Peijnenburg, Jeanne and Atkinson, David
AN ENDLESS HIERARCHY OF PROBABILITIES.
According to radical probabilism, all factual claims are merely probabilistic in character. Throughout the centuries this view has been criticized on the grounds that it triggers an infinite regress: if every claim is probabilistic, then the proposition that something is probable is itself only probable, and so on. An endless hierarchy of probabilities seems to emerge and, as a result, the probability of the original proposition can never be determined. This criticism goes back as far as David Hume, and in the twentieth century it was raised also by statisticians such as Leonard J. Savage. Recently Nicholas Rescher ventured a similar critique of radical probabilism. In this paper it is argued that the criticism does not hold water, for an endless hierarchy of probability statements is no obstacle to attaching a definite probability value to the original proposition. Moreover, it is claimed that radical probabilism can reinforce some of Rescher's own main claims.
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