Ontological Argument | Falsities of Alvin Plantinga

The ontological argument is one of the earliest theodicies created in an attempt to rationalize the existence of a monotheistic God. It was first introduced in the early eleventh century by the Archbishop St. Anselm of Canterbury (1033 — 1109). A modern reiteration was created by the philosopher & theologian Alvin Plantinga PhD. (1932 — ). This version advances the theory using modern Kripke’s modal semantics — possibility & necessity relation (R,w). Where w is a non-empty set of possible worlds and R its accessibility relation. In this reinterpretation the key premise would assert the possibility of a “maximally excellent” being that exists in one world w1; would therefore, have “maximal greatness” in all possible worlds (Rw1w2). This distinction he draws between maximal greatness and excellence will be addressed later. The original syllogism presented by Plantinga in 1965 has gone through several reiterations and therefore can be difficult to interpret. Here is a principled schema of how the argument breaks down,

“As people become more intelligent they care less for preachers and more for teachers”

— Robert G. Ingersoll
  1. The concept of a maximally great being is self-consistent.
  2. If 1, then there is at least one logically possible world in which a maximally great being exists.
  3. Therefore, there is at least one logically possible world in which a maximally great being exists.
  4. If a maximally great being exists in one logically possible world, it exists in every logically possible world.
  5. Therefore, a maximally great being (that is, God) exists in every logically possible world (Himma n.d.).

Plantinga borrows from Kripke’s possible world semantics R(w1,w2) because he wants his theodicy to appear modern and sophisticated. It is however not sophisticated enough to hide its obfuscation. It could be simplified by just saying “God necessarily and possibly exists as a consequence of its nature.” If you want to skip the modal lecturing this is principally his argument. According to the Oppy taxonomy we can categorize Plantinga’s ontological argument as definitional. With (1) being the crux of his argument as it does most of the heavy lifting. Because (1) commits a categorical error as defining existence as a true predicate. It was the 18th century Prussian philosopher Immanuel Kant who first addressed this when responding to traditional theodicies for God. Kant makes the objection that for any propositional statement P a predict cannot be said to be a property of its existence nor existence its predicate. Kant distinguishes between real & logical predication. If the quintessence of (1) is possible its necessity does not guarantee its existence. The example Kant uses is the definition of a perfect triangle. For a perfect triangle to exist it is necessary for it to have three sides but this does not necessarily mean the triangle actually exists. For a more through explanation of Kants objections please refer to my previous article “The Ontological Argument | Falsities of St. Anselm”. Kants now famous categorical distinction leaves the ontological argument crippled. Because the term “existence” would mean that any true-predicate must be referred synthetically. For any statement about “existence” will always be synthetic — by referring to something outside of its subject definition.

As we move to address premises (2) & (3) regarding the possibility relation of maximal greatness (R). It must be repeated that his attempt to prove God as a possibility ◊ or necessity □ is not ontological but definitional. The added use of modal semantics is what creates for him the illusion of complexity, which does nothing to hide its reductivism. Here we are talking about the possibility ◊ and necessity □ of R using possible world semantics R(w1,w2). Where again, we say that w represents possible worlds and R its accessibility relation. Plantinga seems to be following one of the original standard formations of System K — If A is a wff then the □A and ◊A are wff. Or simply put, if A is a well formed argument then the necessity of A and the possibility of A are well formed arguments.

You could reformat his ontological argument by drawing inconsistencies between how Plantinga uses the definitions of Gods quintessence and R’s modal axiom. Because the accessibility relation R of possible worlds and how Plantinga defines quintessence would only be R(ww)’ or accessible in all possibly accessible worlds.

The accessibility response to the modal ontological argument

  1. A necessary being can be said to be maximally great “iff” it possess the accessibility relationship of R for all possible worlds.
  2. The modal axiom for R is necessarily true in all possible world(s) that are accessible. But it may not necessarily be true for some possible world(s) that are inaccessible. Where P implies its contradiction or an inconsistency.
  3. Therefore, (1) is false because the truth of its necessary relation R does not guarantee its truth or necessity in all possible worlds that are inaccessible.
  4. Therefore, the truth/necessity of a being with maximal greatness cannot be said to exist in any possible world as its existence must be consistent in all possible worlds.
  5. Therefore, a maximally great being cannot be said to exist in the actual world.

This version corrects some of the mistakes left by the modal ontological argument presented by Plantinga. Which quickly disseminates into a reductio ad absurdum when trying to satisfy the axiom for the accessibility relation R. Because some possible worlds are inaccessible in which R would either not be true or not be necessary. Here Plantinga semantic slight of hand is revealed. Even if we were to be charitable and grant Plantinga assertion of maximal greatness. He still fails to demonstrated how a God is necessary of all possible worlds given that a being with maximal greatness is only accessible. What Plantaga is arguing is that a being with maximal greatness is only necessary in all possibly accessible worlds. But here we get to the point of contention, inaccessible worlds. An inaccessible world would contain some type of inconsistency or contradiction between R(w1,w2). For instance if it is necessary that P in w1 but only true in w2, then this would contain an inconsistency. So, while it may be □P in w1 it would only be true in w2, but this wouldn’t go both ways. Because while P is necessary in w1 it is only true in w2, which does not exclude the possibility of not P given that P is true. Plantinga semantic trick is to assert God as necessary of all possible worlds but conveniently ignore addressing how all possible worlds are accessible to each-other. I could just as easily conceive of a possible world(s) where some worlds are not accessible. Thereby as a consequence a being with maximal greatness could only exist as a possibility, as some world(s) are inaccessible V(p,w2). So to reiterate what we just learned if (2) & (3) are only true in some possible world(s) but not necessarily-true in possible world(s) that are inaccessible, then God cannot be said to exist necessarily at all.

A theist may attempt to salvage the argument by asserting God as having the Metaphysical property of a transcendent being that can access both accessible and inaccessible worlds. But then that would describe a plethora of inconsistencies. Which would go against Gods nature as a self-consistent being. Remember, a self-consistent being cannot contain a contradiction. Because what defines a transcendent being would not have the property of maximal excellence. Which Plantinga defines as, “a being that is dependent on the properties of each world.” A transcendent being would not be dependent nor limited to the properties of any possible world. Which also raises many other questions as to how God is related to these properties. And how the properties of each and every possible world(s) define its maximal excellence? Is God essential to these properties or accidental, and if essential; then how are these properties transitive? In either case, R is not satisfied as it’s accessibility relation is question begging. It’s a lot to think about and perhaps too much to unpack here. If anything this insight shows that you can poke holes almost anywhere in this argument.

In summary the ontological argument Plantinga presents is not representative of logical-necessity rather it is based on deontologic necessity. Basically put, Plantinga reasons that a God would not be logically-necessary but obligatory — being that you are logically obligated to accept by his initial definition of a maximally great and necessary being; but of course this is only true analytically. Keep in mind that analytical statements are only principally true. Any statement about existence will always be synthetic, as it will necessarily refer to something outside of its subject. According to the Oppy taxonomy, Plantinga’s ontological argument is definitional but fails to validate his assertions of ontological-necessity. (1) simply begs the question by asserting existence as a real/true predict. The accessibility relation of all possible worlds is unsubstantiated as there are other possible worlds that are inaccessible. I would describe this syllogism as a specious attempt by Dr. Plantinga to keep God and the ontological argument relevant; but it still falls short of logical.


Garson, James, “Modal Logic”, The Stanford Encyclopedia of Philosophy (2018 Edition), Edward N. Zalta (ed.), Retrieved from plato.stanford.edu/archives/fall2018/entries/logic-modal

Plantinga, Alvin 1976. Necessary Essential Existence, Canadian Journal of Philosophy 6/1: 105–11.

Himma, K. (n.d.). Anselm: Ontological Argument for God’s Existence Retrieved from http://www.iep.utm.edu/ont-arg/

Oppy, G. (1996). Ontological Arguments and Belief in God Cambridge University Press.

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