Leibniz

Leibniz was one of the last great Rationalists. He believed that reason was infallible and that senses could fool you. He also had some very unique ideas that are miles away from the closest Rationalists. For example, Leibniz believed that something was true only if the two sides of the equation were exactly equal. That means that an apple is a fruit only if apple is the exact same thing as fruit.
Leibniz based all of his proofs off of simple logical principles. His 3 big principles were Plurality & Unity, the Principle of Sufficient Reason, and the Principle of Indiscernibility of Identicals.
Atomic theory was a notion being played with at the tim

Truth

What is Truth
Certain, Necessary and Contingent Truths
Contingent Truths
Atomic Theory
Proof For God

Principles of Rationalism

Plurality and Unity
Principle of Sufficient Reason
Principle of Indiscernibility of Identicals

What are Monads

Predicates
Complete Concepts
Individual Substances
Complete Concepts = Individual Substances = Monads
Simple Monads
Complex vs Simple Monads

Space and Time

Space does not exist
What Space really is

Truth

OTHERS: Truth is when a predicate is contained within a set of propositions.
True Example: Socrates is contained in a set of people who love virtue.

LEIBNIZ: Truth is when a predicate is equal to another proposition.
True Example: Socrates is a lover of virtue, friend of Plato, (etc until Socrates is referenced against the whole universe).

Truth: A proposition wherein the predicate is contained within the subject. (S=P).

A synthetic example: The Melon is Orange. Melon exemplifies orange. Orange is contained in Melon. (Not an obvious example)
An Analytic Example: Orange is a Color. Orange exemplifies color. Orange is contained in Color. (Obvious example)

Certain, Necessary and Contingent

Certain: It will happen (but yet it is possible that it could not happen).
Necessary: The opposite will never happen.
Contingent: Not Necessary. (it depends on something).

Contingent Truths

"The melon is orange" is continently true. But "the melon I ate last year was orange" is necessarily true.
A melon contains all of its properties, but we only know some of them. That is why many things are contingent. But once we know them, they become necessary.
The melon I ate I know for sure is true because I ate the melon. 'The melon is orange' is not necessarily true. Every melon we may have seen is orange, but there could be 1 purple melon that nobody has stumbled upon... yet...
Things are only continently true in our heads. Once we know they are true, they become necessarily true.

Atomic Theory

Early atom theory thought that all the atoms were moving in the same direction at same velocity. Then one atom sways (the sway theory) and now all the atoms are bumping into each other. When they collide, they go flying into other atoms. Everything that we see is a result of these collisions.
Leibniz thought that was crazy. Science of the time claimed that the atom is the smallest possible way to break something down. They also claimed that the atoms were elastic (thus they spring into other atoms upon a collision. They didn't just stop on impact, so they had to have elasticity and bounce.) If atoms have elasticity, then they are not the smallest possible way to break something down. Because you could break down the atom into "the atom" and "elasticity". So Leibniz was against early atomic theory.
Atoms are extended. Leibniz's Monads are not extended.

Proof For God

We are contingent things.
Contingent things only can come from necessary things.
Therefor, God is the necessary thing that created us. And hence God exists.
(P.S. Leibniz is NOT a fatalist.)
(We have free will. Ceasar could have ruined his destiny if he wanted.)

Principles

Plurality and Unity

Plurality presupposes unity.... if you have many things you have to have 1 thing.

Principle of Sufficient Reason

PRINCIPLE OF SUFFICIENT REASON: For every event or object coming into being, there is a sufficient reason for doing so.
A=A because A contains A.
Ceasar was stabbed by Brutus because Ceasar was who Ceasar was.
Ceasar contains an finite, but non-denumerable number of predicates. (There is a finite number, but it is so big we will never know exactly how many.)

Principle of Indiscernibility of Identicals

INDISCERNIBILITY OF IDENTICALS: If 2 things are identical, then you can't tell them apart... thus they are "indiscernible".

Monads

Predicates

All the predicates are related to all the others.
All of Ceasar's predicates HAVE TO BE his predicates to explain all of his other predicates.
Each predicate explains every other predicate.
All the other predicates explain each predicate.

The Complete Concept

THE COMPLETE CONCEPT: A collection of all the predicates.
Only God knows ALL the predicates of an object. You know some, but never all.
Thus, you will never know someone's complete concept, but you will know parts of his complete concept.

