The Fallacies of Faith

Kant's second objection to Anselm's ontological argument still applies to Plantinga's MOA. Some theists claimed that it does not because, supposedly, "Plantinga does not take existence to be a property that is or is not imputed to God." Yet Plantinga said that God's essence "entails the property exist in every possible world." [1]Note 1. Alvin Plantinga, The Nature of Necessity p. 214, PDF p. 141; emphasis Plantinga's. He explicitly called existence a property — not merely existence in the actual world, but in every other possible world too! Plantinga's MOA is not "Kant-proof" simply because it introduced a redundant middle term ("maximally great") while imputing the so-called property of existence to God. Instead, it repeated Anselm's error that Kant exposed."

Plantinga's MOA also presupposes transworld identity. Every part of the following sentence entailed by Plantinga's MOA is highly controversial: "Multiple possible worlds exists which contain the same individual who has the essential property of maximal greatness." Existing in multiple possible worlds (transworld identity) presupposes modal essentialism and the meaningful coherence of possible worlds semantics. The latter presupposes the meaningful coherence of quantified modal logic. All arguments against those presuppositions described earlier in this document are arguments against Plantinga's MOA. Since those arguments refute at least one of the four presuppositions, they refute Plantinga's MOA. Since this document has shown earlier that modal essentialism presupposes universal essentialism, Plantinga's MOA presupposes Aristotelian/universal essentialism, and all of the problems that come with it.

Adam Lee of Daylight Atheism formalized another objection to Plantinga's MOA, which is compelling despite its simplicity and applies even using possible worlds semantics and assuming modal essentialism:

1. There is a possible world in which there is no entity that possesses maximal greatness.
2. Therefore, there is no entity that possesses maximal greatness.
3. Therefore, God does not exist.

One can imagine a possible world in which the only existing entity is a rock, or a single particle, or a mereological simple. If such a world is possible, then it does not contain a maximally great being. Yet the maximally great being is defined to exist in all possible world. If it fails to exist in one possible world, that contradicts its definition and it therefore exists in none.

Dr. Craig objected by questioning that such a world is metaphysically possible. He denied that conceivability entails possibility: according to Craig, one cannot call a world possible just because it is imaginable. As a counterexample to the metaphysical possibility of such worlds, "Leibniz’s cosmological argument would imply that a world consisting of a single particle is metaphysically impossible, since there is, then, no explanation of why the particle exists rather than nothing." Craig's objections fail on two counts.

First, they conflate logical and metaphysical possibility. Arguments for Plantinga's MOA almost always try to justify premise (1) with logical possibility. One theist tried to justify it by claiming that "[i]t contains no logical contradiction of the sort, 'married bachelor,' or 'square circle.'" But the same is true of the following statements: "only a rock exists," "only a single particle exists," "only a mereological simple exists," and "nothing exists." Similarly, Craig claimed that "for the ontological argument to fail, the concept of a maximally great being must be incoherent, like the concept of a married bachelor … [but] the concept of a maximally great being does not seem even remotely incoherent." [2]Note 2. Craig, Reasonable Faith p. 185. Oddly, Craig said in the same place that "[t]he concept of a married bachelor is not a strictly self-contradictory concept (as is the concept of a married unmarried man), and yet it is obvious, once one understands the meaning of the words 'married' and 'bachelor,' that nothing corresponding to that concept can exist." But since "bachelor" means "unmarried man," "married bachelor" is a contradiction. And since "cohere with" is the negation of "contradict," "incoherent" means "contradictory." I think the most charitable interpretation of Craig here is that "married bachelor" is a contradiction, but not an obvious one. If logical possibility makes God's existence possible, it also makes worlds with only a rock or a particle possible precisely because they can be imagined. Since "whatever is intelligible, and can be distinctly conceived, implies no contradiction," []Note . Hume, An Enquiry Concerning Human Understanding 4:2, PDF p. 26. no one can imagine a contradiction. So those worlds entail no contradictions, making them logically possible. But if those possible worlds exist without God, then there is no maximally great being which exists in all possible worlds.

Second, Leibniz's cosmological argument assumes that there could have been nothing, as shown in its section of this document. If it was impossible for nothing to exist, that would explain why there is something rather than nothing. However, if it is possible that nothing exists, then there is some possible world in which nothing exists. In that possible world, God does not exist, because God is something. Therefore, Leibniz's cosmological argument contradicts Plantinga's MOA. Either it is possible for nothing to exist, or it isn't. If it is, then God does not exist in some possible world. If it isn't, then that impossibility explains why there is something rather than nothing.

One may object that God's existence explains why it is impossible for nothing to exist. Yet this objection simply rejects Leibniz's argument in favor of Plantinga's. Leibniz invoked God to explain that something exists given the fact that it could have been the case that nothing exists. Given Plantinga's MOA, that is not a fact, and therefore needs no explanation.

