Title
Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication
Document Type
Article
Publication Date
1-1-2014
Abstract
Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown 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 we 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 related to the subjects of this paper. © 2013 Taylor & Francis.
Publication Title
History and Philosophy of Logic
First Page Number
24
Last Page Number
37
DOI
10.1080/01445340.2013.817076
Recommended Citation
Abeles, Francine F., "Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication" (2014). Kean Publications. 2035.
https://digitalcommons.kean.edu/keanpublications/2035