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Concept Formation in Mathematics
University of Skövde, School of Life Sciences.
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. , 63 p.
Series
Acta Philosophica Gothoburgensia, ISSN 0283-2380 ; 27
Keyword [en]
Explication, Power of arithmetical theories, Formal proof, Informal proof, Indispensability, Mathematical realism
National Category
Natural Sciences
Research subject
Natural sciences
Identifiers
URN: urn:nbn:se:his:diva-5634ISBN: 978-91-7346-705-6 OAI: oai:DiVA.org:his-5634DiVA: diva2:512099
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: 2013-08-27Bibliographically approved

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