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On Leibniz

Nicholas Rescher
University of Pittsburgh Press
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Tom Schulte
, on

This collection of articles explores the life of Leibniz as well as his contributions as a philosopher and mathematician while struggling with life as a frustrated courtier. We learn that the logician that invented calculus independently, setting himself at the same level of Newton, gazed onto the rich land of cryptanalysis. There he was excited by the possibilities but not moved to develop a cryptologic theory. In a way of life I find similar to that revealed in the autobiography of Jean-Jacques Rousseau, much of Leibniz’s energy was absorbed in seeking royal patronage. Frustrations with an unmovable imperial bureaucracy caused the self-important Leibniz to react petulantly. Despite such failings, Leibniz also stands on a level with Spinoza and Kant by creating an organized system as important as theirs to the development of Western philosophy. Rescher’s pieces here explore the development and structure of this system, unique in its mathematical underpinnings.

This expanded edition adds new chapters. These explore Leibniz’s innovative if largely ignored deciphering machine. Here more detailed illustrations would have been helpful. Other added material covers his eternal recurrence theory, Panglossian thoughts on improvability, and an overview of American scholarship on Leibniz, citing key scholars. On eternal recurrence, part-time librarian Leibniz saw, in a thought-experiment worthy of Jorge Luis Borges, that history is discovered by pulling tomes out of the labyrinthine shelves of possibly written histories. Any remembered fact or published history must inevitably occur again, given enough time, due to the narrowly finite ways to state facts; they are strings of characters and thus destined to repeat. Further insight from the imaginative thinker led to parallel universes. Leibniz felt every possible world is real and can be as close as the dream or work of fiction allowing us to experience it, yet simultaneously unreachably distant. One can almost hear Morgan Freeman narrating Leibniz’s views.

The breadth of exploration of Leibniz’s interests and times, his correspondents, and Rescher’s expositions make this a largely self-contained introduction (basic understanding of Kant is helpful) to the man hailed by Bertrand Russell as “one of the supreme intellects of all time.” The lengthy biographical articles include many paragraph-length untranslated passages in French and German, but the explanations herein allow the reader to understand the satire of Voltaire's Candide and grasp basic elements of Leibniz's metaphysics. Rescher also explores the impact of these ideas beyond Leibniz’s place and lifespan. (Gödel was an earnest devotee.) His theories of substance and monads and deep considerations on the nature of space and time, while overtly theistic, give Leibniz’s thought a very modern feel. He confronted questions we are still asking today.

Tom Schulte is a senior software engineer at Plex Systems and enjoys reading Voltaire and Schopenhauer as well as crossword puzzles, single-malt Scotch, and collecting vinyl LPs.