Leibniz’s Monadology and Fundamental Physics

The True Atoms of Nature

In modern physics, fundamental goings on are defined in terms of the way that the pattern of the entire universe, defined by fields of potentials (or causal powers), makes possible new events in the form of ‘modes of field excitation’ or, in common parlance, modes of action. In turn the totality of the modes of excitation occurring provide the field pattern from which further events may arise. The true atom of nature is an indivisible event or mode of action (‘field excitation’) and its nature is a two way causal relation to the rest of the universe.

In 1714 Leibniz laid out the basis for exactly the same fundamental picture in which the indivisible mode of action is a ‘monad’ whose nature is to reflect, and progress in harmony with, the entire universe. At the fundamental level nothing interacts with any particular thing, only with everything. Leibniz also proposed that these true atoms of nature are what we know as points of view. To act in the world is to experience or perceive the world. So every point of view belongs to an indivisible action and vice versa. This provides an elegant, parsimonious way to explain our true relation to the world.


In the late seventeenth century both Isaac Newton and Gottfried Leibniz were involved in the development of basic physical laws for motion and optics. Both discovered the calculus. Newton’s analysis has formed the basis for most practical physics ever since. Leibniz, however, in many ways had a deeper understanding of what must underly those laws. He also made major contributions to other disciplines including logic and law.

Leibniz’s strength lay in the formulation of general principles based on pure reasoning (so that they more or less have to be true), in such a way that they can be used to decide whether theories are coherent and consistent. Examples are the laws of continuity, contradiction and the identity of indiscernibles.

Leibniz believed that the sort of mechanics of physical objects that we call Newtonian gave a valid description of everything happening in the world. He also believed that there was a more fundamental (or meta-physical) description of world events that must be quite different, for reasons of logic. Nevertheless, the two descriptions would always correspond or harmonise.

Many people have noted that Leibniz’s ideas were often decades or centuries ahead of their time. His understanding of the relative nature of space and time is often quoted, as is his analysis of the behaviour of light. After reading and re-reading Leibniz’s key essays I come to a conclusion that goes beyond that. I think that Leibniz tells us why the most fundamental description of what happens in the world must look exactly like modern quantum theory and, more significantly, why there is nothing puzzling or strange about such a theory – it makes perfect sense if we are prepared to free ourselves of false intuitions.

Leibniz’s fundamental meta-physical account of the world is in many ways a mental or experiential account. He talks of appetitions and perceptions and of ‘souls’. Perhaps the most significant claim is that the way things act, in the sense of progressing from state to state, is nothing other than the way an experiencing subject passes from percept to percept. Relating to the universe is both acting in the universe and perceiving the universe.  

Although Leibniz makes clear the logical basis of his metaphysics over the course of thirty years he does not spell it all out in any single short passage. My understanding of the crux of his argument is this. The universe must contain discrete individual entities because there are discrete points of view, and a single continuous entity does not have many discrete points of view (this contrasts with Spinoza). A true individual entity must be indivisible because if it had parts, either in space or time, they would be the individuals and it would be a mere aggregate. Classical mechanics describes entities in terms of size and shape and trajectory. These are all descriptions of spatial or temporal parts so classical mechanics can only apply to aggregates. A true individual entity, that might have a point of view, cannot have size or shape and it cannot have a trajectory.

The reason why it is logically necessary to have a different sort of description for true individuals goes something like this: If we say a particle passes through a slit at time T we cannot be referring to a true indivisible individual because only the temporal part of the individual existing at time T passes through the slit. We would have to say that the essence of the complete entity includes a particular spatiotemporal relation to a slit. Our idea of a particle assumes that there is some entity that exists over and above its relations in time and space (that we can consider the particle then out of time) but Leibniz sees that there is no existence over and above relation. If one follows this through to its logical conclusion a particle is an absurd concept.

The ultimate basis of this sort of argument is Leibniz’s account of truth, which in my view is the only valid account. A truth is a statement in which the predicate is entailed in the subject. That means that any subject concept like ‘particle’ must include all the predicates that are true of it. That implies that we cannot use the same sort of statements that we use for aggregates for true individuals. This may seem a rarified approach to physics but it becomes directly relevant in many of the counterintuitive rules of quantum theory. An example is the rule that if two dynamic units in quantum theory cannot be distinguished in principle then they must behave as a single unit – which may have a dramatic effect on the predictions to be made.

