This book should perhaps come with a mental health warning.

Only the committed lay reader might be expected to negotiate Richard Arthur’s enthusiastic examination of the multifaceted work of Gottfried Wilhelm Leibniz, the philosopher described by Bertrand Russell as one of the supreme intellects of all time.

Born into a 17th-century Europe fermenting with new scientific, political and philosophical ideas, he immersed himself in geometry, mechanics, dynamics, optics, geology and the life sciences while also developing the metaphysical theories which appeared to challenge the very corporeal existence of the physical world.

Arthur demonstrates a comprehensive knowledge of Leibniz’s voluminous writings, which spread over numerous ambitious projects but never synthesised into a definitive master work. The author admits that for a modern reader it is hard to understand the melange of issues from theology, logic, metaphysics and physics that Leibniz deals with.

Nevertheless that reader will be rewarded with the journey through the mind of a man who could encompass practical schemes including the pumping of water from the mines of the Harz Mountains, the mathematical invention of differential calculus and metaphysical explorations of the nature of space and time.

If for non-mathematicians the chapter on Leibniz’s mathematical philosophy could prove difficult, it underlines his efforts to find a universal language that will achieve in every subject matter what arithmetical and algebraical characters do in mathematics — in effect, a computer language with its massive increase in the power of reasoning. Leibniz did in fact invent a calculating machine as early as 1672.

In the struggle to make sense of existence, the elephant in the room was God. In a period when the role of a divine creator was inevitably questioned by increasing knowledge, even the most materialistic and mechanistic of thinkers had to accommodate this uncomfortable intruder.

Leibniz’s famous invention of the monad, a kind of infinitesimal substance or soul, each one mirroring the universe, is clearly part of his attempts to apply logic to metaphysics. Like many Leibniz perceptions, however, the monad  — a world within a world  — looks forward to the development of nuclear physics and the genetic discovery of DNA.

Arthur recognises that Leibniz’s philosophical concerns may seem remote from today but maintains he was a profound and creative thinker, always pushing the boundaries of knowledge, anticipating and engendering new approaches, many of them of surprising contemporary relevance.

Gordon Parsons