The Rise of Modern Logic: from Leibniz to Frege
Edited by Dov M. Gabbay
 John Woods
With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 16851900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centurieslong run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year runup to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the presentday association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be reexpressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic  a development that will be covered in a further volume, British Logic in the Nineteenth Century.
Audience
The Handbook is aimed at senior undergraduate students, graduate students and researchers in Logic, Computer Science, Argumentation Theory and in cognate disciplines such as Cognitive Science and Intellectual History.
Handbook of the History of Logic
Hardbound, 780 Pages
Published: March 2004
Imprint: Northholland
ISBN: 9780444516114
Reviews

This book is the third volume of the Handbook of the History of Logic. The period covered is essentially 1685 to 1900 (although it in fact extends to the deaths of the authors under discussion, whose writings beyond 1900 are cited). Each chapter testifies to the great erudition of its author(s) and includes an important bibliography. The layout and typography are meticulous. Obviously, this review will be able to give only a very weak idea of the number and subtlety of the analyses contained in this work, will be a landmark in this field.
JeanPierre Ginisti (Lyon), Mathematical Reviews, 2005
Contents
 Preface (D.M. Gabbay, J. Woods).List of Contributors.Leibniz's Logic (W. Lenzen).Kant: From General to Transcendental Logic (M. Tiles).Hegel's Logic (J.W. Burbidge).Bolzano as Logician (P. Rusnock, R. George).Husserl's Logic (R. Tieszen).Algebraical Logic 16851900 (T. Hailperin).The Algebra of Logic (V.S. Valencia).The Mathematical Turn in Logic (I. GrattanGuinness).SchrÃ¶der's Logic (V. Peckhaus).Peirce's Logic (R. Hilpinen).Frege's Logic (P. Sullivan).Index.