An Anselmian/Cartesian Argument from Perfection

 ...Anselmian/ Cartesian ontological argument from perfection ...John Konnor...


1) exists a y for all x if y does not exist or x can doubt the existence of y then it is possible x exceeds y in ontological perfection


C) God exists


Let:


DxE!y= x can doubt the existence of y

E!x= x has existence

Pxy= x exceeds y in ontological perfection


g=i(y)~◇(∃x)Pxy


Proof:


1)(∃y)(∀x)~E!y∨DxE!y⊃◇Pxy.                 P

2)(∃y)(∀x)~E!y∨DxE!y.                             AIP

3)~E!g∨DaE!g.                                          2, EI, UI

4)~E!g∨DaE!g⊃◇Pag.                             1,EI,UI

5)◇Pag.                                                      3,4 MP

6)◇(∃x)Pxg.                                                5 EG

7)(∃y)((~◇(∃x)Pxy∧(∀z)(~◇Pxz⊃y=z))∧◇(∃x)Pxy).                            6 TD

8)((~◇(∃x)Pxb∧(∀z)(~◇Pxz⊃b=z))∧◇(∃x)Pxb) 

                                                                      7 EI

9)((∀z)(~◇Pxz⊃b=z)∧~◇(∃x)Pxb)∧◇(∃x)Pxb) 

                                                                      8 Comm.

10)(∀z)(~◇Pxz⊃b=z)∧(~◇(∃x)Pxb)∧◇(∃x)Pxb)

                                                                      9 Assoc.

11)(~◇(∃x)Pxb)∧◇(∃x)Pxb).                    10. Simp.

12)(∃y)(∀x)~(~E!y∨DxE!y).                       2-11 IP

13) ~(~E!g∨DaE!g).                                    12, EI,UI

14)E!g∧~DaE!g.                                           13 DeM.

15)E!g.                                                           14 Simp.

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