Harmonia Praestabilita

The Leibniz-Clarke correspondence includes an interesting discussion of the relations and interactions between mechanical and animal processes.  The subject arises when Leibniz asserts that Newton's force of gravity is a supernatural phenomenon (indeed, a perpetual miracle), because it is not explained by the natural deterministic mechanical motions of bodies.  Clarke replies that, according to this definition, all animal motions involving free will must be called supernatural.  In paragraphs 30-31 of Leibniz's fourth letter he replies

The soul knows things because God has put into it a principle representative of external things...  The soul does not act upon things, according to my opinion, any otherwise than because the body adapts itself to the desires of the soul, by virtue of the harmony, which God has pre-established between them.

Not surprisingly, this didn't satisfy Clarke, who answered in 30-31 of his fourth letter by turning the charge of perpetual miracles back on Leibniz:

What is meant by representative principle I understand not.  The soul discerns things by having the images of things conveyed to it through the organs of sense...  That the soul should not operate upon the body, and yet the body, by mere mechanical impulse of matter, conform itself to the will of the soul in all the infinite variety of spontaneous animal motion, is a perpetual miracle.  Pre-established harmony is a mere word or term of art, and does nothing towards expanding the cause of so miraculous an effect.

In paragraphs 89 and 92 of Leibniz's fifth letter, he replies

The harmony or correspondence between the soul and the body is not a perpetual miracle, but rather the effect or consequence of an original miracle, worked at the creation of things, as all natural things are.  Though indeed it is a perpetual wonder, as many natural things are...  'Tis true that, according to me, the soul does not disturb the laws of the body, nor the body those of the soul, and that nevertheless the soul and body do entirely agree with each other, the one acting freely according to the rules of final causes, and the other acting mechanically according to the laws of efficient causes.  But this does not derogate from the liberty of our souls... for every agent which acts according to final causes is free, though it happens to agree with an agent acting only by efficient causes without knowledge, i.e., mechanically, because God, foreseeing what the free cause would do, did from the beginning regulate the machine in such manner that it cannot fail to agree with that free cause.

Returning to this point in paragraph 124 of the same letter, Leibniz re-iterates that

All the natural forces of bodies are subject to mechanical laws, and all the natural powers of spirits are subject to moral laws.  The former follow the order of efficient causes, and the latter follow the order of final causes.  The former operate without liberty, like a watch; the latter operate with liberty, though they exactly agree with that machine which another cause, free and superior, has adapted to them before-hand.

This is an interesting argument, one that bears directly on the central interpretative difficulty of quantum mechanics, as exemplified in EPR experiments and other tests of Bell inequalities.  In these phenomena the free will of the experimenter (in choosing which measurements to perform) is found to be in harmony with the results of purely mechanical processes involving entangled pairs of particles.  This could easily be regarded as a perpetual miracle, but Leibniz would call it just a perpetual wonder.  According to his view, God knows the outcome of all free choices in advance, and devised the mechanical processes of nature so as to be always harmonious (consistent) with those choices.  Clarke was not persuaded, and challenged the plausibility of the idea that the (presumably) simple laws governing the behavior of mechanical bodies could be flexible enough to conform with the huge variety and subtlety of animal motions governed by free will.  In his fifth letter, Clarke asked

But is it possible that such kinds of motion, and of such variety, as those in human bodies are, should be performed by mere mechanisms, without any influence of will and mind upon them?  Or is it credible that when a man has it in his power to resolve and know a month before-hand what he will do upon such a particular day or hour to come, is it credible, I say, that his body shall by the mere power of mechanism, impressed originally upon the material universe at its creation, punctually conform itself to the resolutions of a man's mind at the time appointed?

As compelling as Clarke's rebuttal may appear, and as vague and unsubstantiated as Leibniz's claims admittedly were, the observed violation of Bell inequalities for entangled particles can be taken as supporting evidence in favor of Leibniz's position.  The interpretation of these experiments depends directly on whether or not we believe it is possible for a pre-established harmony to exist between mechanistic phenomena and the operations of free will. 

There is an interesting parallel - both historical and conceptual - between the Michelson & Morley experiment and modern EPR experiments.  In each case the experiments were designed to detect an incongruity between two putatively different classes of motion.  The ether drift experiments were essentially attempts to compare how inertial forces and electro-magnetic forces transform under changes in speed, and the results showed that, in fact, these two classes of phenomena were the same, i.e., the speed of light is isotropic and invariant with respect to the same class of coordinate systems for which mechanical inertia is isotropic and invariant.  Similarly, EPR experiments are essentially attempts to compare free (or random) processes with deterministic mechanical processes, and the results show that these two putatively distinct kinds of processes actually conform with each other. 

The most popular "explanation" for this somewhat unexpected fact is that the workings of nature must be non-local.  Now, there is undoubtedly a sense in which physics is non-local - since Minkowski spacetime itself is non-local (due to its non-positive definite character of the metric) - but the non-locality required to reconcile the violation of Bell inequalities goes beyond this, and it would not have been agreeable to Leibniz, whose whole thesis was motivated by his objection to "occult action at a distance".  Instead of invoking non-locality, Leibniz proposed pre-existing harmony, and this is indeed a viable alternative explanation for violations of Bell inequalities, as J. S. Bell himself acknowledged.

