Anselm's Dictum Modalized

 ...modal ontological argument from Anselm's dictum/ principle...John konnor...

1) if it is not necessarily the case that God exists then it is necessarily not necessarily the case God exists ( instance of Anselm's dictum)

2) if necessarily it is not the case that necessarily God exists then necessarily God does not exist ( premise)

3)it is possibly the case God exists( premise)

C) God exists

Let:

G!= God exists

□p⊃p (Axiom M)

Proof:

1)~□G!⊃□~□G!          ( I. of A.D.)

2)□~□G!⊃□~G!          ( Premise)

3)◇G!                            ( Premise)

4)~□G!⊃□~G!             (1,2 HS)

5)□G!∨□~G!                (4 M. Impl., DN)

6)~□~G!                       (3 ME)

7)□G!                             (5,6 DS)

8)□G!⊃G!                      ( Axiom M)

9)G!                                (7,8 MP)