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):
- Q = not-p
- If possibly Q, then necessarily possibly Q
- If possibly not-p, then necessarily possibly not-p
- If possibly not-p, then not-possibly not-possibly not-p
- If not-not-possibly not-possibly not-p, then not-possibly not-p
- If possibly not-possibly not-p, then not-possibly not-p
- If possibly necessarily p, then necessarily p
- 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 “If there 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:
- It is possible that God [a perfect being] exists
- If God exists, God exists necessarily
- If possibly A, then A (proof above)
- 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.
Dr. Rasmussen’s proof, along with definition of terms, explanations, and defense, can be found here: http://joshualrasmussen.com/s5/