First, consider Adam Lee's poor objection to Plantinga's MOA:

"Possible worlds, by the definition of what it means to be a possible world, are completely disjoint; they cannot influence each other in any way. (If two possible worlds could affect each other, they would not be separate possible worlds, but the same possible world, again by definition.) Therefore, it is invalid to define something such that its existence in one possible world 'causes' it to exist in another possible world."

"Influence" here conflates epistemology with metaphysics. Plantinga argued from our knowledge of a possible world to our knowledge of all possible worlds, instead of arguing for any metaphysical causal influence between worlds. The objection is simply a misunderstanding.

A more central objection to the MOA seems to emerge when one views it translated out of possible worlds semantics:

1. A maximally great being possibly exists.
2. If a maximally great being possibly exists, then it necessarily exists.
3. If a maximally great being necessarily exists, then it actually exists.
4. Therefore, a maximally great being actually exists.

The argument above is far simpler than its possible-worlds form, but leaves questions. One may wonder what "maximally great" means, and may not see the justification for step 2. These questions can be answered by taking the meaning of "maximally great being" into account, again translated out of possible-worlds semantics.

A maximally great being is defined as a being which exists in all possible worlds. Ignoring Kant's refutation, outside of possible-worlds semantics a maximally great being is defined as a being that exists necessarily. The proposition that a maximally great being exists entails the proposition that such a being exists necessarily. With that in mind, let's translate the MOA again by replacing the phrase "maximally great being."

1. Some being (B) possibly necessarily exists.
2. If a being possibly necessarily exists, then it necessarily exists.
3. If a being necessarily exists, then it actually exists.
4. Therefore, B actually exists.

The problem is how to make sense of premise 1, the proposition that a being possibly necessarily exists. Since a necessarily true proposition cannot be false, it makes no sense to say that a proposition is possibly necessarily true. Either a proposition is necessarily true or it isn't. If a proposition is necessarily true, then it is impossible for it to be false. If a proposition is not necessarily true, then it could have been false, so it is impossible for it to be necessarily true.

It may seem that a proposition can be "possibly necessarily true" because one can often reasonably reply "maybe" to the question, "Is X necessarily true?" Yet that conflates metaphysical and epistemic possibility. If X is epistemically possible, then we do not know that X is true and we do not know that X is false. If X is epistemically impossible, we know that X is false.

Consider the Goldbach conjecture. If the Goldbach conjecture is true then it is a logically (and therefore metaphysically) necessary truth, because mathematical truths cannot be false. 1+1 is always 2, and it is impossible for 1+1 to be anything else. However, it is still epistemically possible that the Goldbach conjecture is false because we do not know that it is true. Conversely, if the Goldbach conjecture is false then it is metaphysically necessarily false, but it is still epistemically possible for the Goldbach conjecture to be true. Epistemic possibility is irrelevant to the current discussion.

In short, no proposition is "possibly necessarily true" unless the proposition is necessarily true. If a proposition (P) seems "possibly necessarily true" to someone, that only means that the person does not know that P is false. The person should not confuse their ignorance for "possible necessity." No proposition is possibly necessarily true unless it is necessarily true. If the previous sentence is false, there would be a counterexample – i.e. a statement that is not necessarily true but has the logical possibility of being necessarily true. Such a counterexample cannot exist.

Consider the MOA specifically. If the necessarily-existent being exists then it possibly exists. Conversely, if the necessarily-existent being does not exist then a contradiction follows – the being does and does not necessarily exist – so the being cannot possibly exist. Like the Goldbach conjecture, the proposition that there exists a necessarily-existent being is either necessarily true or necessarily false and cannot be otherwise.

The assertion that a necessarily-existent being possibly exists is logically equivalent to the assertion that it necessarily exists. Since Plantinga's MOA assumes that a necessarily-existent being possibly exists in its first premise, the MOA assumes that a necessarily-existent being necessarily (and therefore actually) exists, assuming its conclusion. The MOA is therefore circular, since few philosophers would be willing to take "a maximally great being necessarily exists" as an assumption. That is what the MOA was trying to prove all along!

Dr. Craig claimed that "[m]ost philosophers would agree that if God’s existence is even possible, then he must exist," [3]Note 3. Craig, Reasonable Faith p. 185. but this is a mere rhetorical trick. What he should have said is that most philosophers agree that if God necessarily exists, then God exists. Even I agree with that much, but it is not particularly helpful as an apologetics argument.

The short version of the argument above is as follows. A being possibly necessarily exists if and only if it necessarily exists. Therefore, premise (1) is logically identical to the question-begging statement, "Some being (B) necessarily exists." Since the latter is question-begging, the former must also be question-begging.

