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Göteborgs universitets publikationer

Concept Formation in Mathematics

Författare och institution:
Jörgen Sjögren (Institutionen för filosofi, lingvistik och vetenskapsteori)
Datum för examination:
Onsdagen den 8 juni 2011, kl 10.00, Sal T 302, Institutionen för filosofi, lingvistik och vetenskapsteori, Olof Wijksgatan 6.
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Historia och arkeologi
Explication, Power of arithmetical theories, Formal Proof, Informal proof, Indispensability, Mathematical Realism
Ytterligare information:
Submitted by Jörgen Sjögren ( on 2011-05-16T07:51:28Z No. of bitstreams: 2 Spikblad_espik.pdf: 48773 bytes, checksum: 29c853fdf1b707fa11e51b08cee2c6c1 (MD5) Kappa_espik.pdf: 338328 bytes, checksum: 716f7534ef626c55627f235c029f6b29 (MD5)
Postens nummer:
Posten skapad:
2011-11-23 13:41

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