Leibniz’s mature ideas are crystallised in his Monadology of 1714. In 2014 I attempted to redraft the original text with as few changes as possible to illustrate just how well it lays the foundations for modern quantum theories (attached). 

One of the strange features of quantum theory that Leibniz predicts is that events must in some sense be end-directed or telic. This telic aspect may be seen in terms of ‘purpose’ and Leibniz appears to take that view. It is tempting to apply such a concept of purpose to biological processes like evolution. However, the situation is more complicated, as discussed in the attached conference paper on Leibniz and Telicity.

Edwards JC (2014) A 21st Century Monadology. 

Edwards JC (2016) Leibniz and Telicity. In Proceedings of the 10th International Leibniz Conference, vol 1. Gottfried Wilhelm Leibniz Gesellschaft, Hannover. 

Leibniz and Telicity

Fundamental Physics as a Game of Chess

Quantum theory is supposed to be mysterious or impossible to understand. Typically, this is illustrated by the idea that a particle can go through two slits at once. Or, so we are told, that the particle must be thought of as neither in one place nor the other nor both nor neither. 

The reason why there is no such mystery in quantum theory is that there are no particles. There are only points of connection between modes of action. We know enough about the way our brains create images of the world to know that our idea of a ‘particle’ is an inconsistent fiction. In fact the problem was understood in ancient Greece. Either a particle has no size, in which case it isn’t a particle, or it has size with a right side and a left side and a top and bottom, which means it isn’t a particle either, but an aggregate of particles. And what could having a size mean anyway? It would mean discontinuity at the ‘edges’ that would require infinite rates of change of properties. If we think carefully we see that we cannot have a concept of a particle. It is a trick the brain plays as it paints pictures of the world. 

It might seem that if we throw out particles we have to throw out any sense of a real world. There seems to be nothing to hang on to that we can use as an analogy to describe reality. There is perhaps, however, an exception that can work – the game of chess and in particular the game of chess played on two computers, with no pieces. All the game consists of is moves and points of connection between those moves. There is no internal structure to each move, it just happens as a single event, without needing any particular path. There is no need to worry whether the knight hopped over a pawn or a bishop. It neither did nor didn’t.

A theory in which the basic units are modes of action rather than particles, with no size or shape or trajectories, requires completely different sorts of statements from a theory about particles, as Leibniz understood. Nothing is ever half way to where it is going. Forces do not act to change directions of movement. All we have is a theory of what modes of action, or what chess moves, are likely to occur given the way the universe is at a particular time. That is exactly the way statements in quantum theory work. There is no such thing as a ‘progression of a wave function’ or ‘wave function collapse’ just as there no jumping of a knight over a pawn or bishop. Until a mode of action has occurred in its entirely it is not that mode of action. What a wave equation provides is a catalogue of all the possible modes of action of a certain type that might occur under certain conditions and the likelihood of each possible action occurring. It is not a description of the structure of a mode of action, but rather a description of the structure of the rules that govern actions.

A physics in which there are no particles and no movements threatens to be impossible to understand and that might seem to make it almost impossible to know how to find equations that might prove reliable predictions. If our intuitive idea of a work of moving particles is just based on some symbols our brains use to form a representation of reality that, however useful in day to day activities, proves inconsistent, can we allow any alternative props to understanding such as chess moves. Are they just as bad? The history of development of quantum theory suggests that it is possible to tease out more consistent metaphors to help formulate equations, even if we still have to be careful to use them as metaphors.

As an example, quantum theorists realised that the patterns describe by their equations should not allow what are known as ‘preferred positions’. A sine wave goes up and down so we might prefer the up points. In contrast, a complex harmonic oscillation, as use in quantum theory equations, is more like a corkscrew. An infinite corkscrew screwing though space has the interesting property that although it progresses what you see never changes. There is no point in time or space to prefer, every part is equal.

