Ontological Arguments

Deductive arguments

Those in which the premises are supposed to guarantee the conclusion. 

Inductive arguments

Those in which the premises are supposed to support (but not guarantee) the conclusion.

Valid arguments

Applied to deductive arguments where the premises do guarantee the conclusion. 

Sound arguments

Applied to deductive arguments that are valid and have true premises.

Strong arguments

Applied to inductive arguments that are strong and have true premises.

Cogent arguments

Applied to inductive arguments that are strong and have true premises. 

Anselm's ontological argument  

• P1. God is defined as that than which nothing greater can be conceived.  

• P2. A being could exist either just in understanding or in both understanding and reality.  

• P3. It is greater to exist in understanding and in reality than in the understanding alone.  

• C1. Therefore, God must exist in reality as well as in the understanding.  

Descartes' ontological argument 

• P1. I have the clear and distinct idea of God.  

• P2. The idea of God is the idea of a supremely perfect being.,  

• P3. A supremely perfect being does not lack any perfection.  

• P4. Existence is a perfection.  

• C1. Therefore, God has to exist.

What Descartes’ ontological argument relies on

The theory of innate ideas and the doctrine of clear and distinct perception. 

Malcolm's ontological argument 

• P1: Either God exists or God does not exist. 

• P2: God cannot come into existence or go out of existence. 

• P3: If God exists, God cannot cease to exist. 

• C1: Therefore, if God exists, God's existence is necessary. 

• P4: If God does not exist, God cannot come into existence. 

• C2: Therefore, if God does not exist, God's existence is impossible. 

• C3: Therefore God's existence is either necessary or impossible. 

• P5: God's existence is impossible only if the concept of God is self-contradictory. 

• P6: The concept of God is not self-contradictory. 

• C4: Therefore, God's existence is not impossible. 

• C5: Therefore, God exists necessarily.

The four options of God’s existence (Malcolm)

God’s existence is necessarily false, contingently false, contingently true or necessarily true.

Gaunilo's 'perfect island' objection 

• P1. The concept of a supremely excellent island can be understood without difficulty.   

• P2. Claiming its existence based solely on its conceptual excellence is flawed.  

• P3. If it does not exist, then any real land would be more excellent, contradicting the original claim.  

• P4. Accepting such reasoning would be foolish without proof of real existence.  

• C1. One must first demonstrate that the island’s excellence is a real and indubitable fact, not merely conceptual. 

Reductio ad absurdum

Showing an argument must be false because of absurdities that result if followed. 

Why God’s existence cannot be necessary (Hume)

Because we can coherently conceive of God not existing without contradiction.

Hume’s Fork vs Ontological arguments

Hume argues that no matter of existence can be established by pure reason; all existence claims are synthetic and matters of fact.

Why existence is not a predicate

Adding “existence” to a concept does not guarantee a being exists in reality, just as defining a unicorn with existence doesn’t produce real unicorns.

Why God’s existence is not analytically necessary

We can conceive of God not existing without contradiction in it’s concept, so God’s existence cannot be analytically necessary (unlike “a triangle has three sides”).