Dr. Craig objected to this demonstration of the MOA's circular logic by invoking the distinction between truth de re and de dicto. If an entity (x) has a property (P) de dicto, then x is a free variable representing anything that is P. If x is P de re, then x only refers to one specific entity that is P. Consider a person named Jim who said that "x is P." If he is right, either "x is such that (Jim said x is P)" (de re), or "Jim said: (x is P)" (de dicto). According to Dr. Craig, premise (1) of Plantinga's MOA uses possibility de dicto and necessity de re. If Craig is correct, then possibly, some being (B) is such that B necessarily exists.

Unfortunately, Dr. Craig did not explain how the "de re vs. de dicto" distinction defeats the question-begging objection. As an attempt at a charitable interpretation, consider this construal. The argument against Plantinga's MOA says that B possibly necessarily exists ⇔ B necessarily exists. But if "necessarily" is used in a different sense in the former versus the latter, then the statements are not identical.

Necessity de re entails necessity de dicto: if B is such that B necessarily exists, then necessarily, B exists. The second statement says that there is an example of a necessarily existent being, and the first provides an example. The first entails the second, so B has necessity de re and de dicto. If something is necessary in some sense, it is possible in that same sense. Necessity de dicto then entails possibility de dicto. In sum, necessity de re ⇒ necessity de dicto ⇒ possibility de dicto. By implication elimination, necessity de re ⇒ possibility de dicto.

Premise (1) of Plantinga's MOA is a conjunction: (B possibly exists de dicto) ∧ (B necessarily exists de re). Call its first proposition P and its second Q. Premise (2) of this MOA is that (P ∧ Q ⇒ R), but the definition of R is not relevant here. The argument which Craig is trying to refute is that (P ∧ Q ⇒ R) ⇔ (Q ⇒ R), but that can be proven directly and explicitly in symbolic logic. [4]Note 4. (P ∧ Q ⇒ R) ⇔ (Q ⇒ R) will be proven here. To prove a biconditional (if and only if) statement, one can prove each of its conditions: ((P ⇒ Q) ∧ (Q ⇒ P)) ⇔ (P ⇔ Q) by biconditional introduction. So, the statement disputed by Craig will be proven by the conjunction of two proofs: first that (Q ⇒ R) ⇒ (P ∧ Q ⇒ R), and second that (P ∧ Q ⇒ R) ⇒ (Q ⇒ R). Each is a direct proof. The first will assume Q ⇒ R and derive that P ∧ Q ⇒ R by logical inference to conclude that (Q ⇒ R) ⇒ (P ∧ Q ⇒ R). Conversely, the second will assume P ∧ Q ⇒ R and derive that Q ⇒ R to conclude that (P ∧ Q ⇒ R) ⇒ (Q ⇒ R). Here is the first:

1. Q ⇒ R by assumption.
2. P ∧ Q ⇒ Q by conjunction elimination.
3. ∴ P ∧ Q ⇒ Q ⇒ R by conjunction of 1 and 2.
4. ∴ P ∧ Q ⇒ R by implication elimination of 3.
5. ∴ (Q ⇒ R) ⇒ (P ∧ Q ⇒ R) by direct proof.

And here is the second:

1. P ∧ Q ⇒ R by assumption.
2. Q ⇒ P (necessity de re ⇒ possibility de dicto, as shown above).
3. Q ⇒ P ∧ Q by absorption from 2.
4. Q ⇒ P ∧ Q ⇒ R by conjunction of 1 and 3.
5. ∴ Q ⇒ R by implication elimination of 4.
6. ∴ (P ∧ Q ⇒ R) ⇒ (Q ⇒ R) by direct proof.

So premise (1) of Plantinga's MOA is identical to the statement that God necessarily exists, which no atheists would concede as a given. However, Craig also objected that two logically identical statements do not necessarily mean the same thing. He said that the meaning of statements is what matters epistemically. After all, logical rules of inference transform one statement into a logically identical statement with a different meaning. If logically identical statements were semantically identical, then rules of inference would be useless. His purpose in Plantinga's MOA is, allegedly, to prove that God's possible existence entails God's actual existence, convincing people who accept the former to accept the latter.

As previously described, the only apparent reason to accept the former over the latter is a conflation of metaphysical and epistemic possibility. Showing the implications of a proposition can make it more plausible as Craig said, but can also make it less plausible. The reductio ad absurdum style of argument suggests that the absurd implications of an idea make the idea equally absurd.

With that said, I cannot in good conscience list this objection as sufficient to refute Plantinga's MOA [5]Note 5. ...which seems unfortunate, since it required the most mental work. because if one finds "God possibly necessarily exists" more plausible than the semantically different statement "God necessarily exists," then Plantinga's MOA does allow one to infer the latter from the former.