Inference in Nineteenth-Century British Logic

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I trace the development of implication as an inference operator using as the starting point the ideas primarily of R. Whately, W. Hamilton, and in added material, also J. S. Mill, before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Although not appreciated until the first third of the twentieth century, Boole’s fundamental law of thought, x2 = x, initiated an analysis of how the algebra of logic differs from ordinary algebra, and subsequently, gave rise to a new inference rule, resolution. In an added section, I provide a roadmap of this development and then discuss the relevant views of four prominent but underappreciated nineteenth-century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on “implication as inference” where I explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas leading to the mechanization of inference schemes.

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Studies in Universal Logic

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