Synthese

, Volume 79, Issue 3, pp 515–542

The architecture of complexity: A new blueprint

  • Peter Turney
Article

Abstract

The logic of scientific discovery is now a concern of computer scientists, as well as philosophers. In the computational approach to inductive inference, theories are treated as algorithms (computer programs), and the goal is to find the simplest algorithm that can generate the given data. Both computer scientists and philosophers want a measure of simplicity, such that simple theories are more likely to be true than complex theories. I attempt to provide such a measure here. I define a measure of simplicity for directed graphs, inspired by Herbert Simon's work. Many structures, including algorithms, can be naturally modelled by directed graphs. Furthermore, I adapt an argument of Simon's to show that simple directed graphs are more stable and more resistant to damage than complex directed graphs. Thus we have a reason for pursuing simplicity, other than purely economical reasons.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angluin, D. C. and C. H. Smith: 1983, ‘Inductive Inference: Theory and Methods’,Computing Surveys 15, 237–69.CrossRefGoogle Scholar
  2. Ball, M. O.: 1980, ‘Complexity of Network Reliability Computations’,Networks 10, 153–65.Google Scholar
  3. Blum, L. and M. Blum: 1975, ‘Toward a Mathematical Theory of Inductive Inference’,Information and Control 28, 125–55.Google Scholar
  4. Boolos, G. S. and R. C. Jeffrey: 1980,Computability and Logic, Cambridge University Press, Cambridge.Google Scholar
  5. Bunge, M.: 1963,The Myth of Simplicity, Prentice Hall, New Jersey.Google Scholar
  6. Buzacott, J. A.: 1980, ‘A Recursive Algorithm for Finding Reliability Measures Related to the Connection of Nodes in a Graph’,Networks 10, 311–27.Google Scholar
  7. Dawkins, R.: 1976, ‘Hierarchical Organization, a Candidate Principle for Ethology’, in P. P. G. Bateson and R. A. Hinde (eds.),Growing Points in Ethology, Cambridge University Press, Cambridge, pp. 7–54.Google Scholar
  8. Frank, H., R. E. Kahn, and L. Kleinrock: 1972, ‘Computer Communication Network Design — Experience with Theory and Practice’,AFIPS Conference Proceedings 40, 255–70.Google Scholar
  9. Garey, M. R. and D. S. Johnson: 1979,Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co., New York.Google Scholar
  10. Goodman, N.: 1972,Problems and Projects, Bobbs-Merrill Co., Inc., New York.Google Scholar
  11. Kelmans, A. K.: 1972, ‘Connectivity of Graphs Having Vertices which Drop Out Randomly’,Automation and Remote Control 33, 613–20.Google Scholar
  12. Kelmans, A. K.: 1976, ‘Comparison of Graphs by their Number of Spanning Trees’,Discrete Mathematics 16, 241–61.Google Scholar
  13. Laudan, L.: 1977,Progress and Its Problems, University of California Press, Berkeley.Google Scholar
  14. Laudan, L.: 1984,Science and Values, University of California Press, Berkeley.Google Scholar
  15. Putnam, H.: 1975, ‘Probability and Confirmation’, inMathematics, Matter and Method, Cambridge University Press, Cambridge, England.Google Scholar
  16. Simon, H. A.: 1962, ‘The Architecture of Complexity’,Proceedings of the American Philosophical Society 106, 467–82.Google Scholar
  17. Sober, E.: 1975,Simplicity, Clarendon Press, Oxford.Google Scholar
  18. Solomonoff, R. J.: 1964, ‘A Formal Theory of Inductive Inference’,Information and Control 7, 1–22, 224–54.Google Scholar
  19. Thom, R.: 1975,Structural Stability and Morphogenesis: An Outline of a General Theory of Models, Translated by D. H. Fowler, Benjamin/Cummings Publishing, Massachusetts.Google Scholar
  20. Valiant, L. G.: 1979, ‘The Complexity of Enumeration and Reliability Problems’,SIAM Journal of Computing 8, 410–21.Google Scholar
  21. van Fraassen, B. C.: 1980,The Scientific Image, Clarendon Press, Oxford.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Peter Turney
    • 1
  1. 1.Department of PhilosophyUniversity of TorontoTorontoCanada

Personalised recommendations