Another Ontological Argument

In a post last week, we looked at three traditional ontological arguments, and why I think Saint Thomas Aquinas’ essential response works to show that all three are ultimately unsuccessful. In response, philosopher Josh Rasmussen referenced me to a modal proof he’s formulated which, if correct, shows that we can deduce that something is actual from its mere possibility. The implications, then, are that the “if, then” objection I offered against specifically Plantinga’s ontological argument is overcome, and the argument otherwise stands.

Here’s the proof (where A = necessarily p):

  1. Q = not-p
  2. If possibly Q, then necessarily possibly Q
  3. If possibly not-p, then necessarily possibly not-p
  4. If possibly not-p, then not-possibly not-possibly not-p
  5. If not-not-possibly not-possibly not-p, then not-possibly not-p
  6. If possibly not-possibly not-p, then not-possibly not-p
  7. If possibly necessarily p, then necessarily p
  8. If possibly A, then A

This is a lot, especially for those unfamiliar with modal logic, so we’ll try to break it down here. In this proof, Rasmussen uses possibility to mean “consistent with reason,” akin to logical possibility. As such, something is impossible if it is not consistent with reason. Furthermore, he uses necessary to mean impossibility of negation. If x is necessary, then the negation of x is impossible.

The first premise defines Q as the negation of p. Premise two states that if Q is possible, then Q is necessarily possible. This makes sense given what “possibility” is taken as here. If something is logically possible, then it cannot ever be logically impossible, and hence is necessarily logically possible. Premise three restates the second premise but replaces Q with “not-p”.

Premise four follows from the definition of necessity used here. If not-p is necessarily possible, then the impossibility of not-p is not possible. Premise five uses the rule of inference known as “contraposition.” Contraposition can be outlined as follows: if it is the case that if Y, then Z, then it is also the case that if not-X, then not-Y. Premise five is the contrapositive of premise four. Premise four states that if it is the case that if possibly not-p (Y) then not possibly not possibly not-p (X), then it is also the case that if not not possibly not possibly not-p (not-X), then not possibly not-p (not-Y).

Premise six uses the rule of double negation to clean up the antecedent of premise five a bit. Saying “not not possibly not possibly not-p” is logically equivalent to saying “possibly not-possibly not-p.” The consequents are the same in both premises.

Notice that “not possibly not-p” is the same as “the negation of p is impossible,” which means, per the definition, that p is necessary. So premise seven restates premise six in terms of necessity. If possibly necessarily p, then necessarily p. Since A is defined as necessarily p, the conclusion is that if possibly A, actually A.

The proof is logically valid, and we can see its implications for a Plantinga-style ontological argument: if God is defined as a necessarily existent being, then — given the conclusion of the present proof — if God’s existence is possible, God actually exists.

But I’m not completely convinced that the present proof helps such an ontological argument escape the kind of objection I’ve offered. I don’t think that establishing that something is actually necessary is enough to establish that it actually necessarily exists.

Here’s what I mean. As Dr. Rasmussen defines it, A is the hypothesis that necessarily p. Let’s use an example: Let A be the hypothesis that necessarily a triangle has three angles. Given the proof, if it is possible that a triangle necessarily has three angles, then it is in fact the case that a triangle necessarily has three angles. Since this seems obviously possible, it follows that triangles do in fact necessarily have three angles. In other words, it is impossible for a triangle to not have three angles. And this is something that we know to be true.

But from the fact that triangles necessarily have three angles, it does not follow that there exists in actuality any real triangles. All the triangles in the world could be destroyed, and it would still be a true statement that triangles necessarily have three angles. To say “triangles necessarily have three angles” is to say “Ithere are actually any triangles, they will actually have three angles.”

One might respond that the case of God is different, because the property God is said to have necessarily is existence; and doesn’t anything that necessarily have existence, exist? Dr. Rasmussen puts the argument this way:

  1. It is possible that God [a perfect being] exists
  2. If God exists, God exists necessarily
  3. If possibly A, then A (proof above)
  4. Therefore, God exists necessarily

Dr. Rasmussen takes A to be “necessarily God exists,” such that if it is possible that God necessarily exists, God actually necessarily exists. But I think the confusion results from the way we have worded things. To say “God exists necessarily” makes it seem that God exists in reality. But if we word it, “If God exists, God has necessary existence,” things are a bit different. Just as the statement “Triangles have three angles necessarily” tells us about the definitional content of the concept of triangles, and not necessarily whether this concept corresponds to any actually existing things; so too the statement “God has necessary existence” tells us something about the definitional content of the concept of God, but not necessarily whether this concept corresponds to anything actually existing. In other words, the concept of God is the concept of a being which has necessary existence; but knowing this does not tell us whether or not that being actually exists.

