A Meinongian/ Goedelian Modal Ontological Argument for God

 ...a  meinongian/goedelian modal ontological argument for God ...John konnor...


1) if exclusive conceivable existence is a Godlikeness property and exclusive existence in the understanding is a Godlikeness property then God's actual existence is not possible


2) if God has all Godlikeness properties then it is not the case that it is not the case that exclusive conceivable existence is a Godlikeness property and God's actual existence is possible


3) God has all Godlikeness properties


4) Necessarily if God has actual existence then necessarily God has actual existence.


5) if God does not have actual existence then it is necessarily possible God does not have actual existence


C) God has actual existence


Let:


□(p⊃q)⊃(◇p⊃◇q). Theorem of K.

p⊃□◇p                     Brouwer Axiom


@G!= God has actual existence

C!= Exclusive conceivable existence is a Godlikeness property

U!= Exclusive existence in the understanding is a Godlikeness property

G*=God has all Godlikeness properties


Proof:


1)C!∧U!⊃~◇@G!

2)G*⊃~(~C!∧◇@G!)

3)G*

4)□(@G!⊃□@G!)

5)~@G!⊃□◇~@G!

6)◇@G!⊃~(C!∧U!)                               (1 DN, Contra)

7)~◇@G!∨~(C!∧U!)                            (6 M. Impl.)

8)~{(C!∨~◇@G!)∧(U!∨~◇@G!)}       (7 Distr.)

9) ~(C!∨~◇@G!)∨~(U!∨~◇@G!)       (8 DeM.)

10) (~C!∧ ◇@G!)∨(~U!∧◇@G!)         (9 DeM.)

11)~(~C!∧ ◇@G!)                                (2,3 MP)

12)(~U!∧◇@G!)                                   (10,11 DS)

13)◇@G!                                               (12 Simp.)

14)□(@G!⊃□@G!)⊃(◇@G!⊃◇□@G)  ( 4 Th. K.)

15)◇@G!⊃◇□@G!                                 (4,14 MP)

16)◇□@G!                                              (13,14 MP)

17)~@G!⊃□◇~@G!                               (5, I. B. Ax.)

18)~@G!⊃~◇~◇~@G!                          (17 ME.)

19)◇□@G!⊃@G!                                  (18 Cont. ME.)

20)@G!                                                  (16,19 MP)

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