## Efficient convergence implies Ockham’s Razor (2002)

Venue: | Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications, Las Vegas |

Citations: | 18 - 15 self |

### BibTeX

@INPROCEEDINGS{Kelly02efficientconvergence,

author = {Kevin T. Kelly},

title = {Efficient convergence implies Ockham’s Razor},

booktitle = {Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications, Las Vegas},

year = {2002},

pages = {24--27}

}

### OpenURL

### Abstract

A finite data set is consistent with infinitely many alternative theories. Scientific realists recommend that we prefer the simplest one. Anti-realists ask how a fixed simplicity bias could track the truth when the truth might be complex. It is no solution to impose a prior probability distribution biased toward simplicity, for such a distribution merely embodies the bias at issue without explaining its efficacy. In this note, I argue, on the basis of computational learning theory, that a fixed simplicity bias is necessary if inquiry is to converge to the right answer efficiently, whatever the right answer might be. Efficiency is understood in the sense of minimizing the least fixed bound on retractions or errors prior to convergence. Keywords: learning, induction, simplicity, Ockham’s razor, realism, skepticism 1

### Citations

395 |
Classical Descriptive Set Theory
- Kechris
- 1994
(Show Context)
Citation Context ... in (Kelly 1996). 3 The proofs are based on what I call “surprise complexity”: a topological invariant that generalizes both Cantor-Bendixson rank and Kuratowski’s (transfinite) difference hierarchy (=-=Kechris 1991-=-). 2sProposition 2 A solution to a problem is uniformly efficient with respect to retractions or errors only if it never outputs an informative answer other than the (unique) Ockham answer for the cur... |

157 |
Causality
- Pearl
- 2000
(Show Context)
Citation Context ...t most n retractions. 5 Ockham’s razor is often understood as a bias toward fewer causes. Recent years have seen a considerable increase in our understanding of causal inference (Spirtes et al. 2000, =-=Pearl 2000-=-). Instead of “reducing” causes to probabilistic or modal relations, the idea is to axiomatize the connection between probability and causation. A consequence of these axioms is that there is a direct... |

133 |
The Logic of Reliable Inquiry
- Kelly
- 1996
(Show Context)
Citation Context ...ood reference and bibliography may be found in (Jain et al. 1999). What follows is heavily indebted to (Freivalds and Smith 1993) and generalizes the topological perspective on learning developed in (=-=Kelly 1996-=-). 3 The proofs are based on what I call “surprise complexity”: a topological invariant that generalizes both Cantor-Bendixson rank and Kuratowski’s (transfinite) difference hierarchy (Kechris 1991). ... |

127 |
Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory
- Earman
- 1993
(Show Context)
Citation Context ...uts an informative answer other than the (unique) Ockham answer for the current data. It is familiar wisdom that convergence in the limit is compatible with any crazy behavior in the short run (e.g., =-=Earman 1992-=-). The results in this paper show that the wisdom is wrong (with a vengeance) when we require efficient convergence, for then one’s only choice is to accept the unique, Ockham answer or to hold one’s ... |

102 |
Trial and error predicates and solution to a problem of Mostowski
- Putnam
- 1965
(Show Context)
Citation Context ...d an ingenious definition of solving a problem under a transfinite retraction bound that is much more general than the more obvious concept of success with finitely bounded retractions introduced in (=-=Putnam 1965-=-). The following results are based on a refinement of Freivalds and Smith’s idea. The notion of an Ockham answer relative to the current inputs can be defined in a language-invariant manner that refle... |

19 |
Means-Ends Epistemology”, The British
- Schulte
- 1999
(Show Context)
Citation Context ... worlds of type gruet,t ′ whose inputs are green through t, blue through t ′ and then green thereafter, gruet,t ′ ,t ′′, and so forth, as long as there is a finite bound on the number of “surprises” (=-=Schulte 1999-=-a, b). The point of Nelson Goodman’s (1983) gruet construction was to show that uniformity is relative to description and that perfect definitional symmetry blocks any attempt to favor one description... |

12 |
The World of Elementary Particles
- Ford
- 1963
(Show Context)
Citation Context ...ing variety of “simplicity” judgments. For example, a familiar policy in particle physics is to posit the most restrictive conservation laws compatible with reactions that are known to have occurred (=-=Ford 1963-=-). Here, the “spine” world is one in which only the known reactions are possible and “veering” occurs when a new type of reaction that is not permitted by the earlier conservation laws is observed. If... |

11 | Inferring Conservation Laws in Particle Physics: A Case study
- Schulte
- 2000
(Show Context)
Citation Context ...argument like the preceding one, achievement of the least feasible retraction bound in each subproblem demands that one never choose a conservation theory compatible with a non-observed reaction (cf. =-=Schulte 2001-=-). In the context of curve fitting, simplicity is often identified with the polynomial degree of the curve’s equation. Suppose we wish to know the degree of an empirical curve from evidence gathered w... |

5 |
The Logic of Reliable and Efficient
- Schulte
- 1999
(Show Context)
Citation Context ... worlds of type gruet,t ′ whose inputs are green through t, blue through t ′ and then green thereafter, gruet,t ′ ,t ′′, and so forth, as long as there is a finite bound on the number of “surprises” (=-=Schulte 1999-=-a, b). The point of Nelson Goodman’s (1983) gruet construction was to show that uniformity is relative to description and that perfect definitional symmetry blocks any attempt to favor one description... |

3 |
Schulte and Goodman’s Riddle”, The British
- Chart
- 2000
(Show Context)
Citation Context ...evidently leaves branching structure of the problem intact. 4 This conception of simplicity is contextual, in the sense that the same world can be simple or complex, depending on the problem we face (=-=Chart 2000-=-). For example, we can make the “forever grue9” world into the spine by considering only the worlds “forever grue1”, . . ., “forever grue9”, “forever green”, and “forever grue9,t”, for all t > 9. Why ... |

1 | Fact, Fiction, and Forecast, fourth edition, Cambridge: Harvard University Press. 5 The argument doesn’t recommend the choice of a unifying theory over the conjunction of the unified laws, however, as these alternatives are not mutually exclusive - Goodman - 1983 |

1 | neglect the small probability of a mistaken rejection. For a more literal learning theoretic analysis of statistical tests, cf. (Kelly 96, chapter 3). For an explicitly statistical treatment of related issues, cf. (Robins et al - Here - 2000 |