## Hume's Problem: Induction and the Justification of BeliefColin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. No matter how many experimental tests a hypothesis passes, nothing can be legitimately inferred about its truth or probable truth. But physical theory routinely predicts the values of observable magnitudes to many places of decimals andwithin very small ranges of error. The chance of this sort of predictive success without a true theory seems so remote that the possibility should be dismissed. This suggests that Hume's argument must be wrong; but there is still no consensus on where exactly the flaw in the argument lies. Howson argues that there is no flaw, and examines the implications of this disturbing conclusion for the relation between science and its empirical base. |

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### Contents

INTRODUCTION | 1 |

RELIABILISM | 22 |

REALISM AND THE NOMIRACLES ARGUMENT | 35 |

Copyright | |

6 other sections not shown

### Common terms and phrases

accept actually answer assign assumed assumption Bayes factor Bayes's Bayesian model Bayesian probability Bayesian theory called chance distribution Chapter claim conditional probability conditionalization consistent constraints context course deductive logic defined definition degree of belief denumerably determine discussion Dutch Book emeralds empirical entails epistemic epistemic probability equal evaluation evidence example experiment explanation fact false Fisher formal frequency given grue Hence Howson Hume Hume's argument Hume's Problem Humean inconsistent independent inductive inferences inductive reasoning infinite infinity interval intuitively justified large numbers logical truth mathematical ment merely modus ponens natural No-Miracles argument null hypothesis objection observed outcomes Popper possible posterior probability predictions premisses principle of indifference prior probability prob proba probabilistic probability axioms probability calculus probability function problem of induction propositions question random rational regarded reliable result rule scientific seems sense sequence simple statement Suppose theorem tion truth-values