The Modal Ontological Argument and the refutation of parody using Kalam

Plantinga’s Modal Ontological Argument (MOA) is a clever argument that uses modal logic and possibility semantics to affirm the existence of a Maximally Great Being (an MGB). It is a development and formalisation, of past ontological arguments - most notably Ibn Sīna (Avicenna)’s and Anselm’s - and relies upon modal axiom S5 at its crux. In this article we will also counter-argue against its parody with Kalam.

Anselm argued that God, as “that than which nothing greater can be conceived,” must exist in reality and not merely in the mind: since a being that exists only in the mind is lesser than one that also exists in reality. Before him, Avicenna in his ‘Proof of the Truthful’ outlined a formal ontological argument for God.

Laying out the Modal Ontological Argument

Let M(x) mean “x is a Maximally Great Being.” We first define what maximal greatness requires:

A being can be said to have Maximal Excellence in a world w (see more on worlds below) if it is omnipotent, omniscient, and morally perfect in w. A being can be said to have Maximal Greatness if it has maximal excellence in every possible world; its excellence is necessary, not contingent.

Therefore, judging by this distinction a being could be omnipotent in our world but fail to exist elsewhere. Maximal greatness rules that out. From this, the MOA looks something like this symbolically:

\[\begin{gather} &\Diamond \exists x\, M(x) \tag{1. possibly, a MGB exists}\\ &\Diamond \exists x\, M(x) \rightarrow \Diamond\Box \exists x\, M(x) \tag{2. by definition of MG}\\ &\Diamond\Box \exists x\, M(x) \tag{3. from 1, 2}\\ &\Diamond\Box \exists x\, M(x) \rightarrow \Box \exists x\, M(x) \tag{4. S5}\\ &\Box \exists x\, M(x) \tag{5. necessarily, a MGB exists}\\ &\Box \exists x\, M(x) \rightarrow \exists x\, M(x) \tag{6. reflexivity}\\ &\therefore \exists x\, M(x) \tag{7. a MGB exists}\\ & QED :) \end{gather}\]

There are two mainly contested premises (P1 and Axiom S5):

Premise One (On the possibility of an MGB)

Note that P1 is where most of the friction in embracing the MOA sprouts from. P1 states that that it is rationally possible for an MOA to exist, meaning there is no logical contradiction to the MGB existing. Given how rigorous the argument is, accepting an MGB accepts the conclusion outright.

A symmetric ‘parody’ argument can be countered with an alternatively Maximally Evil Being, possibly contradicting and undermining the MGB:

Since a maximally evil and a maximally great being cannot coexist (their natures being contradictory), at most one can be genuinely possible. The burden then falls on the theist to explain why MGB possibility is more credible than MEB possibility.

In addition, some have countered the idea of maximal evil:

On the ‘Maximally Evil Being’

To recap, the MEB parody (introduced by John Mackie and others) runs symmetrically to the MGB:

\[\begin{gather} &\Diamond \exists x\, MEB(x) \tag{1. possibly, a MEB exists}\\ &\Diamond \exists x\, MEB(x) \rightarrow \Diamond\Box \exists x\, MEB(x) \tag{2. by definition of maximal evil}\\ &\Diamond\Box \exists x\, MEB(x) \tag{3. from 1, 2}\\ &\Diamond\Box \exists x\, MEB(x) \rightarrow \Box \exists x\, MEB(x) \tag{4. S5}\\ &\Box \exists x\, MEB(x) \tag{5. necessarily, a MEB exists}\\ &\Box \exists x\, MEB(x) \rightarrow \exists x\, MEB(x) \tag{6. reflexivity}\\ &\therefore \exists x\, MEB(x) \tag{7. a MEB exists}\\ \end{gather}\]

Firstly, Plantinga has mentioned that the MOA is not meant to prove the existence of the MGB but rather to justify it (belief) rationally. (Conversely, the parody could be argued to show someone who finds P1 to be unacceptable is also rational. Both positions are supposedly reasonable: which is Plantinga’s modest conclusion.)

That being said, one could still argue against the MEB based on how evil is merely a privation or negation of good. (I will cover this below using Kalām).

Premise Two (on Maximum Greatness)

P2 states that maximal greatness (MG) entails necessary existence. This is largely accepted, since if a being failed to exist then it would not be maximally great.

A deeper breakdown of S5 and worlds

“S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic.” (Wikipedia)

Symbolically, S5 can be written as: \(\Diamond\Box P \rightarrow \Box P\)

• □ symbolises ‘necessity’
• ◇ means ‘possibility’ Consequently, S5 practically means that if it’s possible that P is necessarily true, then it is necessarily true.

