Abstract
Ever since the 1980s, the dominant trend in the field within philosophical logic concerning the logic of theory change has been to work with models lying rather close to the well-known AGM approach. In particular, most of the (normative, formal) theories on the subject of theory change that can be found in the literature seem to be in relatively close agreement on how to represent theories; roughly, it is assumed that theories are representable as sets of statements. In this paper, I will try to draw the outlines of a model for theory change in which this assumption is revised: instead of the usual representation of theories, the foundation of the model will be based on the structuralistic notion of a theory net. Structuralism proceeds from the idea that scientific theories have what we may call a deep structure, and aims to provide a formal representation of theories that respects this structure and describes it in as much detail as possible. The result is a formal notion of “theory” which is considerably more fine-grained than the AGM-style representation in terms of logically closed sets of sentences, and my hope is that it will help shed some new light on the problems studied in the preexisting frameworks for theory change, as well as open up new and interesting research problems in the field.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Proof: we focus on CL1. As a model for {A1,A3,A4} where CL1 fails, take the set of natural numbers N, evaluate e as 0, and evaluate ⊗ as the function \(\delta :N \times N \to N\) given by
\(\delta (x,y) = 0\), if \(x = y\),
\(\delta (x,y)\) is the greatest number of x and y otherwise.
A1 is clearly satisfied, A3 is satisfied since if \(x = 0\), then \(\delta (x,0) = \delta (x,x) = 0\), and if \(x > 0\), then \(\delta (x,0)\) is the greatest number of x and 0, i.e. x. A4 is also satisfied; the inverse of any x is simply x itself. CL1 fails, for \(\delta (4,3) = \delta (4,2) = 4\), but \(3 \ne 2\) of course. As a model for {A1, A2, A4} where CL1 fails, take the set \(\wp(N)\), and evaluate e as ∅, and ⊗ as ∩. A1 holds of course, A2 holds since intersections are associative, and A4 holds since the inverse of every set is simply ∅. CL1 fails, as \(\{ 1\} \cap \{ 1,2\} = \{ 1\} \cap \{ 1,3\} = \{ 1\}\). Finally, as a model for {A1, A2, A3} where CL1 fails, take the set N and evaluate e as 1, and ⊗ as multiplication on natural numbers. A1 holds, A2 holds as multiplication is associative, and A3 clearly holds as well. But CL1 fails, since \(0^*1 = 0^*2 = 0\), for instance. □
References
Balzer, W., and C.U. Moulines. (eds.). 1996. Structuralist theory of science (focal issues, new results). Berlin, NY: Walter de Gruyter.
Balzer, W., C.U., Moulines, and J.D. Sneed. 1987. An architectonic for science. Dordrecht: Reidel.
Gärdenfors, P. 1988. Knowledge in flux: Modeling the dynamics of epistemic states. Cambridge, MA: MIT.
Gärdenfors, P. 1992. Sneeds rekonstruktion av teoriers struktur och dynamik. In Metod eller anarki, ed. B. Hansson, 93–105. University of Lund.
Grove, A. 1988. Two modellings for theory change. Journal of Philosophical Logic 2(17):157–170.
Levi, I. 1991. Fixation of belief and its undoing: Changing beliefs through inquiry. Cambridge, MA: Cambridge University Press.
Lindström, S., and W. Rabinowicz. 1991. Epistemic entrenchment with incomparabilities and relational belief revision. In The logic of theory change, eds. A. Fuhrmann and M. Morreau, 93–126. Berlin: Springer.
Olsson, E.J. 2006. Lindström and Rabinowicz on relational belief revision. Festschrift to Wlodek Rabinowicz on the occasion of his 60th birthday.
Olsson, E., and D. Westlund. 2006. On the role of the research agenda in epistemic change. Retrieved December 3, 2007, from Lund University, Department of Philosophy web site: http://www.fil.lu.se/publicationfiles/pp91.pdf
Segerberg, K. 1998. Irrevocable belief revision in dynamic doxastic logic. Notre Dame Journal of Formal Logic 39(3):287–306.
Segerberg, K., and H. Leitgeb. 2007. Dynamic doxastic logic: Why, how and where to? Synthese 155:167–190.
Sneed, J.D. 1971. The logical structure of mathematical physics. Dordrecht: Reidel.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Enqvist, S. (2010). A Structuralist Framework for the Logic of Theory Change. In: Olsson, E., Enqvist, S. (eds) Belief Revision meets Philosophy of Science. Logic, Epistemology, and the Unity of Science, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9609-8_5
Download citation
DOI: https://doi.org/10.1007/978-90-481-9609-8_5
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9608-1
Online ISBN: 978-90-481-9609-8
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)