Article ID: CBB001213926

Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication (2014)

unapi

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.

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Authors & Contributors
Bar-Am, Nimrod
Barrett, Lindsay
Boole, George
Cohen, Daniel J.
Connell, Matthew
Davis, Martin
Journals
British Society for the History of Mathematics Bulletin
Historia Mathematica
Annals of Science: The History of Science and Technology
British Journal for the History of Science
History and Philosophy of Logic
Physis: Rivista Internazionale di Storia della Scienza
Publishers
Princeton University
Clarendon Press
Cork University Press
MIT Press
W. W. Norton & Co.
Concepts
Logic
Mathematics
Science and religion
Biographies
Philosophy
Algebra
People
Boole, George
De Morgan, Augustus
Jevons, William Stanley
Hamilton, William Rowan
Venn, John
Babbage, Charles
Time Periods
19th century
18th century
20th century, early
Places
Great Britain
Australia
Europe
France
Germany
North America
Institutions
Royal Geographical Society
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