Monthly Archives: May 2011

Plantinga’s Ontological Argument

Things have been pretty crazy lately and so I have been forced to slow my posting while I try to meet some deadlines. However, I thought I would start a series on the Ontological Argument as it is of interest to me.

Here is Plantinga’s version of the argument as laid out by R.E. Maydole (The Blackwell Companion to Natural Theology 2009, 590):

Ax =df x is maximally great
Bx =df x is maximally excellent
W(Y) =df Y is a universal property
Ox =df x is omniscient, omnipotent, and morally perfect


1. ◊(∃x)Ax                                      pr                           
2. □(x)(Ax ≡ □Bx)                               pr
3. □(x)(Bx ⊃ Ox)                                pr
4. (Y)[W(Y)≡(□(∃x)Yx ∨(□~(∃x)Yx)]              pr
5. (Y)[∃(Z)□(x)(Yx ≡ □Zx)⊃ W(Y)]               pr
6. (∃Z)□(x)(Ax ≡ □Zx)                          2,EG
7. [(∃Z)□(x)(Ax ≡ □Zx) ⊃ W(A)]                5,UI
8. W(A)≡(□(∃x)Ax ∨(□~(∃x)Ax)                 4,UI
9. W(A)                                         6,7 MP
10. W(A)⊃(□(∃x)Ax) ∨ (□~(∃x)Ax)               8,Equiv, Simp
11*. □(∃x)Ax ∨ □~(∃x)Ax                     9,10 MP
12. ~◊~~(∃x)Ax ∨ □(∃x)Ax                     11,Com, ME
13. ◊(∃x)Ax ⊃ □(∃x)Ax                         DN, Impl
14. □(∃x)Ax                                    1,13 MP
15. □(x)(Ax ≡ □Bx) ⊃ (□(∃x)Ax ⊃ □(∃x)□Bx)    theorem
16. □(∃x)□Bx                                   14,15 MP (twice)
17. □(x)(Bx ⊃ Ox) ⊃ (□(∃x)□Bx ⊃ □(∃x)□Ox)    theorem
18. □(∃x)□Ox                                   16,17 MP (twice)
19. (∃x)□Ox                                    18,NE

*Premise 11 seemed to contain an error. I added the disjunctive symbol as it was missing from Maydole’s account.

So, the argument is valid. The question is with the premises. Most take issue with premise 1, that it is possible that there exists something that is maximally great. One response that I have heard is that while the burden of proof is on the person making the positive assertion, in the cases of probability, the benefit of the doubt sides with the person supposing possibilities. In other words, one must provide me with good reasons to suppose some proposition could not obtain in any possible world. How would one do this in this case? Any thoughts?

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