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Variational problems with fractional derivatives: EulerLagrange equations
 J. Phys. A: Math. Theor
"... ar ..."
Efficient convergence implies Ockham’s Razor
 Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications, Las Vegas
, 2002
"... A finite data set is consistent with infinitely many alternative theories. Scientific realists recommend that we prefer the simplest one. Antirealists 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 ..."
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Cited by 16 (12 self)
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A finite data set is consistent with infinitely many alternative theories. Scientific realists recommend that we prefer the simplest one. Antirealists 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
A close shave with realism: How Ockham’s razor helps us find the truth
, 2002
"... Many distinct theories are compatible with current experience. Scientific realists recommend that we choose the simplest. Antirealists object that such appeals to “Ockham’s razor ” cannot be truthconducive, since they lead us astray in complex worlds. I argue, on behalf of the realist, that alwa ..."
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Cited by 5 (1 self)
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Many distinct theories are compatible with current experience. Scientific realists recommend that we choose the simplest. Antirealists object that such appeals to “Ockham’s razor ” cannot be truthconducive, since they lead us astray in complex worlds. I argue, on behalf of the realist, that always preferring the simplest theory compatible with experience is necessary for efficient convergence to the truth in the long run, even though it may point in the wrong direction in the short run. Efficiency is a matter of minimizing errors or retractions prior to convergence to the truth.
The codiscovery of conservation laws and particle families
 Studies in the History and Philosophy of Modern Physics
"... This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include a ..."
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Cited by 4 (2 self)
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This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include an appeal to a plenitude principle, a maxim for inductive inference, looking for a parsimonious system of generalizations, and unifying particle ontology and particle dynamics. The connection between conservation laws and ontological categories is a major theme in my analysis: While there are infinitely many conservation law theories that are empirically equivalent to the laws physicists adopted for the fundamental Standard Model of particle physics, I show that the standard family laws are the only ones that determine and are determined by the simplest division of particles into families.
Ockham’s Razor, Truth, and Information
, 2007
"... In science, one faces the problem of selecting the true theory from a range of alternative theories. The typical response is to select the simplest theory compatible with available evidence, on the authority of “Ockham’s Razor”. But how can a fixed bias toward simplicity help one find possibly compl ..."
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Cited by 2 (0 self)
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In science, one faces the problem of selecting the true theory from a range of alternative theories. The typical response is to select the simplest theory compatible with available evidence, on the authority of “Ockham’s Razor”. But how can a fixed bias toward simplicity help one find possibly complex truths? A short survey of standard answers to this question reveals them to be either wishful, circular, or irrelevant. A new explanation is presented, based on minimizing the reversals of opinion prior to convergence to the truth. According to this alternative approach, Ockham’s razor does not inform one which theory is true but is, nonetheless, the uniquely most efficient strategy for arriving at the true theory, where efficiency is a matter of minimizing reversals of opinion prior to finding the true theory. 1
Simplicity, Truth, and the Unending Game of Science
, 2005
"... This paper presents a new explanation of how preferring the simplest theory compatible with experience assists one in finding the true answer to a scientific question when the answers are theories or models. Science is portrayed as an infinite game between science and nature. Simplicity is a structu ..."
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This paper presents a new explanation of how preferring the simplest theory compatible with experience assists one in finding the true answer to a scientific question when the answers are theories or models. Science is portrayed as an infinite game between science and nature. Simplicity is a structural invariant reflecting sequences of theory choices nature could force the scientist to produce. It is demonstrated that among the methods that converge to the truth in an empirical problem, the ones that do so with a minimum number of reversals of opinion prior to convergence are exactly the ones that prefer simple theories. The idea explains not only simplicity tastes in model selection, but aspects of theory testing and the unwillingness of natural science to break symmetries without a reason. In natural science, one typically faces a situation in which several (or even infinitely many) available theories are compatible with experience. Standard practice is to choose the simplest theory among them and to cite “Ockham’s razor ” as the excuse (figure
Confirmation and Chaos *
"... that certain procedural accounts of model confirmation are compromised by nonlinear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach. ..."
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that certain procedural accounts of model confirmation are compromised by nonlinear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach. 1. Introduction. Presented
How Particle Physics Cut Nature At Its Joints
, 2008
"... This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include a ..."
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This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include an appeal to a plenitude principle, a maxim for inductive inference, looking for a parsimonious system of generalizations, and unifying particle ontology and particle dynamics. The connection between conservation laws and ontological categories is a major theme in my analysis: While there are infinitely many conservation law theories that are empirically equivalent to the laws physicists adopted for the fundamental Standard Model of particle physics, I show that the standard family laws are the only ones that determine and are determined by the simplest division of particles into families. 1 Introduction: Conservation Laws
Puzzle of Simplicity Standard Explanations Simplicity Examples “Mixed ” Strategies and Ockham’s Razor
"... in terms of minimizing retractions en route to the truth, relative to all deterministic scientific strategies (Kevin T. Kelly and Oliver Schulte). Extension: Ockham’s deterministic razor minimizes retractions en route to the truth, relative to a broad class of random scientific strategies. Further s ..."
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in terms of minimizing retractions en route to the truth, relative to all deterministic scientific strategies (Kevin T. Kelly and Oliver Schulte). Extension: Ockham’s deterministic razor minimizes retractions en route to the truth, relative to a broad class of random scientific strategies. Further significance: Extending the argument to expected retractions is a necessary step for lifting the idea to a theory of statistical theory choice.
Why Probability Does Not Capture the Logic of Scientific Justification
"... Here is the usual way philosophers think about science and induction. Scientists do many things — aspire, probe, theorize, conclude, retract, and refine — but successful research culminates in a published research report that presents an argument for some empirical conclusion. In mathematics and lo ..."
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Here is the usual way philosophers think about science and induction. Scientists do many things — aspire, probe, theorize, conclude, retract, and refine — but successful research culminates in a published research report that presents an argument for some empirical conclusion. In mathematics and logic there are sound deductive arguments that fully justify their conclu