Johnson - Research Article from Encyclopedia of Philosophy

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Johnson

Keynes's collaborator William Ernest Johnson (1858–1931) did not publish Part I of his own Logic until 1921 (Part II, 1922; Part III, 1924), although he had published a series of three articles titled "The Logical Calculus" in Mind in 1892 (17: 3–30, 235–250, 340–357) and two titled "The Analysis of Thinking" in Mind in 1918 (27: 1–21, 133–151). In the first series the variables in Boolean equations were explicitly given the propositional interpretation, the logical product ("x and y") being represented by juxtaposition and negation by a superimposed bar. The logical product and negation being taken as primitive, "If x then y" is defined as "Not (x and not y)"—that is, xȳ̄—the logical sum "x or y" as "Not (not x and not y)," and universal and particular quantification as continued logical multiplication and addition. "The Analysis of Thinking" is more philosophical and seems to reflect the influence of...

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This section contains 518 words
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Encyclopedia of Philosophy
Johnson from Encyclopedia of Philosophy. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.
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