Sunday, August 21, 2022

Alvin Plantinga, Modal Actualism, and the Modal Ontological Argument

Socrates is a contingent being; his essence, however, is not. Properties, like propositions and possible worlds, are necessary beings. If Socrates had not existed, his essence would have been unexemplified, but not nonexistent. ... so being exemplified by Socrates if at all is essential to Socrateity, while being exemplified by Socrates is accidental to it. [Alvin Plantinga, "Actualism and Possible Worlds," in Michael J. Loux, ed., The Possible and the Actual: Readings in the Metaphysics of Modality, 268]

The Christian philosopher Alvin Plantinga is well-known for his modal ontological argument for the existence of God, a modification of the original ontological argument first expressed by Anselm in the Proslogion. A version of the modal ontological argument can be expressed as follows:

  1. It is at least possible for God to exist.
  2. If God’s existence is possible, then necessarily, God does exist.
  3. Therefore, necessarily, God exists.

The argument is expanded as follows:

  1. It is possible for God to exist.
  2. Therefore, God exists in some possible world.
  3. Necessarily, God exists in some possible world.
  4. Necessarily, God exists.
  5. God exists.

Premise 1 seems true for certainly the existence of God is conceivable, thus it is possible for God to exist and therefore statement 2 is true. From statement 2, one arrives at statement 3 through the modal axiom S5. Since the definition of God is that He has necessary existence, therefore if God necessarily exists in some possible world, he exists necessarily (Statement 4). Therefore, God exists (Statement 5).

Another way to frame the modal ontological argument is taken from "Formulation 4" of the entry on "Ontological Argument" on the Stanford Encyclopedia of Philosphy (accessed Aug 20, 2022), and simplified and expanded as follows:

  1. For any being x, there is a possible world w where x exists.
  2. For any beings x and y, there are possible worlds w and v, such that x exists in w and v, while y exists in w and not v.
  3. Being x is superior to being y as it exists in both w and y.
  4. If being x exists in worlds w, y, z, while God exists in y and z, then being x is superior to God.
  5. God, being defined as maximally great, cannot have any being superior to Him. Therefore, God must exists in more possible worlds than other beings
  6. A being that exists in the actual world would exists in more worlds than a being that does not exist in the actual world.
  7. God in order to be maximally great must exists in the actual world and all possible worlds.
  8. God exists.

Premises 1 and 2 are statements about possible worlds. Statements 3 and 4 are normally taken to be true, based on the premise that existence is greater than non-existence. Statement 5-7 flow from statements 3 and 4 and the idea that God is defined as a maximally great being, which is defined as such for the purpose of this argument.

So here we have two slightly different versions of the modal ontological argument. Unlike Anselm's original ontological argument, these arguments have more meat in them, and does not seem to require us to hold to some idea that God is defined as "greater than that can be conceived," with all its attendant problems. Are these arguments sound then? Have Christian philosophers like Alvin Plantinga stumble upon a viable form of the ontological argument that does indeed, as Natural Theology, prove the existence of God without appeal to special revelation?

Analyzing the arguments

The first argument form looks sound. However, note here that the argument depends on how one interprets premise 1. What does it mean for God to "exist in some possible world"? Most certainly, if one means that God ontologically exist in some possible world, then certainly the argument is sound, but is that what one means by premise 1?

The second argument form looks a bit more problematic. This form is closer to the traditional ontological argument, but it deals with maximal greatness through linking it with existence in possible worlds. The possible issues with this argument are the hidden premises correlating greatness with existence, and the idea that the actual world is a possible world that we see of as actual.

Existence is certainly better than non-existence, but this this only applies for creatures who can differentiate between the two states. For non-creatures, non-existence could mean imaginery existence, as in the case of imaginery numbers in Mathematics or virtual particles in quantum physics. Therefore, the idea that existence is always better than non-existence does not apply to everything. While in the case of God (and all creatures) it is true that existence is better than non-existence, to assert that is to assume God (or at least creaturely existence as superior to non-creaturely existence) from the start and therefore cannot truly function as an axiom to prove God's existence.

The key problem: Actualist modal ontology

Both argument forms when analyzed seem sound, until one digs deeper. For the first argument form, premise 1 states that God exists in some possible world. But does this possible world truly and actually exist? For the second argument form, the hidden premise is that the actual world is a possible world that we see as actual to us. Presumably, individuals in some possible world w would see theirs as an actual world and ours as a possible world.

Underlying this is a commitment to an actualist modal ontology. What is an actualist modal ontology? An actualist modal ontology states that all modal entities truly and actually exist. How that is so divides the actualists. Plantinga's form of actualist modal ontology borrows from Platonism and differentiates existence from examplification. As seen in the quote above, for Plantinga, all modal entities exist as "things" or haecceities, which are analogous to the Platonic forms. In any possible world, these forms all exist but the actual thing exist only if the form is "exemplified" in any particular world. Therefore, the existence of Socrates in world w is due to the "exemplification" of "Socrateity" in that possible world. In possible world v however where Socrates does not exist, "Socrateity" still exists in that possible world v but "Socrateity" was not "exemplified" in possible world v.

According to Plantinga's modal ontological argument therefore, that God exists in some possible world can start as something as simple as the Platonic form of "God" being present in that possible world. Likewise, there is nothing essentially different between the actual world and possible worlds except in the perspectives of the ones in that world. The actual world in this case is a possible world that we are in. With this actualist modal ontology, things possible are more than mental conceptions but are possible existing objects.

Plantinga's modal ontological argument therefore seem to depend on an actualist modal ontology. It is a question if the argument can survive without actualism. For many of us, possible worlds are taken as hypothetical worlds, creations of the mind to explore alternate forms of the world. We are possibilists, and believe in one actual world where things ontologically exist.


The modal ontological argument is indeed a stronger argument that seems to point to the success of Natural Theology to prove God's existence. However, at least one variation of that argument by Alvin Plantinga seems to demand an actualist modal ontology which I do not hold to. Therefore, it stands to reason that the modal ontological argument has not been proven to be sound, and the goal of Natural Theology seems unrealized.

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