A Thomistic Ontological Argument

 ...the thomistic ontological argument...john konnor...


axiom 1


whatever is pure act is complete

(∀x) Ax⊃Cx


axiom 2


whatever is complete is existence by essence

(∀x) Cx⊃(∃¥)[(¥=E) & (Ex)]


1. for all x if x is understood x is in potency to act or pure act


2. God is understood


3. God is not in potency to act


c. God exists


let:


Ax=x is pure act

Cx=x is complete

Px=x is in potency to act

Ux=x is understood

¥=is an essence

E= is existence


g=(℩x)(∃¥)[(¥=E) & (Ex)] 


proof:


1.  (∀x)Ux⊃ (Px ∨ Ax)         premise

2.   Ug.                                      premise

3.  ~Pg                                     premise

4.   Ug⊃ (Pg ∨ Ag)                1 UI

5.   Pg ∨ Ag.                            2,4 MP

6.   Ag.                                      3,5 DS

7.   Ag ⊃ Cg.                             Ax1. UI

8.   Cg.                                       6,7 MP

9. Cg⊃[(¥=E) & (Eg).              Ax 2 EI, UI

10. [(¥=E) & (Eg)]                   8,9 MP

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