St. Anselm's Arguments

First Argument

1. The fool understands something greater than which cannot be thought (SGTWCB). (Premise)
2. If x understands S, then S exists in x's thought. (Premise)
3. SGTWCB exists in the fool's thought. (By (1) and (2))
4. If SGTWCB exists in someone's thought and in reality, it is greater than if it exists only in someone's thought. (Premise)
5. If SGTWCB exists only in someone's thought, then something greater can be thought than SGTWCB. (By (4))
6. It is impossible that something greater be thought than SGTWCB. (Premise)
7. Therefore, it is false that SGTWCB exists only in someone's thought. (By (5) and (6).)
8. Things cannot exist in anything other than thought and reality. (Implicit premise)
9. Therefore, SGTWCB exists in reality. (By (3), (7) and (8).)

Validity?

• The derivation of (5) from (4) is iffy. It depends not just on the truth of (4) but also on the fact that we understand the antecedent of (4).

Second Argument

1. If SGTWCB can be thought of as not existing, it is not greater than that which cannot be thought. (Premise)
2. SGTWCB is greater than everything else. (Implicit premise)
3. SGTWCB cannot be thought of as not existing. (By (1) and (2).)

Third Argument

1. If x can be thought of as existing but doesn't exist, then x can be thought of as having a beginning. (Premise)
2. But SGTWCB cannot be thought of as having a beginning. (Premise)
3. SGTWCB can be thought of as existing. (Premise)
4. Therefore, SGTWCB exists. (By (1)-(3))