gregory Chaitin, explication, measurement, power of arithmetical theories
National Category
Algebra and Logic
Identifiers
urn:nbn:se:his:diva-2753 (URN)10.1007/s10992-007-9077-8 (DOI)000253572500005 ()2-s2.0-40049102285 (Scopus ID)
Available from: 2009-02-18 Created: 2009-02-18 Last updated: 2017-12-13Bibliographically approved
Sjögren, J. (2006). Om begreppsbildning i matematik. Filosofisk Tidskrift, 27(1), 49-57
Open this publication in new window or tab >>Om begreppsbildning i matematik
2006 (Swedish)In: Filosofisk Tidskrift, ISSN 0348-7482, Vol. 27, no 1, p. 49-57Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Bokförlaget Thales, 2006
Identifiers
urn:nbn:se:his:diva-1794 (URN)
Available from: 2008-01-08 Created: 2008-01-08 Last updated: 2017-12-12Bibliographically approved
Organisations

Search in DiVA

Show all publications