Sources

Dr. Rasmussen’s proof, along with definition of terms, explanations, and defense, can be found here: http://joshualrasmussen.com/s5/

18 thoughts on “Another Ontological Argument

  1. “the concept of God is the concept of a being which has necessary existence; but knowing this does not tell us whether or not that being actually exists.”

    Exactly! Whenever I ask for proof or evidence, I am always given arguments for god such as this. The theist and I hash it out over several hours or in some cases, days, lol. The end result is, they are no closer to proving a god… much less their own.

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    1. It’s kind of odd that your entire interactive experience with theists has been with those who defend the ontological argument. The Thomistic arguments (as Harrison states) from motion and contingency are very good.

      I have a question for you. Why do some atheists insist on spelling God with a lower-case G? Atheists like Michael Martin never did that because they recognize that the theistic term God is a proper noun and as such, should be capitalized. It’s a proper noun because people overwhelmingly use the term God as a name. It represents, correctly or incorrectly, a being which is known most commonly by that label. Hence, it is proper to capitalize it.

      English Grammar 101:

      The names of gods and goddesses are capitalized. The Judeo-Christian god is named God, since they believe He is the only one. Believers also capitalize pronouns (like he and him) when referring to God. “God” is only capitalized when being used as a name. The Muslim name Allah is a translation of the name God. When referring to Greek, Roman, and other groups of gods and goddesses, only the name is capitalized.

      God, Allah
      Greek god Zeus, Egyptian goddess Isis

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      1. My “correctly or incorrectly” are the wrong words. I should have written, It represents, whether He really exists or doesn’t exist, a being known most commonly by that label.

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      2. I don’t insist that people capitalize pronouns relative to God. That’s merely my preference to show extra respect.

        You’re not speaking generically when you refer to God. Were you to say something like, “I don’t need a god to tell me the difference between right or wrong,” you’d be speaking generically. But if you said, “I don’t need God to tell me the difference…,” you’re NOT speaking generically; you’re referring to a particular god.

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      3. “I am always given arguments for god such as this. The theist and I hash it out over several hours or in some cases, days, lol. The end result is, they are no closer to proving a god… much less their own.”

        Looks like I was referring a generic god. The blog was an argument for a gods existence.

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      4. Sigh. When you say, “I am always given arguments for god…,” you’re not referring to a generic god; you’re referring to a particular god. It’s no different than saying, “I am always given arguments for Zeus such as this.” You don’t use a lowercase ‘z’ for Zeus, and you don’t use a lowercase ‘g’ either. As stated, in that context, “God” is a proper noun and should be capitalized.

        Your second example of using the lowercase ‘g’ is proper because you said “a god.” In that instance, you are being generic due to your use of the indefinite article.

        If you’re that insistent on denying standard grammar, it’s no wonder no substantive dialog can be had with you. As I said, intelligent atheists like Michael Martin never used a lowercase ‘g’ when referring to God.

        Anyway, I don’t want to fill up Harrison’s blog with grammar lessons.

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      5. I sea know wear in his blog post in witch… he mentioned which god, just an ontological argument.

        “The end result is, they are no closer to proving a god… much less their own”

        I’m not sure how much more generic one can get between the argument and my comment. The words He and Him don’t get capitalized but you insist on doing that despite standard grammar.

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      6. But you said, “Whenever I ask for proof or evidence, I am always given arguments for god such as this.” Where I come from, “always” means: every time, on every occasion, without exception.

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      7. And “such as” means “similar to.” There are several versions of the OA. Look, I now get it that your debates haven’t been restricted to the OA, but that’s not what you said.

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  2. Well, you are certainly right that there are substitutions for A where you don’t get an interesting result. But let A be the hypothesis that necessarily, there *actually exists* an x, such that x is God. The proof goes through just the same. It establishes that if A is possibly true, then God actually exists.

    Sure, it may seem initially surprising that a concept’s possible application to reality could imply that the concept actually applies to reality. But that’s one of the important discoveries of twentieth-century modal logic. Keep in mind that the possibility claim in question is substantial, and as I point out, there is still the problem of reverse arguments.

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