Concept Formation in Mathematics

Simple item page
dc.contributor.authorSjögren, Jörgen
dc.date.accessioned2011-05-19T10:11:14Z
dc.date.available2011-05-19T10:11:14Z
dc.date.issued2011-05-19
dc.description.abstractThis 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.sv
dc.gup.defencedate2011-06-08
dc.gup.defenceplaceOnsdagen den 8 juni 2011, kl 10.00, Sal T 302, Institutionen för filosofi, lingvistik och vetenskapsteori, Olof Wijksgatan 6.sv
dc.gup.departmentDepartment of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteorisv
dc.gup.dissdb-fakultetHF
dc.gup.mailjorgen.sjogren@his.sesv
dc.gup.originGöteborgs universitet. Humanistiska fakultetenswe
dc.gup.originUniversity of Gothenburg. Faculty of Artseng
dc.gup.price189
dc.identifier.isbn978-91-7346-705-6
dc.identifier.issn0283-2380
dc.identifier.urihttp://hdl.handle.net/2077/25299
dc.language.isoengsv
dc.relation.haspartI. Sjögren, J. (2004). Measuring the Power of Arithmetical Theories. Dept. of Philosophy, University of Göteborg, Philosophical Communications, Red Series number 39, ISSN: 0347-5794.sv
dc.relation.haspartII. Sjögren, J. (2008). On Explicating the Concept the Power of an Arithmetical Theory. Journal of Philosophical Logic, 37, 183-202::doi::10.1007/s10992-007-9077-8sv
dc.relation.haspartIII. Sjögren, J. (2010). A Note on the Relation Between Formal and Informal Proof. Acta Analytica, 25, 447-458::doi::10.1007/s12136-009-0084-ysv
dc.relation.haspartIV. Sjögren, J. (2011). Indispensability, The Testing of Mathematical Theories, and Provisional Realism. Unpublished manuscript.sv
dc.relation.haspartV. Bennet, C., & Sjögren, J. (2011). Mathematical Concepts as Unique Explications. Unpublished manuscript.sv
dc.relation.ispartofseriesActa Philosophica Gothoburgensiasv
dc.relation.ispartofseries27sv
dc.subjectExplication, Power of arithmetical theories, Formal Proof, Informal proof, Indispensability, Mathematical Realismsv
dc.titleConcept Formation in Mathematicssv
dc.typeText
dc.type.degreeDoctor of Philosophysv
dc.type.svepDoctoral thesiseng

Files

Original bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
gupea_2077_25299_1.pdf
Size:
330.4 KB
Format:
Adobe Portable Document Format
Description:
Thesis
Download
No Thumbnail Available
Name:
gupea_2077_25299_2.pdf
Size:
47.63 KB
Format:
Adobe Portable Document Format
Description:
Abstract
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
gupea_2077_25299_3.txt
Size:
4.68 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Doctoral Theses / Doktorsavhandlingar Institutionen för filosofi, lingvistik och vetenskapsteori
Acta Philosophica Gothoburgensia
Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet