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Saturday, 26 December 2015

Worlds and monads

The last sections of part 3 of Leibniz's Theodicy makes clear that interaction were part of what happened between the monads in the simulation process that takes place in the Palace of Destinies that Palas Athena guards. In fact, God had to consider all possible worlds in order to choose the right combination. Monads could be taken as building blocks that are agents or reagents. They have all their history encapsulated in themselves and therefore they are repositories of events. In Leibniz, there is an infinite number of them (and not an indefinite number). It is enough for God to choose a collection of monads in order to choose a world. God would consider the different classes of monads. Every contingent alternative was considered in the Palace: sinning Adam with the serpent and non-sinning counter-Adam with the iguana. God considered every counterpart of Adam and therefore the interactions between Adam and the rest of the world were played in the Palace before God. What is missing in Leibniz's monadology is the sense of present time: present time interaction among monads is dispensable (the interaction that matters happens in the Palace), present time decision-making is no more than a shadow of what took place in the Palace and present time hesitation is no more than lack of knowledge. In the simulation process, on the other hand, interaction is present between each monad, their counterparts and the rest of the world.

However, because Leibniz (and, I argue, every monadology) is contingentist, there is no room for trans-world monads. Monads are not like
the alphabet in which worlds could be written. Leibniz has that God chose monads and not aggregates of monads. Plus, worlds cannot be understood in terms of different elements in the set of parts of all monads for monads are never trans-worldly. If one conceive worlds as composed of building blocks of an alphabet, we can consider all worlds in this alphabet as elements of the set of parts of the building blocks. Such a class would be the class of all worlds, possible or impossible - that is, they would form a superset of the class of all possible worlds. In our current work on galaxy theory (exploration of the relation between different logics by considering the different classes of possible worlds - galaxies - associated to each of them) we are considering the relation of access between words of different galaxies. Each galaxy is a subset of the set of parts above. But each logic could be build as a relation from a given galaxy to any other. Monadologies are beginning to look like no more than a small portion of a far ampler space of worlds and relations between them.

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