Cantor's slash and Leibniz's monads

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In summary, the conversation discusses the relationship between set theory and Leibniz's monadology. The speaker has reached a conclusion, based on their understanding of Cantor's diagonalization, that the possible temporal experiences of a monad cannot be put in one-to-one correspondence with the possible states of the world. This raises questions about the nature of monads and their ability to observe the world. There is also a discussion about the properties of monads and how they relate to the physical world.
  • #1
cabias
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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.
 
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  • #2
Since you seem to be interested in Leibniz's philosophy, rather than mathematics, I'm going to move this over to the philosophy forum.
 
  • #3
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.
 
  • #4
kant said:
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.
 

1. What is Cantor's slash and Leibniz's monads?

Cantor's slash refers to the diagonal slash symbol used in set theory to represent an uncountable set. Leibniz's monads, on the other hand, are a philosophical concept that suggests that all substances are made up of individual, self-contained units or "monads". These two concepts are often studied together in mathematics and philosophy.

2. How are Cantor's slash and Leibniz's monads related?

Cantor's slash is often used in the study of Leibniz's monads to represent the infinite nature of these individual units. It is used to show that even though each monad is unique and self-contained, they are all connected within the larger framework of the universe.

3. What is the significance of Cantor's slash and Leibniz's monads in mathematics?

Cantor's slash and Leibniz's monads have had a significant impact on mathematics, particularly in the study of infinity and set theory. These concepts have also influenced other areas of mathematics, such as topology and calculus.

4. Are there any criticisms or controversies surrounding Cantor's slash and Leibniz's monads?

Yes, there have been several criticisms and controversies surrounding these concepts. Some philosophers have argued that Leibniz's monads are too abstract and cannot be proven or disproven, while others have criticized Cantor's slash as being a flawed symbol that does not accurately represent uncountable sets.

5. How can Cantor's slash and Leibniz's monads be applied in real-world situations?

Although these concepts are primarily studied in mathematics and philosophy, they have also been applied in other fields such as computer science and linguistics. For example, Cantor's slash has been used in computer algorithms and Leibniz's monads have been applied in the study of language and cognition.

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