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?

Posted on May 4, 2011, in Arguments for God and tagged , , , , , . Bookmark the permalink. 5 Comments.

  1. numbers 1 through 19 look suspicious. i'm not familiar with these symbols. i though the ontological argument involved words.



  2. heh… Words only muddy things. Here is the original argument as given by Plantinga… It actually starts around proposition 29.


  3. By the way, you should consider weakening the inner iff in (3) to just material implication. Plantinga only uses the claim that if Ax, then necessarily Bx, not the equivalence claim.


  4. Dr. Pruss,

    Thanks for the comment! You are correct on this point. Plantinga writes:

    “(30) Necessarily, a being is maximally great only if it has maximal excellence in every world.”

    Maydole put this as an equivalence in (2), which I think makes sense, but may be a stronger claim can be justified by the text.

    The best argument I could give for its use is that (30) is described by Plantinga as an analogue to (27). Plantinga writes elsewhere:

    “Indeed, if we regard (27) and (28) as consequences of a definition — a definition of maximal greatness — then the only premise of the argument is (25).”

    Perhaps Maydole could justify his use of equivalence on the grounds that Plantinga’s (27), though stated as material implication, is later said to be a definitional premise. If the analogy holds, then Plantinga’s (30) is also definitional and the use of equivalence could be explained by that fact. Then again, Maydole doesn’t follow the same rule when deriving premise (3). There he is content to use material implication! So if this is his justification, he is inconsistent in its application.

    Best Regards,



  5. Dan,

    That's interesting.

    I think in the best form of this sort of argument, it's not definitional. Rather, it's a substantive claim about maximal greatness. This means makes the possibility premise even less question-begging.

    So I'd press on the fact that Plantinga says “if we regard…”.


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