Abstract

We use the method of fixed points to describe a form of probabilistic truth approximation which we illustrate by means of three examples. We then contrast this form of probabilistic truth approximation with another, more familiar kind, where no fixed points are used. In probabilistic truth approximation with fixed points the events are dependent on one another, but in the second kind they are independent. The first form exhibits a phenomenon that we call ‘fading origins’, the second one is subject to a phenomenon known as ‘the washing out of the prior’. We explain that the two phenomena may seem very similar, but are in fact quite different.

Highlights

  • We shall consider two kinds of systems in which one can say that there is an ‘approach to the probabilistic truth’.1 In the first kind, one event is made more likely by another event, which in turn is made more likely by still another event, and so on

  • We use the method of fixed points to describe a form of probabilistic truth approximation which we illustrate by means of three examples

  • The prime example of the first kind is a biological population in which the relative number of individuals with some property approaches a fixed value; this value corresponds to a steady state of affairs or a stable ratio which we call the probabilistic truth for that system

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Summary

Introduction

We shall consider two kinds of systems in which one can say that there is an ‘approach to the probabilistic truth’.1 In the first kind, one event is made more likely by another event, which in turn is made more likely by still another event, and so on. The prime example of the first kind is a biological population in which the relative number of individuals with some property (like having blue eyes or hammer toes or an aptitude for mathematics) approaches a fixed value; this value corresponds to a steady state of affairs or a stable ratio which we call the probabilistic truth for that system. The coin tossing scenario is subject to what Bayesians call the ‘washing out of the prior’: the probabilistic truth does not depend on the value of the prior. These two effects, fading origins and the washing out of the prior, seem superficially to be similar, they are very different, as we shall explain.

A mitochondrial trait
Inheritance in two dimensions
Genetics in three dimensions
Bayes and Carnap
Concluding remarks: mind the gap
B Two-dimensional iteration

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