Pp. xxvii, 623 , Cambridge University Press , 2009 , £25.00/$39.95.

Antognazza richly fulfils the reader's hope of having received the definitive intellectual biography of Leibniz for our time. She does this by building gratefully upon her predecessors and having worked through the mountain of finished, half-finished, and only roughly sketched projects that this perpetual-motion machine left as his Nachlass in 1716. She has worked through it all, and has pieced together the embryology and probable date of each work she uncovers. Leibniz was a generous listener who enjoyed and depended upon the stimulus of conversation, not to launch his projects but to determine the style, shape, audience and objections to be addressed in each. The vast majority ended up half-finished not because he was lazy, but because he was pursuing so many projects simultaneously.

The child is father to the man, and Antognazza is expert at locating the psycho-social origin of Leibniz's life-project in the (broken) condition of the Holy Roman Empire in the wake of the Reformation and 30 Years War. Geography is metaphysics, and central Europe had no literal or intellectual ‘frontier’ to serve as a cultural safety valve into which people who found the pressure too great could escape. Lutheranism, Calvinism, and Catholicism were the three unalterable dispensations that had to be stitched back together again; this defined the intellectual-cultural project that became ‘German Philosophy’ (although Leibniz wrote primarily in Latin and French) with a remarkable consistency from Leibniz to Hegel. Heresy and ‘colonies’ did not exist as options, as they did for residents of the more outlying regions, such as France and England. In fact, there was as yet no ‘Germany’, only a sorry crazy-quilt of independent duchies and principalities derived from ‘cuius region, eius religio’ after the Treaty of Westphalia. German philosophy was conceived ‘after the Fall’ and was playing ‘intellectual catch-up’ from its inception. Leibniz embraced this cultural restitution as a vocation (he speaks of it at one point as his ‘vow’, and never married, or apparently even seriously considered marriage).

It will come as a surprise to some to learn that he was first a jurist and counsellor, not a mathematician. He developed his mathematics only during his first visit to Paris when he realized he had to become more rigorous in his mathematics to be taken seriously as a thinker. In the event, he tied his advances in mathematical thinking to his grand project of ‘reform’ and ‘reconciliation’ in all areas, not the least philosophy and theology; this explains the enthusiasm and novelty of the latter, but also their weaknesses. None of the ancients claimed that this was the ‘best’ possible world, that God made the world as a clockmaker, or in the face of apparently insuperable differences proposed ‘let us calculate.’ Much of his thinking was based on the correct insight that different traditions are attached to different words – which, by the ‘identity of indiscernibles’, often have a very near meaning. If we could demonstrate this through a neutral language, the fighting might cease. His grand project from the beginning was not knowledge (or mathematics) for its own sake, but ‘the glory of God and the advancement of the public good by means of useful works and beautiful discoveries.’ Finding new ways to pump water out of the Hartz mines, founding the first journals and scientific societies in Berlin, Vienna, and St. Petersburg, and silkworm cultivation on mulberry trees in Saxony were all part of the same grand project. Antognazza shows how even during his lifetime the vulnerable points of his ‘system’ were identified – for example, the Dutch professor De Volder was ‘baffled’ trying to understand how an immaterial monad could generate our experience of bodies, and the Frenchman Jaquelot claimed that Leibniz's system differed from ‘occasionalism’ only because he stuffed all the soul's ideas into it in advance, whereby they came out in proper succession according to a ‘pre-arranged harmony’. Rather than following Aquinas in taking God out of time entirely (for Whom all moments are ‘perpetually present’), Leibniz preferred to take a ‘phenomenal’ perspective and talk about, for example, God stuffing both the ‘laws of nature’ and ‘miracles’ into the cosmos ‘at the beginning’. This jack-in-the-box approach to Nature intrigued more than it persuaded. Perhaps the deepest problem with his mathematical rhetoric and indefatigable ‘optimism’ was that they inevitably raised the suspicion ‘Methinks he doth protest too much’. Leibniz could not see (as Lessing and Schopenhauer later pointed out) that if we are always making progress but never arriving at our destination, this is equivalent (by the ‘identity of indiscernibles’) to a deep cosmic frustration and provides grounds for pessimism. It is the mirage in the desert constantly receding as we approach it. Leibniz had no sense for the tragic, and tried to outflank evil with mathematics and technology. These two remain the resources for many today in dealing with the evil today, but it is difficult for us to maintain his optimism.