Ontological Argument Improved Again

Let,

Rx ≝ x exists in re
Ix ≝ x exists in intellectu
Gx ≝ x admits of more greatness
G[Px,~Px] ≝ x having P is greater than x not having P
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…

g ≝ (ɿx)(~©Gx ∧ ~©(∃y)Gyx)

1. (∀x)[(Ix ∧ ~Rx) ⊃ ©Rx] (premise)
2. (∀x)G[Rx,~Rx] (premise)
3. (∀x){[[~Rx ∧ G] ∧ ©Rx] ⊃ ©Gx}(premise)
4. Ig (premise)
5. ~Rg (IP)
6. Ig ∧ ~Rg (4,5 Conj)
7. (Ig ∧ ~Rg) ⊃ ©Rg (1 UI)
8. ©Rg (6,7 MP)
9. G[Rg,~Rg] (2 UI)
10. ~Rg ∧ G[Rg,~Rg] (5,9 Conj)
11. [~Rg ∧ G[Rg,~Rg]] ∧ ©Rg (8,10 Conj)
12. {[~Rg ∧ G[Rg,~Rg]] ∧ ©Rg} ⊃ ©Gg (3 UI)
13. ©Gg (11,12 MP)
14. (∃x){{[~©Gx ∧ ~©(∃y)Gyx] ∧ (∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = x)]}} ∧ ©Gx} (13 theory of descriptions)
15. {[~©Gμ ∧ ~©(∃y)Gyμ] ∧ (∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]}} ∧ ©Gμ (14 EI)
16. {(∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ [~©Gμ ∧ ~©(∃y)Gyμ]} ∧ ©Gμ (15 Comm)
17. {(∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ [~©(∃y)Gyμ ∧ ~©Gμ]} ∧ ©Gμ (16 Comm)
18. {(∀z){[[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ ~©(∃y)Gyμ] ∧ ~©Gμ} ∧ ©Gμ (17 Assoc)
19. (∀z){[[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ ~©(∃y)Gyμ] ∧ {~©Gμ ∧ ©Gμ} (18 Assoc)
20. ~©Gμ ∧ ©Gμ (19 Simp)
21. ~~Rg (5-20 IP)
22. Rg (21 DN)

Posted on April 9, 2017, in Arguments for God and tagged . Bookmark the permalink. 1 Comment.