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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 17 (14 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
Inferring Conservation Laws in Particle Physics: A Case Study
 in the Problem of Induction”, The British Journal for the Philosophy of Science, Forthcoming
, 2001
"... This paper develops a meansends analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an ..."
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Cited by 10 (1 self)
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This paper develops a meansends analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions–including prescriptions for when exactly to introduce hidden particles.
2007b)How Simplicity Helps You Find the Truth Without Pointing at it
 Philosophy of Mathematics and Induction
"... It seems that a fixed bias toward simplicity should help one find the truth, since scientific theorizing is guided by such a bias. But it also seems that a fixed bias toward simplicity cannot indicate or point at the truth, since an indicator has to be sensitive to what it indicates. I argue that bo ..."
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Cited by 10 (9 self)
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It seems that a fixed bias toward simplicity should help one find the truth, since scientific theorizing is guided by such a bias. But it also seems that a fixed bias toward simplicity cannot indicate or point at the truth, since an indicator has to be sensitive to what it indicates. I argue that both views are correct. It is demonstrated, for a broad range of cases, that the Ockham strategy of favoring the simplest hypothesis, together with the strategy of never dropping the simplest hypothesis until it is no longer simplest, uniquely minimizes reversals of opinion and the times at which the reversals occur prior to convergence to the truth. Thus, simplicity guides one down the straightest path to the truth, even though that path may involve twists and turns along the way. The proof does not appeal to prior probabilities biased toward simplicity. Instead, it is based upon minimization of worstcase cost bounds over complexity classes of possibilities. 0.1 The Simplicity Puzzle There are infinitely many alternative hypotheses consistent with any finite amount of experience, so how is one entitled to choose among them? Scientists boldly respond with appeals to “Ockham’s razor”, which selects the “simplest ” hypothesis among them,
Ockham’s Razor, Empirical Complexity, and Truthfinding Efficiency
 THEORETICAL COMPUTER SCIENCE
, 2007
"... The nature of empirical simplicity and its relationship to scientific truth are longstanding puzzles. In this paper, empirical simplicity is explicated in terms of empirical effects, which are defined in terms of the structure of the inference problem addressed. Problem instances are classified acc ..."
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Cited by 6 (6 self)
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The nature of empirical simplicity and its relationship to scientific truth are longstanding puzzles. In this paper, empirical simplicity is explicated in terms of empirical effects, which are defined in terms of the structure of the inference problem addressed. Problem instances are classified according to the number of empirical effects they present. Simple answers are satisfied by simple worlds. An efficient solution achieves optimum worstcase cost over each complexity class with respect to such costs such as the number of retractions or errors prior to convergence and elapsed time to convergence. It is shown that always choosing the simplest theory compatible with experience and hanging onto it while it remains simplest is both necessary and sufficient for efficiency.
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 4 (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.
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
Learning, Simplicity, Truth, and Misinformation
"... Both in learning and in natural science, one faces the problem of selecting among a range of theories, all of which are compatible with the available evidence. The traditional response to this problem has been to select the simplest such theory on the basis of “Ockham’s Razor”. But how can a fixed b ..."
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Both in learning and in natural science, one faces the problem of selecting among a range of theories, all of which are compatible with the available evidence. The traditional response to this problem has been to select the simplest such theory on the basis of “Ockham’s Razor”. But how can a fixed bias toward simplicity help us find possibly complex truths? I survey the current, textbook answers to this question and find them all to be wishful, circular, or irrelevant. Then I present a new approach based on minimizing the number of reversals of opinion prior to convergence to the truth. According to this alternative approach, Ockham’s razor is a good idea when it seems to be (e.g., in selecting among parametrized models) and is not a good idea when it feels dubious (e.g., in the inference of arbitrary computable functions). Hence, the proposed vindication of Ockham’s razor can be used to separate vindicated applications In science and learning, one must eventually face up to the problem of choosing among several or even infinitely many theories compatible with all available information. How ought one to choose? The traditional answer is to choose the “simplest ” and to invoke
Ockham Efficiency Theorem for Stochastic Empirical Methods
, 2010
"... Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computa ..."
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Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is the Ockham efficiency theorem (Kelly 2002, 2004, 2007ad, Kelly and Glymour 2004), which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their nonOckham competitors. The theorem neglects, however, to consider competitors following random (“mixed”) strategies and in many applications random strategies are known to achieve better worstcase loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors.
Noname manuscript No. (will be inserted by the editor) Ockham Efficiency Theorem for Stochastic Empirical Methods
"... the date of receipt and acceptance should be inserted later Abstract Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues l ..."
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the date of receipt and acceptance should be inserted later Abstract Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is the Ockham efficiency theorem (Kelly 2002, 2004, 2007ad, Kelly and Glymour 2004), which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their nonOckham competitors. The theorem neglects, however, to consider competitors following random (“mixed”) strategies and in many applications random strategies are known to achieve better worstcase loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors.