During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about ‘symbolical logic’. The letters to the editor shed interesting light on the early reception of MacColl’s contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of the development of (...) British algebraic logic in the confusing intermediary period between the 1870s and 1890s. (shrink)

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came (...) from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. (shrink)

The debate on the a fortiori and the universal that took place between April 1914 and April 1919 in the journal Mind has a double interest for argumentation theorists. First, the discussion is an example of a philosophical polylogue that exhibits the characteristics of a quasi-engaged dialogue (Blair Blair, J. A. (2012 [1998]). “The Limits of the Dialogue Model of Argument”. Argumentation 12, pp. 325–339. Reprinted in J.A. Blair, Groundwork in the Theory of Argumentation, pp. 231–244. Dordrecht: Springer, 2012.), confirming (...) Blair’s hypothesis that journal papers and scholarly monographs can be analyzed as turns in non-engaged or quasi-engaged dialogues. It could be said that philosophical argumentation is dialectical but not dialogical. Second, the debate is a discussion in argumentation theory. Generalism in the theory of argument claims that the very possibility of arguing depends on a suitable supply of general rules that specify what kinds of conclusions can be drawn from what kinds of data, while particularism denies this. Although the terminology may be alien, I will also show that the debate on the a fortiori and the universal was a debate on generalism and particularism. (shrink)

This paper explores the ways in which truth is better than falsehood, and suggests that, among other things, it depends on the kinds of proposition to which these values are attached. Ordinary singular propositions like “It is raining” seem to fit best the bivalent “scheme” of classical logic, the general proposition “It is always raining” is more appropriately rated according to how often it rains, and a “practically vague” proposition like “The lecture will start at 1” is appropriately rated according (...) to its nearness to exactness. Implications for logic of this “rating system” are commented on. (shrink)

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. (shrink)

Few, if any, logicians deserve the title 'precursor of modern argumentation theory' more than the largely neglected English logician, Alfred Sidgwick. Sidgwick developed a coherent and original theory of argumentation with a distinctly 'mo dern' flavour. This paper outlines his idea of a 'negative' view of logic, an important aspect of which is the thesis that the distinctions and inference schemata of formal logic should not be applied as criteria of the validity or invalidity of natural language arguments, but rather (...) 'rogatively'--as suggesting the kinds of objections or demands for clarification that are relevant at specific stages of a discussion. (shrink)