Therefore, if there exists a world where P is necessary, P can be said to be necessary in all worlds. But what is a world?

‘Worlds’, and why they matter

In Modal Logic, we imagine different possible ‘worlds’. Simply put, a world is a way reality could have been, it is a conceivable existence: for instance, Obama never having been made President is another world. The world we have just imagined is known to be an ‘accessible’ world, because we can ‘access it’ (consider it possible) from our reality.

S5 in relation to worlds.

S5 assumes that every world can access every other world.

S5 imposes three constraints upon the accessibility relation. The relation must be reflexive (every world can access itself), symmetric (B can access A just as A can access B), and transitive (A can access C if A can access B which can access C). Together these mean every world accesses every other world. This means the accessibility relation is universal.

Knowing all of this, we can recap.

• Let ◇□P be true in world W.
• This means that there exists some accessible world where □P
  • World W can access all worlds
• Therefore □P in all worlds because necessity is implied.
• Additionally, as per S5’s constraints W is reflexive
• Therefore □P holds in W as well. Again, in conclusion, what is possibly necessary (take P) is necessarily necessary because
• It means a world can be accessed where P is necessary
• If P is necessary in one world, it is necessary in every world P can access because accessibility is in relation to plausibility
• Every world can access every other world, so the world where □P holds can access W, meaning □P holds in W too (P is true for all worlds)
• □P (QED)

  S5’s significance in the MOA

  S5 is a key axiom in that we affirm (in a nutshell) an MGB which is possibly necessary, entailing true necessity, entailing existence.

Without S5, the inference from possibly necessary to necessary simply does not hold, and the argument collapses at P4. As mentioned, the axiom is at the epicentre of the argument.

There are objections to S5, but it’s getting too late and I need to revise, so I may update this post at a later date.

Trying to refute the modal parody using Kalam

Let’s return to a critique of P1 in the form of parody. This argument runs symmetrically to the MOA.

As I am approaching this using Kalam, we first must distinguish a few definitions and concepts.

Firstly, existence can be divided into two (this is an Avicennian doctrine (and was later supported by Aquinas and more.)):

• Necessary existence (called “Wājib al-wujūd”): That which cannot not exist by virtue of its own essence alone.
• Contingent existence (called “Mumkin al-wujūd”): That which depends on something external to exist. A necessary being does not depend on anything external. Therefore, everything about this being must be positive and self-subsisting, and it neither borrows nor lacks nor is constrained by anything.

Now, we can define evil. Evil is by its essence parasitic, in the sense that it is the negation of goodness / positivity. Therefore, there isn’t really a sort of ‘pure, free-floating evil’ as evil is the absence (or corruption) of good. This is as much metaphysically as theologically. Evil has no trult independent reality of its own, and is always defined relative to what it falls short of.

Where the MEB falls

If maximal evil is the negation of every perfection then: \(MEB(x) \iff \forall w \in W : \neg\text{omnipotent}(x,w) \wedge \neg\text{omniscient}(x,w) \wedge \neg\text{morally perfect}(x,w)\) x is an MEB iff in every possible world, x is not omnipotent and not omniscient and not morally perfect.

Every negation introduces a dependence. Not being omnipotent posits the MEB is bounded by something outside itself. Not being omniscient is to be defined relative to knowledge that one lacks.

By construction, the MEB is contingent because every conjunct makes the MEB depend on something external.

\(MEB(x) \implies \text{contignent}(x)\) Contrastingly, the parody argument requires the MEB to necessarily exist across all worlds. Necessary and contingent existence are mutually exclusive:

\[\begin{gather} &\text{contingent}(x) \implies \neg\Box\exists x, MEB(x)\\ &\therefore MEB(x) \implies \bot \end{gather}\]

The MEB fails to satisfy the modal conditions of the parody. It is therefore metaphysically incoherent.

The MOA works because MG consists of positive and self-subsisting (سمة ذاتية الاكتفاء) attributes which are compatible - no, rather which found necessary existence. The MEB is a construction of privations which by essence implies contingency.

The parody operates under the assumption that evil and greatness are symmetric, which is at ends with Kalam. Evil is the absence of good rather than being a positive attribute. Applying a negating attribute to the being negates the very qualities that ‘maximise’ the being.

Concluding

In all, the weight of the Modal Ontological Argument primarily rests upon two concessions: being able to embrace the possibility of an MGB without contradiction, and that it is necessary for metaphysics to obey S5. Both are arguably false or true, being the reason that the MOA is still an argument with some controversy. We also explored a counterargument against parody borrowing from Kalam. In all, the MOA’s significance may lie in the fact that it reduces a great philosophical debate to a simple ◇.