After challenging the plausibility of the idea that mechanical processes could somehow be supple enough to conform with all the actions of free will, Clarke went on to consider the implications of this alleged harmony.  He says

If the world can once be persuaded that a man's body is a mere machine, and that all his seemingly voluntary motions are performed by the mere necessary laws of corporeal mechanism, without any influence or operation or action at all of the soul upon the body, they will soon conclude that this machine is the whole man, and that the harmonical soul in the hypothesis of a harmonia praestabilita is merely a fiction and a dream.

This is the same objection that Bell raised in his book "Speakable and Unspeakable in Quantum Mechanics".  In his enumeration of the ways in which what he calls "local realism" could survive, he includes the possibility that

The [measurement] quantities a and b are not independently variable as we supposed.  Whether apparently chosen by apparently independent radioactive devices, or by apparently separate Swiss National Lottery machines, or even by different apparently free-willed experimental physicists, they are in fact correlated with the same causal factors (l,m) as the A and B.  Then Einstein local causality can survive.  But apparently separate parts of the world become deeply entangled, and our apparent free will is entangled with them.

This possibility was dismissed by Bell, just as it had been by Clarke, illustrating the persistent reluctance with the scientific tradition to seriously consider anything other than complete independence and individual freedom in the operations of "free will".  Newton wrote about Leibniz's ideas in a letter to Conti

His harmonia praestabilita is miraculous and contradicts the daily experience of all mankind, every man finding in himself a power of seeing with his eyes, and moving his body by his will.

Another interesting aspect of Leibniz's position is the distinction he draws between mechanical processes, which he says "follow the order of efficient causes", and processes involving the mind or will, which he says "follow the order of final causes".  His thesis is that the efficient causes of things are automatically consistent with the final causes, because of the pre-established harmony between them.  Leibniz was referring to the usual categories of proximate causes and teleological causes, but his words are suggestive of a combination of forward and backward causation.

The correspondence between Leibniz and Clarke (who is often regarded as a spokesman for Newton) was actually carried on through an intermediary, Caroline, the Princess of Wales.  Leibniz had been Caroline's tutor in Hanover, but she moved to England with her husband, the Electoral Prince of Hanover, who later became King George II of England.  Caroline was an intelligent woman who took a genuine interest in the scientific issues of the day.  She witnessed experiments and participated actively in scientific discussions.  One question that was much debated in those days was whether or not there is such a thing as a vacuum.  Like Aristotle, the Cartesians held that no empty space can exist, and there must be something everywhere, i.e., there is no such thing as an unoccupied "place".  Leibniz agreed.  On the other hand, the neo-Epicureans (often thought to include Newton, although his writings are equivocal on the subject) viewed the world as comprised of atoms of substance moving about in an empty void.  Caroline wrote to Leibniz

I have been watching experiments and I am more and more charmed by colours.  I cannot prevent myself from being a little biased toward the vacuum; but I think there is a misunderstanding, since what these gentlemen call a vacuum is meant to signify nothing but something which is not matter.

Describing the vacuum as "nothing but something which is not matter" may seem a bit muddled and naive at first, but she may actually have been ahead of her more learned tutors in realizing that there might be "something which is not matter".  Indeed, the colours of light (electromagnetic waves) passing through an evacuated jar is an example of something which is not matter.  The concept of a "field" had not been developed in those days, but once this concept is granted, and considering that a field permeates all of space, it's clear that any question about the possibility of unoccupied places becomes moot.

The concept of pre-established harmony re-appeared in the later efforts of Einstein to develop a “unified field” theory, which he hoped would not only unify electro-magnetism and gravitation, but more importantly would account for “the structure of the quanta”.  He expressed his basic idea in a letter to Max Planck (as quoted in Pais’ biography) in 1931.

Natural phenomena seem to be determined to such an extent that not only the temporal sequence but also the initial state is fixed to a large extent by law.  It seemed to me that I should express this idea by searching for over-determined systems of differential equations… I strongly believe that we shall not end up with a Subkausalitat [subcausality] but that, in the indicated sense, we will arrive at an Uberkausalitat [supercausality].

The field equations of general relativity already exhibit a certain degree of what might be called Uberkausalitat, because of the constraint on the initial conditions imposed by the Bianchi identity.  This is one of the most significant respects in which Einstein’s gravitational field equations differ from Maxwell’s equations of the electromagnetic field.  Of course, the idea of physical laws that constrain the initial conditions of the universe is essentially equivalent to Leibniz’s notion of pre-established harmony.  Perhaps we can understand a little better the fundamental contrast between the view of Clarke (“the soul discerns things by having the images of things conveyed to it through the organs of sense...”) and of Leibniz (“the soul knows things because God has put into it a principle representative of external things”).

Return to MathPages Main Menu