Another useful idea is that all events are responses to possibilities set up by asymmetries. If the world was homogenous throughout, with no asymmetries, there would be no reason for anything to happen. But if at one place there is a more positive charge (a proton) that provides the possibility of a specific set of electron ‘moves’ we call an s orbital. In macroscopic solid objects ordered internal structure will provide directional asymmetries that can allow more complicated moves. Thus a crystal allows phonon ‘moves’ that form the fundamental basis of sounds. But, as for the chess piece, there is no real sense in which a phonon is a particle that itself moves. The crystal offers possibilities for certain types of change, just as in a game of draughts (checkers) a pattern on the board with alternating empty and full squares allow for a change in position of a draught, only notionally hopping over others.

As will be mentioned in the next topic below, all of this is metaphor based on the symbols our brains use to try to find the best way to predict what will happen in the world. None of it is ‘what the world is really like’, yet there seems no doubt that some metaphors are better than others for different purposes and the ones we want for fundamental physics are quite different from those we use in everyday life.

A feature of a theory based on indivisible modes of action or chess moves of this sort is that the tendency for actions to occur is as much dependent on their ends as their beginnings. This in a sense makes the theory telic. The universe seems to choose where to move next, like a chess player. Physics seems to be based on ‘reasons’ (as Leibniz described it) or even purposes. This is explored in the attached paper on a chess move approach to the cosmos. In some ways it seems to make sense of the idea of a ‘God’s purpose’. However, just as for particles, our intuitive concept of purpose turns out to be full of inconsistencies and so this is not a justification for teleological theories like creationism or Lamarckism. Nor does it provide any support for the claims of organised religions.

Edwards JC(2019) A Chess Move Approach to ‘Choices’ in a Mental Cosmos Activitas Nervosa Superior 61, 108–111.

Experience as the Centre of Physics

It is commonly said that conscious experience is somehow outside of or alien to physics, or that mental events are not physical events. Sometimes the suggestion is that mental processes involve causes that are in some way ‘not physical’ (dualism) and sometimes the suggestion is that there is nothing over and above the physical (eliminativism).

There is something strange about the idea that experience is alien to physics because if we look at a dictionary we see that the definition of ‘physical’, however indirectly expressed, boils down to anything that determines the patterns of our experiences through sensory input. Physical events are more than mathematical patterns only in that they ‘actually happen’ and to actually happen can only be defined as having the power to influence experience. 

Put another way, all attempts to define what we mean by physical have to draw on experience.

It might be argued that what we experience is the physicality of the world – we perceive that physicality. However, studies of perception show that all the components of our experiences are signs concocted by the brain to represent the world. Both the ‘secondary qualities’, like colours and smells, that John Locke recognised as inventions of the brain, and the ‘primary qualities’ like spaciousness and duration, are internal signs that represent the external world. The hardness of the stone kicked by Dr Johnson that made it for him physical rather than ideal, is absolutely an idea in the head. That does not alter the reality of the world being represented but it means that ‘physicality’ can only ever be defined as the patterns of mathematical regularity in the way the world determines our experiences.

A useful example is our experience of movement. That experience must derive from comparing input from the retina at one time with input at a later time. A difference is then identified and a signal indicating that difference sent to wherever movement is experienced. But that signal does not span the two times samples originally. It arrives just once.  Moreover, we can be fairly sure that its meaning is encoded in its spatial relation to other signals in the brain, not any temporal relation. So our experience of movement does not involve time in the way that movement does. It cannot be actual movement. 

Fundamental physics provides further evidence for the ‘metaphorical’ nature of our experience of outside events. In modern fundamental physics there is no movement of the sort we think of intuitively anyway. Fields interact. No micro-billiard balls fly about.

Both relativity and quantum theory have highlighted something about physics that has been recognised for centuries but often ignored – that it is always and only about interactions. Einstein complained that physics does not have a definition of ‘now’, but experience provides a natural one. Now is the time of interaction for something experiencing an interaction. It is something local, which is why, as relativity proves, there is no such thing as two separate events being simultaneous. 

The extent of ‘now’ as we experience it is something that has interested Steven Savitt and Richard Arthur, both of whom have suggested that it forms what is known as a ‘causal diamond’. A causal diamond is a domain of spacetime formed by two back to back light cones that defines the extent of possible interactions of something passing from one point in spacetime to another. In the fundamental physics of condensed matter this would fit with the domain of a mode of excitation of a field interacting with a field of potentials within neural tissue. The key question is what sort of mode of excitation would it be.

Proximal Experience as an Essential Part of Physics (submitted manuscript) 

Proximal Experience as an Essential Part of Physics

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