Article ID: CBB001213926

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


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.

Citation URI

Similar Citations

Chapter Peckhaus, Volker; (2009)
The Mathematical Origins of Nineteenth-Century Algebra of Logic (/isis/citation/CBB001210344/)

Article Merrill, Daniel; (2005)
Augustus De Morgan's Boolean Algebra (/isis/citation/CBB000740616/)

Article Verburgt, Lukas M.; (2015)
The Objective and the Subjective in Mid-Nineteenth-Century British Probability Theory (/isis/citation/CBB001553591/)

Chapter Cohen, Daniel J.; (2005)
Reason and Belief in Victorian Mathematics (/isis/citation/CBB000740675/)

Article Valente, K. G.; (2010)
Giving Wings to Logic: Mary Everest Boole's Propagation and Fulfilment of a Legacy (/isis/citation/CBB000933057/)

Article Donal Murphy; (2016)
George Boole and Walsh's Delusions (/isis/citation/CBB926782871/)

Article Simmons, Charlotte; (2008)
William Rowan Hamilton and George Boole (/isis/citation/CBB000931920/)

Book Boole, George; De Morgan, Augustus; (1982)
The Boole-De Morgan correspondence, 1842-1864. [Edited by] Smith, G. C. (/isis/citation/CBB000002427/)

Book Brendan Dooley; (2018)
The Continued Exercise of Reason: Public Addresses by George Boole (/isis/citation/CBB539223859/)

Article Bar-Am, Nimrod; (2004)
Extensionalism and Induction in Boole (/isis/citation/CBB000630825/)

Thesis David E. Dunning; (2020)
Writing the Rules of Reason: Notations in Mathematical Logic, 1847–1937 (/isis/citation/CBB517005733/)

Book Desmond MacHale; Yvonne Cohen; (2018)
New Light on George Boole (/isis/citation/CBB196236062/)

Chapter Storari, Gian Pietro; (1995)
Newtonianesimo e scienza della mente: George Boole e le leggi del pensiero (/isis/citation/CBB000067606/)

Article Barrett, Lindsay; Connell, Matthew; (2005-2006)
Jevons and the Logic “Piano” (/isis/citation/CBB000931937/)

Article Withers, Charles W J; (2013)
Science, Scientific Instruments and Questions of Method in Nineteenth-Century British Geography (/isis/citation/CBB001421530/)

Book Davis, Martin; (2000)
The Universal Computer: The Road from Leibniz to Turing (/isis/citation/CBB000102163/)

Authors & Contributors
Bar-Am, Nimrod
Barrett, Lindsay
Boole, George
Cohen, Daniel J.
Connell, Matthew
Davis, Martin
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
Princeton University
Clarendon Press
Cork University Press
MIT Press
W. W. Norton & Co.
Science and religion
Boole, George
De Morgan, Augustus
Jevons, William Stanley
Hamilton, William Rowan
Venn, John
Babbage, Charles
Time Periods
19th century
18th century
20th century, early
Great Britain
North America
Royal Geographical Society

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment