A Modal Ontological Argument

 ...modal ontological argument...John Konnor...


1) if it is not necessarily the case God exists then it is necessarily not necessarily the case God exists


2) necessarily if God exists then it is necessarily the case God exists


3) it is possibly the case God exists


C) God exists of necessity


Let:


G!= God exists

□(p⊃q)⊃(◇p⊃◇q). Theorem of K.


Proof:


1)~□G!⊃□~□G!

2)□(G!⊃□G!)

3)◇G!

4)~□~□G!⊃~~□G!                    (1, Contra.)

5)◇□G!⊃□G!                               (4, ME, DN)

6)□(G!⊃□G!)⊃(◇G!⊃◇□G!).     (2, Theorem)

7)◇G!⊃◇□G!                               (2,6 MP)

8)◇G⊃□G!                                   (5,7 HS)

9)□G!                                            (3,8 MP)

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