Concept Formation in Mathematics
| Sjögren, Jörgen | ||
| 2011-05-19T10:11:14Z | ||
| 2011-05-19T10:11:14Z | ||
| 2011-05-19 | ||
| 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. | sv | |
| 2011-06-08 | ||
| Onsdagen den 8 juni 2011, kl 10.00, Sal T 302, Institutionen för filosofi, lingvistik och vetenskapsteori, Olof Wijksgatan 6. | sv | |
| Department of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteori | sv | |
| HF | ||
| jorgen.sjogren@his.se | sv | |
| University of Gothenburg. Faculty of Arts | eng | |
| Göteborgs universitet. Humanistiska fakulteten | swe | |
| 189 | ||
| 978-91-7346-705-6 (printed) | ||
| 0346-7740 | ||
| 0283-2380 | ||
| http://hdl.handle.net/2077/25299 | ||
| eng | ||
| Acta Universitatis Gothoburgensis | ||
| I. 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 | |
| II. Sjögren, J. (2008). On Explicating the Concept the Power of an Arithmetical Theory. Journal of Philosophical Logic, 37, 183-202::doi::10.1007/s10992-007-9077-8 | sv | |
| III. Sjögren, J. (2010). A Note on the Relation Between Formal and Informal Proof. Acta Analytica, 25, 447-458::doi::10.1007/s12136-009-0084-y | sv | |
| IV. Sjögren, J. (2011). Indispensability, The Testing of Mathematical Theories, and Provisional Realism. Unpublished manuscript. | sv | |
| V. Bennet, C., & Sjögren, J. (2011). Mathematical Concepts as Unique Explications. Unpublished manuscript. | sv | |
| Acta Philosophica Gothoburgensia ; 27 | ||
| Explication, Power of arithmetical theories, Formal Proof, Informal proof, Indispensability, Mathematical Realism | sv | |
| Concept Formation in Mathematics | en | |
| Text | ||
| Doctor of Philosophy | sv | |
| Doctoral thesis | eng |
Files
License bundle
1 - 1 of 1
Loading...
- Name:
- gupea_2077_25299_3.txt
- Size:
- 4.68 KB
- Format:
- Item-specific license agreed upon to submission
- Description: