Abstract
This article explicates and defends Peirce's views on the relation of inductive inference to the concept of probability and to the concept of what Peirce calls or likelihood. In particular it discusses the difference between probability and verisimilitude, and it expands upon Peirce's claim that induction does not have a probability but rather has a verisimilitude. The article shows that Peirce rejected as absurd the dominant Bayesianism of his day, as famously utilized by his predecessor Pierre Simon Laplace and by his almostcontemporaries Augustus De Morgan and Adolphe Quetelet. The article argues that in this rejection of Bayesianism, and in Peirce's own account of verisimilitude as the crucial notion to be used in assessing the strength of an inductive argument, Peirce by 1878 had anticipated several standard ideas of twentieth-century statistics in connection with sampling theory and hypothesistesting, ideas often associated with, for example, R. A. Fisher and Jerzy Neyman.
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