Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.

Reprint of the original, first published in 1840.

When Augustus De Morgan died in 1871, he was described as ‘one of the profoundest mathematicians in the United Kingdom’ and even as ‘the greatest of our mathematicians’. But he was far more than just a mathematician. Because much of his voluminous written output on various subjects was scattered throughout journals and encyclopaedias, the breadth of his interests and contributions has been underappreciated by historians. Now, renewed interest in De Morgan’s life and work has coincided with the digitization of his extensive library, revealing the extent to which he pioneered and influenced the development of not merely mathematics but also logic, astronomy, the history of mathematics, education, and bibliography. This edited collection celebrates De Morgan as a polymath. Drawing together multiple elements of his activity from a range of publications and archives, its contributors re-assess his academic work, his place in his intellectual environment, and his legacy. The result offers new insight into De Morgan himself as well as the wider circles in which he moved, including his family life.

Reprint of the original, first published in 1876.