Abstract

The Principle of Indifference says that if there are a finite number of propositions and a state of knowledge according to which none of the propositions is more plausible than any other, then, conditional on that knowledge, all of them have the same probability. Most researchers reject the principle because there exist counterexamples believed to prove that it leads to contradictions. We analyse three examples representative of the objections to the principle and show that, rather than disproving it, they suffer from a common error in applying it. From this and the fact that the Principle of Indifference complies with plausible reasoning we conclude that it does not lead to contradictions.

Highlights

  • The Principle of Indifference, which dates back to Jakob Bernoulli, can be expressed as follows: If, given some proposition C, one of the propositions A1, · · ·, An must be true and the others must be false and none of the Ai is more plausible than any other, conditional on C, all Ai have the same probability p(Ai|C) = 1/n .C is often referred to as someone’s knowledge, which may or may not contain reasons to favour some proposition over some other

  • The examples seem to disprove the Principle of Indifference; we will find that they suffer from a common error in applying it

  • We have analysed three examples representative of the objections to the Principle of Indifference and found that, rather than disproving the principle, they suffer from a common error in applying it

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Summary

Introduction

In the 1950s, Jaynes derived it from a set of desiderata for plausible reasoning (Jaynes 1958, 2003). In his probability theory, the principle is a proven theorem; it cannot be contradictory there, unless the whole theory were contradictory. The principle is a proven theorem; it cannot be contradictory there, unless the whole theory were contradictory If it is not, it must be possible to eliminate the contradictions on the ground of Jaynes’ desiderata. It must be possible to eliminate the contradictions on the ground of Jaynes’ desiderata This is what we are going to undertake

Counterexamples to the Principle
Desiderata for Plausible Reasoning
Example 1
Example 2
Example 3
Results
Discussion and Conclusions

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