John Venn's Hypothetical Infinite Frequentism and Logic
The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance (1866) as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic (1889) and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. An Essay on the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, but also brought him to do so in strictly non-mathematical terms, he was able to anticipate much of the content (and problems) of his twentieth-century fellow frequentists.
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