Abeles, Francine F. (Author)
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.
...More
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
Panteki, Maria;
(2003)
French “Logique” and British “Logic”: On the Origins of Augustus De Morgan's Early Logical Inquiries, 1805--1835
(/isis/citation/CBB000340653/)
Article
Donal Murphy;
(2016)
George Boole and Walsh's Delusions
(/isis/citation/CBB926782871/)
Article
Laita, Luis M.;
(1979)
Influences on Boole's logic: The controversy between William Hamilton and Augustus De Morgan
(/isis/citation/CBB000008037/)
Article
Strong, John V.;
(1976)
The infinite ballot box of nature: De Morgan, Boole, and Jevons on probability and the logic of induction
(/isis/citation/CBB000022464/)
Article
Simmons, Charlotte;
(2008)
William Rowan Hamilton and George Boole
(/isis/citation/CBB000931920/)
Book
Desmond MacHale;
Yvonne Cohen;
(2018)
New Light on George Boole
(/isis/citation/CBB196236062/)
Thesis
David E. Dunning;
(2020)
Writing the Rules of Reason: Notations in Mathematical Logic, 1847–1937
(/isis/citation/CBB517005733/)
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/)
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/)
Chapter
Storari, Gian Pietro;
(1995)
Newtonianesimo e scienza della mente: George Boole e le leggi del pensiero
(/isis/citation/CBB000067606/)
Chapter
Rice, Adrian;
(2012)
Vindicating Leibniz in the Calculus Priority Dispute: The Role of Augustus De Morgan
(/isis/citation/CBB001251316/)
Article
Wang, Xiaoqin;
(2004)
A Strange Mathematical File Which Will Never Be Out of Date
(/isis/citation/CBB000401218/)
Article
Sloan Evans Despeaux;
Adrian C. Rice;
(2016)
Augustus De Morgan's anonymous reviews for The Athenæum: A mirror of a Victorian mathematician
(/isis/citation/CBB414838849/)
Be the first to comment!