Modal Ontological Argument

 ...modal ontological argument...John konnor...


1) necessarily if God does not exist then it is necessarily the case God does not exist


2) God's existence is possible


C) Necessarily God exists


Let:


G!= God exists

□(p⊃q)⊃(◇p⊃◇q).  Theorem of K.

◇p⊃□◇p.                  Ax. 5


Proof:


1)□(~G!⊃□~G!).                             p

2)◇G!                                                p

3)□(~G!⊃□~G!)⊃(◇~G!⊃◇□~G!)    Theorem of K.

4)(◇~G!⊃◇□~G!)                           (1,3 MP)

5)~◇□~G!⊃~◇~G!                        4 Contra.

6)~◇~◇~~G!⊃~◇~G!                  5 M.E.

7)□◇G!⊃□G!                                   6 M.E., D.N.

8)◇G!⊃□◇G!                                   Ax.5

9)□◇G!                                            (2,8 MP)

10)□G!                                             (7,9 MP)

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