Responding to McHugh’s Modal Ontological Argument from Divine Justice (MOADJ)

New Apologetics is a Roman Catholic apologetics, theology, and philosophy organization devoted, among other things, to ministering to atheists. For a couple years now, I have been friends with the organization’s head — Christopher McHugh — whose arguments interest me due to their originality. Chris defends a novel version of the ontological argument he calls the Modal Ontological Argument from Divine Justice (herein: MOADJ), of which I’ve long been suspicious. However, it’s only recently that I’ve been able to articulate where, exactly, the argument goes wrong. In this post, I will offer several critical responses. I encourage Chris — and his followers — to offer a reply.

Chris’s theological positions are summed up in a deeply technical document entitled The Tractatus, written in the style of medieval disputatio, and is located here. To read the MOADJ, scroll down to the section entitled “The Modal Ontological Argument from Divine Justice”. If that gave you a headache to read, you’re not alone. I find it incredibly dense and difficult to slog my way through. Nonetheless, I’ve read it multiple times (I hope you’re happy,  Chris!). The argument concludes that, contrary to appearances, injustice does not ultimately exist because there is a necessarily existent justice-making power that rectifies all injustices:

  1. Since “not being an unjust situation” is situationally necessary, either there is no sense to the concept of “injustice”, or there is an infallible justice-making power which is also situationally necessary. The action of this power “redeems” and transforms unjust situations reconciling them to perfect justice. Such a reconciliation would have to be metaphysically coextensive with the commission of the injustice itself such that every situation is transubstantiated to be exactly the right thing at the right time, otherwise “not being an unjust situation” could not be situationally necessary.
  2. It is not the case that there is no sense to the concept of injustice.
  3. There is a situationally necessary justice-making power. [from 6 and 7 modus tollendo ponens]

However, a parallel argument can be constructed for the non-existence of cats. First, we need to modify the second axiom to read:

Axiom 2: The property of “being situationally necessary” is not compatible with the property “being a cat.” [For any instance of a cat, there is a logically possible situation in which some other animal replaces the cat. For example, if there is a cat on my bed, there is a logically possible situation in which there is a dog on my bed.]

Next, we replace sentences about injustice with sentences about cats in the argument: 

  1. If the property of “being situationally necessary” is not compatible with another given property, then it is compatible with the complement of that property. [from Axiom 1]
  2. The property of “being situationally necessary” is not compatible with the property “being a cat.” [Axiom 2]
  3. The property of “being situationally necessary” is compatible with “not being a cat” [from Axiom 1 and premise 2, modus ponens]
  4. If the property of “being situationally necessary” is compatible with “not being a cat”, then the property of “not being a cat” is situationally necessary. [from Axiom 3 and premise 3]
  5. The property of “not being a cat” is situationally necessary. [from 3 and 4 modus ponens]
  6. Since “not being a cat” is situationally necessary, either there is no sense to the concept of “being a cat”, or there is an infallible not-cat-making power which is also situationally necessary. The action of this power “redeems” and transforms cats reconciling them to perfect non-cathood. Such a reconciliation would have to be metaphysically coextensive with the commission of the cat itself such that every possible cat is transubstantiated to be exactly the perfect non-cat at the right time, otherwise “not being a cat” could not be situationally necessary.
  7. It is not the case that there is no sense to the concept of cats.
  8. There is a situationally necessary non-cat-making power. [from 6 and 7 modus tollendo ponens]

This parody argument provides an important clue as to what went wrong in the original argument. The first axiom of the MOADJ states:

For any property “a”, necessarily one of the following is true:

1) Property “a” is compatible with either property “b” or its complement, “non-b.”

2) Property “a” is compatible with both property “b” and its complement, “non-b.”

The problem is that (1) and (2) are not exhaustive. Some properties are compatible with neither b or non-b. The first premise of Chris’s argument depends on the assumption that if the property of “situational necessity” is not compatible with some property p, then situational necessity is compatible with the complement of p, thereby entailing that p’s complement is situationally necessary. The parody argument suggests we consider the property of being a cat. Situational necessity is not compatible with there being a cat, because cats are contingent, but the situation of there not being a cat is not necessary either, because the situation of there not being a cat is also contingent. Thus, we should add a third condition to the first axiom:

3) Property “a” is compatible with neither property “b” or its complement, “non-b”.

However, granting a condition like (3) halts the original MOADJ. The conclusion no longer follows, because, among other things, one can no longer make inference from premise 2 to premise 3. I am reasonably sure that no fix could be made to the MOADJ either. To see why, notice that the inference from premise 2 to premise 3 has implications that would be illegitimate for modal logic S5. Premise 2 states that the property of unjust is not compatible with the property of being situationally necessary. In other words:

Screenshot 2015-08-10 at 12.01.10 AM

When commuting modal operators with a negation, you simply switch box to diamond and diamond to box, so commuting the negation with the two modal operators yields:

Screenshot 2015-08-10 at 12.02.32 AM

But necessarily x entails x. Thus, we can conclude:

Screenshot 2015-08-10 at 12.05.45 AM

In other words, Chris should conclude that, for any situation, that situation is possibly not unjust. But not being unjust is equivalent to either being just or morally neutral. Therefore, while Chris’s MOADJ concludes that all situations are necessarily just, at best, we can conclude that all situations are possibly either just or morally neutral: Screenshot 2015-08-10 at 12.06.38 AM

Chris’s conclusion is mistaken. Note that no characteristic of injustice is drawn upon other than that injustice is contingent and not necessary. Had Chris’s argument succeeded, we would have to conclude that for any contingent property, there is some necessary opposite property. Obviously, that’s not true; the property of there being a cat is contingent, but so is the property of there not being a cat.

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