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Musings of British mathematician and logician Augustus de Morgan (1806-1871) provide a light-hearted look at particular types of character that inhabit the world of mathematics and places around it. [ABSTRACT FROM AUTHOR]

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Ada Lovelace is widely regarded as an early pioneer of computer science, due to an 1843 paper about Charles Babbage's Analytical Engine, which, had it been built, would have been a general-purpose computer. However, there has been considerable disagreement among scholars as to her mathematical proficiency. This paper presents the first account by historians of mathematics of the correspondence between Lovelace and the mathematician Augustus De Morgan from 1840–41. Detailed contextual analysis allows us to present a corrected ordering of the archive material, countering previous claims of Lovelace's mathematical inadequacies, and presenting a more nuanced assessment of her abilities. [ABSTRACT FROM AUTHOR]

Pascal's treatise on the arithmetic triangle (see Pascal (1665)) described the separate findings on this topic made mostly in the 16th century. Pascal showed how to apply the triangle to the theory of figurate numbers and combinatorics. Bayes completed the first version of the theory of probability and possibly considered that it belonged to pure science. Laplace's Essai was a barely successful popular treatise but it included interesting side issues such as the natural scientific study of moral sciences, psychology, and final causes. De Morgan was the first to note the normal distribution in De Moivre but was considered a logician rather than a mathematician. For 150 years Todhunter's history of probability has remained a necessary and useful source of information. [ABSTRACT FROM AUTHOR]

In his Essay Concerning Human Understanding, John Locke created a special epistemological category for mathematical and religious knowing. This category of knowledge was quickly brushed to the side in the French Enlightenment, but the English preserved it well into the nineteenth century. This article considers the ways that the neo-Lockian joining of mathematics and theology fundamentally affected both mathematical and theological thinking in the first half of the English nineteenth century. It argues that these developments set the stage for the post-Darwinian conflicts between science-including mathematics-and religion. [ABSTRACT FROM AUTHOR]

Abstract: In the early nineteenth century, Henry Brougham endeavored to improve the moral character of England through the publication of educational texts. Soon after, Brougham helped form the Society for the Diffusion of Useful Knowledge to carry his plan of moral improvement to the people. Despite its goal of improving the nation’s moral character, the Society refused to publish any treatises on explicitly moral or religious topics. Brougham instead turned to a mathematician, Augustus De Morgan, to promote mathematics as a rational subject that could provide the link between the secular and religious worlds. Using specific examples gleaned from the treatises of the Society, this article explores both how mathematics was intended to promote the development of reason and morality and how mathematical content was shaped to fit this particular view of the usefulness of mathematics. In the course of these treatises De Morgan proposed a fundamentally new pedagogical approach, one which focused on the student and the role mathematics could play in moral education. [Copyright &y& Elsevier]

Hamblin held that the conception of 'fallacy' as an argument that seems valid but is not really so was the dominant conception of fallacy in the history of fallacy studies. The present paper explores the extent of support that there is for this view. After presenting a brief analysis of 'the standard definition of fallacy,' a number of the definitions of 'fallacy' in texts from the middle of this century – from the standard treatment – are considered. This is followed by a review of the definitions of 'fallacy' in the earlier history of logic books, including those of Aristotle, Whately, Mill and De Morgan. The essay concludes that there is scarcely any support for Hamblin's view that this particular definition of 'fallacy' was widely held. [ABSTRACT FROM AUTHOR]