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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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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
(will be inserted by the editor) Ockham Efficiency Theorem for Stochastic Empirical Methods
, 2010
"... 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
Ockham’s Razor, Hume’s Problem, Ellsberg’s Paradox, Dilation, and Optimal Truth Conduciveness
, 2008
"... Classical Bayesianism represents ignorance, if at all, by flatness of prior probabilities. Such probabilities are an essential part of the standard Bayesian explanation of Ockham’s razor. But flatness as a model of ignorance is called into question by Ellsberg’s paradox, which has led to the conside ..."
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Classical Bayesianism represents ignorance, if at all, by flatness of prior probabilities. Such probabilities are an essential part of the standard Bayesian explanation of Ockham’s razor. But flatness as a model of ignorance is called into question by Ellsberg’s paradox, which has led to the consideration of incoherent or inexact degrees of belief, both of which undermine the usual explanation of Ockham’s razor. An alternative explanation of Ockham’s razor is presented, according to which always favoring the uniquely simplest theory compatible with experience keeps one on the shortest or most direct path to the truth. It turns out that minimization of total distance to the truth implies coherent degrees of belief strongly biased toward simplicity. If one focuses on retractions or drops in credence, then a more reasonably moderate bias toward simplicity results but optimal efficiency then demands either incoherence or inexact probabilities, both of which are solutions to Ellsberg’s paradox. Finally, it turns out that dilation, or increasing imprecision in light of new information, is necessary if agents with inexact probabilities are to minimize total retractions. So, in place of paradox and tension, one obtains a unified perspective on Ockham’s razor, Ellsberg’s paradox, dilation, and the justification of inductive inference. 1
Ockham Efficiency Theorem for Random Empirical Methods
, 2009
"... Ockham’s razor is the principle that, all other things being equal, rational scientists ought to prefer simpler theories to more complex ones. In recent years, philosophers have argued the simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pr ..."
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Ockham’s razor is the principle that, all other things being equal, rational scientists ought to prefer simpler theories to more complex ones. In recent years, philosophers have argued the 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 why and how 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 this 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 bounds than deterministic strategies. In this paper, we describe an extension of the result to a very general class of random, empirical strategies. 1
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 ..."
Abstract
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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.