The Complete Concept contains everything including when and where Caesar would brush his teeth.
The Complete Concept is about EXPLANATION, not existence. The Complete Concept explains things.
Hence, we are contingent. Our Complete Concept doesn't FORCE us to do anything, it just explains why we did certain things.

The Complete Concept of Ceasar would be like a movie about everything in Ceasar's life.

All the Complete Concepts we have of things are concepts of things that exists.

We never actually have a complete Complete Concept since it is impossible to know all the predicates of something. But all the predicates we have of something that exists adds up to our Complete Concept of that object. (Not to be confused with God's Complete Concept of an object, which is actually complete.)

Individual Substances

Individual Substances perceived in thought are Complete Concepts.

Complete Concepts define Individual Substances.
Individual Substances define Complete Concepts.

Complete Concept of Ceasar is the Individual Substance of Ceasar perceived in our thoughts.
Complete Concept of Ceasar is made real by Individual Substances.

Every substance contains the history of the universe (past and present).
Every substance contains what it was and everything it will ever be.
My death is contained within me.
Every true predicate is necessary.

Substance: All true predicates of it are contained within it. Substance can be simple or complex.

A Monad = Individual Substance = Complete Concept

Individual Substances	Complete Concepts
Have Existence. (Take up 'space' and Interact).	Explanations
Have Properties	Contain Predicates
"Space like"	Propositions

The Simple Monad

(The same as a Complete Concept or Individual Substance)

Window-less
Mirrored. Every monad mirrors every other monad. That means that they don't change.
Not Extended (since there is no space to extend into, they can't take up 'space'.)
Simple (Because you can't pull anything out. If you pulled out a predicate or property, it would no longer be the same monad).
Relative... Monads are relative to each other. (Location is a property of monads. Monads are not in a location)
Self Sufficient (thus they are windowless. Nothing needs to go into them since they are self sufficient)
Can not perish naturally (only by divine intervention).

Simple vs Complex Monads

Your soul is a simple monad, since EVERY BIT of your soul is your soul.
Your body is a complex monad, since it can be broken into different parts.

Complex Monads are not windowless, but Simple ones are.
You soul is simple monad that controls your body (a complex monad).

If someone sees you when they have sunglasses on, they do not "connect" you with the sunglasses.
Similarly, just because people see your soul through your body doesn't mean that your soul is "connect" to your body.

Space

Space Doesn't Exist

OTHERS: Space is like a mile marker. It never moves on you. It exists.
Leibniz: Space doesn't exist.

Proof #1 against the existence of Space:
INDISCERNIBILITY OF IDENTICALS: If 2 things are identical, then you can't tell them apart... thus they are "indiscernible".

You can empty space.
When space is empty, then every part of space is identical to every other part of space.
If it is identical, you can't discern between different parts of space.
So how can you tell movement if it is all the same?
Hence, Space does not exist.

Proof #2 against the existence Space
PRINCIPLE OF SUFFICIENT REASON: For every event or object coming into being.... there is a sufficient reason for doing so.

Space is absolute.
So why is space located where it is instead of 2 meters to the right?
Since we don't have sufficient reason, we can't prove it exists.

Counter Argument against Proof #2:
To make earth "perfect" god put space where he did.
Leibniz Reply:
When you empty space, you empty it of everything including God.
Thus, without God there is no reason why it is where it is.

So, What is Space?

Space, Time and Motion exist only in our heads, not in the "physical world."

A Change in location is a change within the object.
(A change in location is a change in the Complete Concept of an object.)

Example:
I call the Spanish House my "home".
When I move to Bogstad next year, the Spanish House doesn't Change.... I change.
One of my properties/propositions/predicates is "home". The current value of "home" is The Spanish House.... but next year, I will change that value to Bogstad.
So my Complete Concept / Individual Substance / Monad is actually changing.

If you actually believe in Space and Time, it is like....
Driving down a highway looking at a map and wondering when you are going to reach the big black dot named Minneapolis.

Space and time are ways we perceive the virtual relation of monads.
Space and time are virtual (illusions).... but well founded illusions based on the the internal properties of the monad.
Like Descartes' "Strong inclination to believe".... Monads project a strong inclination of their spatial and temporal references. (Although Space and Time don't actually exist.)

(draw line on chalkboard). There is no line. There is only an infinite sequence of points. There is no space, just the "location property" of monads relative to other monads. Just like a point could be identified between the 49th and 51st point... the same RELATIVE location is true of monads.

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