Cantor's slash and Leibniz's monads

[cabias]

Hi,

Sort of a mish-mash of set theory and ontology here. I've been reading over Leibniz's monadology and I've reached a few conclusions that are different from his, based on my naive understanding of set theory. As I understand it Leibniz's monads function by ordering possible states of the world (the world in which they exist) in a series, similar to the way we experience time, I would wager. I'm making the assumption that the possible states of the world are discrete and can therefore be represented by the natural numbers, so the conclusion I've reached based on my understanding of Cantor's diagonalization would seem to be that the range of possible temporal experiences that a monad could have cannot be put in one-to-one correspondence with the possible states of the world. To me this implies that a monad is capable of observing the world as being in a state that it cannot actually be in, and thus capable of observing nothing, which seems to go against Leibniz's conception of the world as plenary. I feel certain that I do not fully grasp the nuances of Cantor's argument and I would be very interested if anyone could point out the flaws in my use of it. I've encapsulated my argument very roughly here and I can expand if necessary.

Warm regards, C.

 

[Hurkyl]

Since you seem to be interested in Leibniz's philosophy, rather than mathematics, I'm going to move this over to the philosophy forum.

 

[kant]

Well if monad is infinite, and each monad process a plurity of properties. Since monad is different from properties.(is each property a monad as well?)The properties themselve must also be infinite.

 

[cabias]

Well if monad is infinite, and each monad process a plurity of properties. Since monad is different from properties.(is each property a monad as well?)The properties themselve must also be infinite.

i don't have the text in front of me but Leibniz says something to the effect that there is nothing distinguishable within a monad other than its properties, meaning that a monad isn't really different from its properties. since the monads are dimensionless the physical world as leibniz describes it consists solely of relations between empty placeholders.

a monad's whole range of properties might necessarily be infinite but there's no reason each individual property couldn't be a variable with a finite range of values. a sticky question is whether that range of values is discrete or continuous.