Concept Formation in Mathematics

Sammanfattning
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.
Delarbeten
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.
 
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
 
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
 
IV. Sjögren, J. (2011). Indispensability, The Testing of Mathematical Theories, and Provisional Realism. Unpublished manuscript.
 
V. Bennet, C., & Sjögren, J. (2011). Mathematical Concepts as Unique Explications. Unpublished manuscript.
 
Examinationsnivå
Doctor of Philosophy
Universitet
Göteborgs universitet. Humanistiska fakulteten
University of Gothenburg. Faculty of Arts
Institution
Department of Philosophy, Linguistics and Theory of Science ; Institutionen för filosofi, lingvistik och vetenskapsteori
Disputation
Onsdagen den 8 juni 2011, kl 10.00, Sal T 302, Institutionen för filosofi, lingvistik och vetenskapsteori, Olof Wijksgatan 6.
Datum för disputation
2011-06-08
E-post
jorgen.sjogren@his.se
URL:
http://hdl.handle.net/2077/25299
Samlingar
Fil(er)
Datum
2011-05-19
Författare
Sjögren, Jörgen
Nyckelord
Explication, Power of arithmetical theories, Formal Proof, Informal proof, Indispensability, Mathematical Realism
Publikationstyp
Doctoral thesis
ISBN
978-91-7346-705-6
ISSN
0283-2380
Serie/rapportnr.
Acta Philosophica Gothoburgensia
27
Språk
eng
Metadata
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