General philosophy Leibniz

[Cubey]

Leibniz was a metaphysician and a logician. As a logician he drafted some wonderful theories that unfortunately were the victim of mockery by his jealous contemporaries. Putting that aside let’s talk about what is today known as Leibniz’s Law.

Leibniz’s Law is the syntactic correspondence of two premises. One is “The Identity of Indiscernibles” and the other is “The Indiscernability of Identicals”.

Let’s talk about the former first. The identity of indiscernibles says that if all that is true of X is true of Y, then X and Y are identical.

The latter-

The indiscernability of identicals says that if X and Y are identical, then all that is true of X is true of Y.

These two together make up Leibniz’s Law:

X and Y are identical if, and only if, for every property Z, X has Z if, and only if, Y has Z.

Restated this way it becomes more isomorphic and less recursive:

No two or more distinct things exactly resemble each other.

In other words, the qualities - and quantities of them, of two objects, determine the quantity and identity of the object(s).

Further reading

 

[Cubey]

The Monadology is [arguably] Leibniz’ magnum opus. It’s an ambitious endeavor [that he is trying to accomplish] to say the least.

The monads, to quickly go over the basic premise, are immaterial particles - simple and indivisible, eternal and infinite (both in quantity and quality) - which together constitute the entire universe. These “monads” all are striving towards an end based on a pre-established harmony from the beginning of the universe.

Leibnizian monads are an extremely elaborate idea which requires intricate explanation.

I will start by defining the monads. They are the simplest substance, compounds of which result in the physical world. They are capable only of internal action as they are partless within, so they are without duplicate. Because of this, we have two basic, but not solitary, actions: perceptions and appetitions. The perception is what the monad reflects based on its unique perspective of all other monads around it. This perception is constantly changing as the monads around it change. The second action, appetition, is the desire or striving towards an end held within the monad. So as each monad combines its perception with its appetition, its perspective changes.

Now this is where Leibniz’s ambition really shines through. He leaves here a special reservation to discuss God, creation and perfection. He describes God as the Perfect Monad, where his power (to produce - not only his own being but the entire universe), his wisdom (to know what is best) and his goodness (to choose what is best) allow him to create reciprocals of himself, where, while he alone can sustain the universe, these reciprocals - the monads - together sustain the universe.

He goes on to give a treatment of perfection. Obviously perfection is derived from God. His perfection however is infinite (meaning lacking in limitations), and thus the creature is distinguished from God by his limits and lack of perfection, to whichever degree.

Leibniz goes back to discussing monads here and gives a great analogy. The monads, being expressive of all others, are living mirrors (he calls them souls at certain times) of the entire universe.

“And as the same city regarded from different sides appears entirely different and in perspective is as if multiplied, so also it happens that, because of the infinite multiplicity of simple substances, there are as it were so many different universes, which are different points of view of each monad.”

In other words, the universe is full of variety, varying in degrees of perfection and of character. Each monad represents one of these varieties and expresses all the others with its own perspective. Each of these perspectives is a personal universe for the corresponding monad.

Leibniz next anticipates some possible criticisms and responds accordingly. “If every monad can express the universe, aren’t they all the same?”

Leibniz answers by saying that each monad can only most accurately express those others which are nearest to it, otherwise they’d all be God. The next analogy is a pendulum. Since the universe is full, and bodies in motion are affected by and fully understand the first body to come into contact with them and, that very body is affected by the bodies which come into contact with the first body to come into contact with it.

He concludes this corollary by stating that since everything in the universe can feel everything that has ever happened, one who sees all could state in each all that happens everywhere.

He continues into a grand conclusion which you guys will just have to read for yourselves if you want to know the ending