The middle years of the nineteenth century saw two crucial develop ments in the history of modern logic: George Boole's algebraic treat ment of logic and Augustus De Morgan's formulation of the logic of relations. The former episode has been studied extensively; the latter, hardly at all. This is a pity, for the most central feature of modern logic may well be its ability to handle relational inferences. De Morgan was the first person to work out an extensive logic of (...) relations, and the purpose of this book is to study this attempt in detail. Augustus De Morgan (1806-1871) was a British mathematician and logician who was Professor of Mathematics at the University of London (now, University College) from 1828 to 1866. A prolific but not highly original mathematician, De Morgan devoted much of his energies to the rather different field of logic. In his Formal Logic (1847) and a series of papers "On the Syllogism" (1846-1862), he attempted with great ingenuity to reformulate and extend the tradi tional syllogism and to systematize modes of reasoning that lie outside its boundaries. Chief among these is the logic of relations. De Mor gan's interest in relations culminated in his important memoir, "On the Syllogism: IV and on the Logic of Relations," read in 1860. (shrink)

Mary Everest, Boole's wife, claimed after the death of her husband that his logic had a psychological, pedagogical, and religious origin and aim rather than the mathematico-logical ones assigned to it by critics and scientists. It is the purpose of this paper to examine the validity of such a claim. The first section consists of an exposition of the claim without discussing its truthfulness; the discussion is left for the sections 2?4, in which some arguments provided by the examination of (...) the inner consistency of Mary Everest's writings, Boole's own writings, and other sources, lead to the conclusion that there are sound reasons to accept Mary Everest's viewpoint. (shrink)

This paper studies the possible influences on Boole's logic of the writings related to the controversy over the quantification of the predicate between the philosopher William Hamilton and the mathematician Augustus De Morgan. As Boole himself testified in the introduction to his book The mathematical analysis of logic , this controversy was the external agent that stimulated him into writing up his earlier thoughts about a new conception of logic. But in addition to the external role that was played by (...) the controversy, it seems that other kinds of influences on Boole of Hamilton's and De Morgan's ideas about logic, which were made explicit in writings related to the controversy, can also be traced. (shrink)

Despite its basically syllogistic character, Richard Whately's Elements of logic presents the subject in a modern theoretical setting. Whately, for instance, regarded logic as an abstract science, and defined the syllogism as a purely formal device to be used as a means of determining the validity of all arguments. In this paper, I argue that such instances of abstractive ascent place Whately's theory in closer proximity to later 19th-century developments than to the work of his 17th-century predecessors. In addition to (...) discussing the theory itself, other sections deal with its historical setting, and various reactions to it. (shrink)

In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

Although the existence of correspondence between George Boole (1815?1864) and William Stanley Jevons (1835?1882) has been known for a long time and part was even published in 1913, it has never been fully noted; in particular, it is not in the recent edition of Jevons's letters and papers. The texts are transcribed here, with indication of their significance. Jevons proposed certain quite radical changes to Boole's system, which Boole did not accept; nevertheless, they were to become well established.