ietsnut / Autonomonadology
Leibniz sees monads as the building blocks of reality, comparable to ‘ancient atomism’ (2008, 82), and similar to souls. A monad is ‘indivisible, non-physical and windowless’ (Leibniz 2008). Combining Leibniz’ identity of indiscernibles and principle of sufficient reason results in the view that every substance must be unique (Leibniz 2008, 68). Recursive cutting of a physical object in half (dividing it into parts, almost like a fractal) shows us that for something to be indivisible it must be immaterial and non-physical. The monads ‘synchronize’ and get ‘coordinated’ in universal harmony with God, the Deity (Leibniz 2008, 86).
The existence of a God in a metaphysical theory is what Immanuel Kant would consider a ‘scandal’; there is still no rational proof of the existence of the external world. This type of ‘scandal’ can also be seen in Cartesianism in the form of an evil genius; ‘If we do not know of his existence, we cannot ward off sceptical doubts about the reality of our bodies and the physical world’ (Descartes 2008, 12), and in subjective idealism; ‘matter is not perceived by us, but is perceived by God, to whom it is the occasion of exciting ideas in our mind’ (Berkeley 1874, 20). It should be noted that Descartes was born in 1596, Leibniz in 1646 and Berkeley in 1668, explaining a similar zeitgeist concerning metaphysics.
In this day and age, how can the Monadology provide a rational proof of the existence of the external world? Without a God, how do we explain uniqueness and creation/annihilation?
Monads are differentiated by their perceptions (Leibniz 2008, 80), and limited in these as to distinct them from being a Deity. Monads are ‘living mirrors’ (Leibniz 2008, 86), together a ‘perpetual living mirror of the universe’ (Leibniz 2008, 79). When a monad is created, it doesn’t have any perceptions, comparable to being a ‘tabula rasa’. In this state a monad isn’t unique, so there must be perception after creation. These perceptions are what makes them unique, and needs to be achieved without a God.
Relations between monads can be visualized using graph theory. As a monad is an indivisible point, it resembles a mathematical point in a hypergraph. Perceptions can be plotted as lines between the monads, resulting in a complete overview of all monads and their current locations as perspectives.
In this hypergraph, monads can change their position, their perspective, by themselves. Monads evolve according to an internal rule, they are similar to a cellular automata (Wolfram 2020, 7-9). However, this hypergraph is different from a cellular automaton as every instance of a monad is its own Deity. Monads aren’t controlled but act according to their individual nature. This nature is unique and differentiates monads (their movement in the hypergraph) from one another. Different behavior results in different perceptions, making monads unique again.
As monads aren’t a compound, they are without parts. Monads can only come into being or come to an end all at once (Leibniz 2008, 67). They are created by the Deity when the world begins; ‘animals and souls begin from the very commencement of the world and that they come to an end no more than does the world’ (Leibniz 2008, 85-86), suggesting no more can be created or annihilated after the world begins in the Christian sense.
The creation and annihilation of monads can also be explained as being in- and outside the hypergraph. A comparison can be made to the optical spectrum, only a tiny bit of the entire electromagnetic spectrum is visible to humans, as might be the external world; monads can’t perceive other monads outside the hypergraph.
This phenomenon can be explained using the 4th dimension. If our space is 3 dimensional, it is a ‘slice’ of the 4th dimension; ‘your country of Two Dimensions is not spacious enough to represent me, a being of Three, but can only exhibit a slice or section of me, which is what you call a Circle.’ (Abbott 1884, 71). When a monad is present in this slice (our world), it is perceiving other monads inside the hypergraph. Creation and annihilation of monads as we know it means the passing of monads through our plane of existence.
The Monadology can remain logical and valid without a Deity by viewing monads as autonomous and their relations as a 3-dimensional hypergraph in a 4th dimensional space.