An Intensional Anselmian Ontological Argument

 ...the intensional ontological argument...john konnor...


1) for all x if x exists exclusively definitionally then x admits of more ontological greatness


2) if God does not exist exclusively definitionally then God exists in reality


c) God exists in reality


let:


r= ontological operator for status in reality

ə=limiting ontological exclusivity operator

E!x= x exists

D!x= x exists definitionally

Gx= x admits of more ontological greatness


g=(℩x)~Gx


proof:


1) (∀x)əD!x⊃Gx                                     p

2) ~əD!g⊃rE!g                                         p

3) əD!g                                                      AIP

4) əD!g⊃Gg                                             1 UI

5) Gg                                                         3,4 MP

6) (∃x){(~Gx∧∀y(~Gy⊃x=y))∧Gx}   5TD

7) (~Ga∧∀y(~Gy⊃a=y))∧Ga              6 EI

8) (∀y(~Gy⊃a=y)∧~Ga)∧Ga               7 comm

9)  ∀y(~Gy⊃a=y)∧(~Ga∧Ga)              8 assoc

10)(~Ga∧Ga)                                           9 simp

11) ~əD!g                                                  3-10 IP

12) rE!g                                                      2,11 MP

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