## Tough modal logic formalization

Source.

Gamgee wrote:

In the Ontological Argument, Anselm refutes Guanilo’s Perfect Island criticism by stating that God has Aseity. Anselm does not, as far as i know, make any attempt to prove that God has Aseity, or even if Aseity is logically possible.

I argue that it is not, for the following reason:

1) We accept that God does not exist in the physical world.

2) Therefore, there must exist some realm outside of normal time and space (realm x, for conveniency)

3) God exists in realm x

4) Therefore, God requires realm x to exist so that he can exist in it.

5) Without realm x, God would not exist

6) Therefore, God is contingent upon realm x for his existence. Aseity is false.

Any obvious holes in my logic?

Definitions

D:x ≡ things

D:y ≡ things

Ex ≡ x exists

Fxy ≡ x exists in y

Cxy ≡ x in contingent upon y.

a ≡ God

b ≡ non-physical world

c ≡ physical world

Desired conclusion: God is contingent upon the non-physical world.

Desired route: Something to do with worlds.

Version one

1a. Ea

God exists. (Premise)

2a. ¬Fac

God does not exist in the physical world. (Premise)

3a. (∀x)(Ex→(Fxc∨Fxb))

For all x, if x exists, then x exists in the physical world or x exists in the non-physical world. (Premise)

4a. ⊢ Fab (1, 2, 3)

Therefore, God exists in the non-physical world.

5a. (∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex

For all x, if x exists in y and y does not exist, then x does not exist.

6a. ((∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex)→Cxy

If, for all x, for all y, if, if x exists, then x exists in y and y does not exist, then x does not exist, then x is contingent upon y.

7a. ⊢ Cab (5, 6)

Therefore, God is contingent upon the non-physical world.

But 5 is false. It says that if x exist, then x does not exist. I got stuck there. Trying to figure out how to formulate it in some other way to avoid this.

Version two

1b. Ea→Fab

If God exists, then God exists in the non-physical world. (premise)

2b. (∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex

For all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist. (premise)

3b. ((∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex)→Cxy

If for all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist, then x is contingent upon y. (premise)

And here I got stuck. I couldn’t find a way to get to Cxy without assuming ¬Eb.

Version three

1c. ¬Eb→¬Ea

If the non-physical world does not exist, then God does not exist. (Premise)

2c. (∀x)(∀y)(¬Ey→¬Ex)→Cxy

If for all x, for all y, if y does not exist, then x does not exist, then x in contingent upon y. (Premise)

3c. ⊢ Cab (1, 2)

Therefore, God is contingent upon the non-physical world.

This works. Premise two is analytic. Premise one is sometimes true per definition.