seems to lead ineluctably to what was later called Laplacian determinism. If the behaviour of all objects can be explained in terms of spatiotemporal atoms, and if the atoms’ behaviour, in turn, is subject to Newton’s deterministic mathematical laws, then there is no room for free will. Humans are robots and religion is a fraud.
Newton was aware of this problem. He had no intention of promulgating a philosophy that stripped humans of free will. He seems to have got around it by positing supernatural intervention, i.e., by recourse to entities and powers that lay outside the system described by his science. Leibniz’s approach, bizarre as it might be in many respects, was, in a sense, more scientific; free will was no longer a problem that needed to be explained away, but an intrinsic feature of every monad.
Monadology spent the next two centuries on the ash-heap of intellectual history. After Leibniz’s death, a faulty version was published by one of his disciples, and its errors laid at Leibniz’s feet. Then it swam into the gunsights of Immanuel Kant. In his Critique of Pure Reason, Kant begins by saying a few complimentary things about Leibniz. Three hundred pages later, having carefully set his pieces out on the board, he annihilates Leibniz’s metaphysics in a few sentences. According to Kant’s philosophy, Leibniz is correct in thinking that space and time, cause and effect, are not ultimate realities, but rather constructs of mental activity. But by the same token, Kant says, the human mind is powerless to think in any useful or productive way about anything that is outside space and time, cause and effect, and so Leibniz’s entire Monadology – or any thinking that attempts to transcend spatiotemporality – is rubbish.
In the day of Newton and Leibniz, metaphysics had been as respectable as mathematics, but the hard-headed empiricists of the scientific world began to kick dirt on it during the nineteenth century and, in the first half of the twentieth, the logical positivists buried it. And indeed, Leibniz’s work seems unsound at best, ludicrous at worst, by the scientific standards of the era before relativity, quantum mechanics and Gödel’s proof.
Today, metaphysics in general has regained much of its former respectability among philosophers. For almost everyone else, though, it retains the connotations of woolliness that it picked up during that century or so of rough treatment at the hands of empiricists and positivists. Many hard scientists still use ‘metaphysics’ as a byword for undisciplined, conjectural thinking. Nevertheless, metaphysics is still being practised today: by philosophers openly, by physicists under other names.
A straightforward way of defining metaphysics is as the set of assumptions and practices present in the scientist’s mind before he or she begins to do science. There is nothing wrong with making such assumptions, as it is not possible to do science without them. The lepidopterist who records in her notebook that a butterfly is blue may not stop to consider that this is true only because the giant ball of nuclear fuel ninety-three million miles away happens to maintain a surface temperature just right for shedding certain wavelengths of electromagnetic radiation on the Earth; that the eyes of humans have evolved to be sensitive to those wavelengths; that the eye can discriminate slightly different wavelengths as colours; that one of those colours has, by cultural consensus, been defined as ‘blue’, and so on. Nevertheless, science benefits from the lepidopterist’s note that the butterfly is blue.
Even the hardest of hard sciences is replete with assumptions that may fairly be classified as metaphysical. Almost all mathematicians, for example, presume that they are discovering, rather than creating, mathematical truths. Ask a roomful of mathematicians whether three was a prime number a billion years ago (i.e. before there were humans to define it as such) and every hand will go up. And yet to say so is to espouse the metaphysical position that primeness and all the other subject matter of mathematics have a reality independent of the human mind. This assumption goes under various names, one of which is Mathematical Platonism. Likewise, physicists can hardly go about their work without assuming that the physical world answers to laws that may be expressed and proved mathematically – an assumption for which there is plenty of empirical evidence, dating back (at least) to Galileo, but no proof as such.
The revival of Leibniz’s fortunes may be dated to approximately 1900, when Bertrand Russell began to publish his studies of Leibniz’s unpublished work. While unsparing in his criticisms of Leibniz’s character and of his more popular writings, Russell had a high opinion of Leibniz’s work on mathematical logic and was fascinated by some of the ramifications of the
Bertrand Russell.
Monadology. In his History of Western Philosophy (1945) he ends his chapter on Leibniz as follows: ‘What I…think best in his theory of monads is his two kinds of space, one subjective, in the perceptions of each monad, and one objective, consisting of the assemblage of points of view of the various monads. This, I believe, is still useful in relating perception to physics.’
Leibniz then came to the attention of a wide range of thinkers. To tell the story in chronological order, including all of the requisite details about those who have knowingly or unknowingly echoed Leibniz’s views, would require a substantial book in itself, of which the following might serve as a brief sketch or outline.
1. The debate on free will vs. determinism is no more settled today than it was at the time of the Leibniz–Clarke correspondence, and so in that sense (at least) Monadology is still interesting as a gambit, which different observers might see as heroic, ingenious, or desperate, to cut that Gordian knot by making free minds or souls into the fundamental components of the universe.
2. Leibniz’s interpreters made use of the vocabulary at their disposal to translate his terminology into words such as ‘mind’, ‘soul’, ‘cognition’, ‘endeavour’, etc. This, however, was before the era of information theory, Turing machines and digital computers, which have supplied us with a new set of concepts, a lexicon, and a rigorous science pertaining to things that, like monads, perform a sort of cogitation but are neither divine nor human. A translator of Leibniz’s work, beginning in AD 2010 from a blank sheet of paper, would, I submit, be more likely to use words like ‘computer’ and ‘computation’ than ‘soul’ and ‘cognition’. During Leibniz’s era, the only person who had thought seriously about such machines was Leibniz himself; building on earlier work by Blaise Pascal, he designed, and caused to be built, a mechanical computer, and envisioned coupling it to a formal logical system called the Characteristica Universalis. He invented binary arithmetic, and, according to no less an authority than Norbert Wiener, pioneered the idea of feedback.
3. In particular, the monads’ production rule scheme clearly presages the modern concept of cellular automata. Quoting from Mercer’s work:
The Production Rule of F is a rule for the continuous production of the discrete states of F so that it instructs F about exactly what to think at every moment of F’s existence. Following Leibniz’s suggestion, if F exists from t1 to tn and has a different thought at each moment of its existence, then at every moment, there will be an instruction about what to think next. The present thought occurring at t1, together with the Production Rule, will determine what F will think at t2.
Combined with the monadic property of being able to perceive the states of all other monads, this comes close to being a mathematically formal definition of cellular automata, a branch of mathematics generally agreed to have been invented by Stanislaw Ulam and John von Neumann during the 1940s as an outgrowth of work at Los Alamos. The impressive capabilities of such systems have, in subsequent decades, drawn the attention of many luminaries from the worlds of mathematics and physics, some of whom have proposed that the physical universe might, in fact, consist of cellular automata carrying out a calculation – a hypothesis known as Digital Physics, or It from Bit.
4. Leibniz insisted that each monad perceived the states of all of the others, a premise that runs counter to intuition, given that this would seem to require that an infinite amount of information be transmitted to and stored in each monad. Of all the claims of Monadology, this must have seemed the easiest to refute a hundred years ago. Since then, however, it has been given a new lease on life by quantum mechanics. Consider, for example, the Pauli exclusion principle,