Leibniz’s Principles

It just happened.vs.

It happened for a reason.

Case #1First Facts:You approach the outdoor swimming pool in your neighbor’s backyard one morning and find him in the middle of the pool—dead. There’s a large abrasion and bump on his forehead. He’s in his swim suit, and you know he often practices diving each morning. No one else is home, and none of the neighbors heard or saw anything unusual. What kinds of preliminary conclusions can you draw?

Case #1Some more facts:

• The dead neighbor is floating in the water.• The sky is cloudless and has been for two months.• The pool is chlorinated.• There are small puddles of non-chlorinated water

gathered at the side of the pool adjacent to a step down area in the deep end of the pool.

• There is a garden hose coiled nearby.• There is a small ice cube floating in the pool, but no

drinking glass in the pool area.• What additional conclusions might you know draw?• Has foul play been involved?

Case #2First facts:In the upstairs office of a very wealthy businessman lay two people, the businessman and his professional, armed security guard. They are both dead from gunshot wounds.

Case #2Some more facts:

• The business man has been shot twice in chest and is slumped over onto the top of his desk.

• Less than five feet away, the security guard has been shot once in the back, and his body is crumpled under a large picture window that over looks a pond.

• The security guard’s gun is in its hip holster and has not be fired.

• Both bodies are on the opposite of the room from the doorway and are about 20 feet from the door. There is no sign of forced entry.

• What conclusions can you draw about this murder?

Induction vs. DeductionInduction

• Process of drawing conclusions from recognized patterns in observations.

• “Because I have observed sample X, I believe that Y.

• Premises support the conclusion.

• Support indicates degree of probability of the conclusion.

Deduction

• Process of drawing conclusions by applying knowledge/principles.

• “X; therefore, Y.” • “If X, then Y.”

• Premises demonstrate conclusion.

• Premises indicate certainty of conclusion.

Inductive or Deductive?• Every teacher I have at CR this

semester has a beard. There must be a lot of teachers at CR with beards.

• To teach an academic subject at any California community college, a teacher must possess at least a master’s degree in the subject area. Todd Olsen teaches math at CR, so Todd must have at least a master’s in math.

• All quadrilaterals have 4 sides. A square has 4 sides. So a square is a quadrilateral.

• I’ve owned two Dell computers, and both have lasted 8 years without ever failing. Dell makes good computers.

• A good computer is one which never crashes. Dell computers never crash, so Dell computers are good computers.

More Formal Logic

Suppose there are twin sisters; one which always tells the truth and one which always lies.

What single yes/no question could you ask to either sister to figure out which one is which?

Would your sister say you always tell the truth?

Whoever says “no” is the sister who always tells the truth.

Sister A: “No.” (because sister B always lies).

Sister B: “Yes.” (because sister B always lies)

Sister A Sister B“No.” “Yes.”

Necessary Statements (i.e. analytic statements)

A statement is necessary if and only if it is impossible for that statement to be false.

A priori: express knowledge we do not acquire through or verify with experience.

All triangles have three sides.

It is raining or it is not raining.

A married woman has a spouse.

2+2=4.

Contingent Statements (i.e. synthetic statements)

A statement is contingent if it is both possible for that statement to be true and possible for it to be false.

The truth value of the proposition is contingent (dependent) upon the facts of the world.

A posteriori: Contingent statements express knowledge that is acquired through and verified by experience..

It is not raining.

We are at College of the Redwoods right now.

Barack Obama was elected president of the United States in 2008 and in 2012.

The cat is on the mat.

Necessary or Contingent?A cup can contain water.

A cup is 8 ounces.

The cup contains 8 ounces.

A bicycle has two wheels.

A right angle is 90 degrees.

The corner in my room forms a perfect right angle of 90 degrees.

A perfect thing is a thing without flaw.

Descartes’ 1st Argument: Argument from Perfection

A being that doubts is an imperfect being (because a perfect being would have full knowledge, hence no room for doubt).

I doubt; therefore, I am an imperfect being.

Yet I could know that I am imperfect only by having the concept of perfection; therefore, I do have the concept of perfection.

I could not have received the concept of perfection from something imperfect; therefore, my concept was not derived from myself.

Therefore, my concept of perfection was derived from something that is perfect.

Only God is perfect (i.e. God is perfection), so I derived my concept of perfection from him, and therefore, he exists.

Is “Existence” Necessary or Contingent?

Imagine an automobile.

Imagine that the automobile is blue.

Imagine that the blue automobile has four doors and a trunk.

Imagine that this blue, four-door automobile has tinted windows.

Imagine that this blue, four-door automobile with tinted windows exists.

How does existence function as a quality?

Descartes’ 2nd Argument: The Ontological Argument (ala Anselm of Canterbury 1033-1109 )God, by definition, is that being that is absolutely perfect.

It is more perfect to exist than to not exist.

Therefore, to conceive of God (i.e. to conceive of a being that is absolutely perfect) is to conceive of him as existing (because to conceive of God as not existing is self-cancelling).

Therefore, to say “God does not exist” is to contradict oneself.

Therefore, the sentence, “God exists” is necessarily true.

Leibniz’s Principle #1: Principle of Identity

All bachelors are men.

2+3=5.

Either A or not-A.

The cat is on the mat. Obama is president of the US. Leibniz is dead.

Leibniz’s Big Move: Sub Specie Aeternitatis (consider it from Gods’ point of view)

If God is omniscient, omnipotent, omnipresent, and perfect and if God has a plan, then synthetic propositions are necessarily true from God’s point of view.

Leibniz’s Principle #2: Principle of Sufficient Reason

Anything that exists exists for a reason and exists as it does for a reason.

God saw all possibilities at the moment of creation and chose what and how to create.

God makes no mistakes and leaves nothing to chance.

The sky is blue because God made it that way.

John is talking to his philosophy class about Leibniz right now because God made the world in a way that requires John to be talking to the philosophy class about Leibniz right now.

What does this mean?

Just as “2+3=5” is necessarily true, so is “Obama is president of the US.”

It can’t be any other way.

The cat is on the mat…..and IT HAS TO BE.

Leibniz’s Principle #3: Principle of Internal Harmony

An omnibenevolent God wants….

Maximum existence (Metaphysical Perfection).

Maximum Activity (Moral Perfection).

So God considered all possibilities and arranged the individual parts of his creation to harmonize to the greatest extent possible.

Aspects of the world may appear imperfect to us, but the possible worlds God rejected were worse.

“Hence the world is not only the most admirable machine, but in so far as it consists of minds, it is also the best Republic, that in which the minds are granted the greatest possible happiness and joy.”