The Logic of Perfection

A New Ontological Argument

If you are familiar with contemporary ontological arguments, you know that they face the problem of parody arguments. A parody argument uses the same reasoning to generate an opposite or absurd conclusion. I give an argument that avoids this problem.

The Axioms

I begin with an axiom that characterizes positive (great-making, value-conferring) properties:

positive

To illustrate, suppose Jeff is happy, kind, and wise. These properties illustrate the concept of positivity. We can think of positive properties as properties that are desirable for their own sake. Suppose, by contrast, Jeff is also paralyzed. Being paralyzed is not positive. In fact, Jeff's paralysis limits his total positivity. I stipulate that any property that limits positivity is "negative." Negative properties, then, limit positivity, while positive properties contribute to positivity.

Given this understanding of "positive" and "negative," Axiom P says this: properties that contribute to positivity do not thereby limit positivity. For example, someone can be wise without thereby being paralyzed. More generally, being wise does not entail any limit with respect to positivity.

For the sake of focus, I will put aside properties that are mixes of positive and negative. An example of a mixed property is being happy and in pain. This property contains both a positive and negative aspect. But it doesn't count as positive simpliciter. When I talk of "positive" properties, then, I am talking about purely positive properties, which contain no negative properties.

Next, we need three axioms about perfection. By "perfection," I mean maximal positivity. We may characterize perfection (maximal positivity) with the following axioms:

Perfection

positive

being inconsistent with reason

perfection

perfect

necessary existence

These axioms draw out some implications of perfection. A perfect thing, in this context, is something that has maximal positivity. Thus, perfection is itself positive (Axiom M). Axiom B records the idea that a perfect being would have a coherent nature. If instead its nature departs from reason, then its positivity is not maximal. A truly maximal being, by contrast, would have a nature that is consistent with reason. Finally, we have axiom N, which records the idea that the greatest being would enjoy the strongest grip on existence. That is to say, it would have necessary existence.

Note that the "perfection" axioms do not assume that a perfect being actually exists or even possibly exists. These axioms are only about the implications of perfection. They say that if there is a perfect being, then (i) its nature is consistent with reason, and (ii) its existence is necessary.

Finally, we will use an axiom that characterizes possibility:

possible

impossible

I am treating "possible" as consistency with reason. For more about this notion of possibility, see my discussion of S5 modal logic.

The Argument

From the above axioms, we can deduce something surprising and significant. We can now deduce the following theorem:

Perfect Being Theorem: there is a perfect being.

Here is the deduction. First, we show that a perfect being (i.e., something that has maximal positivity) is possible. Suppose, for reductio, that a perfect being is impossible. Then, since we have defined "possibility" as consistency with reason, it follows that perfection is inconsistent with reason. Therefore, necessarily, if there is a perfect thing, that thing contradicts reason. Being inconsistent with reason detracts from perfection (Axiom B). Therefore, necessarily, if there is a perfect thing, then that thing has a property—being inconsistent with reason—that detracts from perfection. A property that detracts from perfection is negative, since it limits positivity. Therefore, necessarily if there is a perfect thing, then that thing has a negative property. In other words, perfection entails a negative property. Yet, perfection is a positive property (Axiom M). Therefore, a positive property entails a negative property. This result contradicts Axiom P, which says that if a property is positive, then it does not entail a negative property. Therefore, the reductio assumption is false. It is false that a perfect being is impossible. Instead, a perfect being is possible.

Next, we show that if a perfect being is possible, then it actually exists. First, by Axiom N, if a perfect being exists, then it necessarily exists. Then, building on the previous result that a perfect being is possible, it follows that it is possible that it is necessary that there is a perfect being. From Axiom 5, it follows that if it is possible that it is necessary that P, then it is actually the case that P (see proof here). Therefore, it is actually the case that there is a perfect being.

Q.E.D.

Parody?

Traditional ontological arguments suffer from various parody objections. For example, a famous objection to Anselm's argument is that its reasoning generates the absurd result that a great island necessarily exists. More recent formulations face the objection that they can be "reversed" to show, by parallel reasoning, that no perfect being exists.

The perfection argument avoids these problems. The reason is this: the perfection argument focuses on the implications of maximal positivity. We avoid the island parody, then, because no island could be maximally positive (unless the "island" is synonymous with the perfect being).

We also avoid the "reversal" problem because the axioms are not reversable. Take, for example, the axiom that positive properties do not entail negative ones. A reverse axiom would say that negative properties do not entail positive ones. But that is false: the propery of being cruel (for example) entails the positive property of being capable of thinking. If there is a way to reverse the argument, it is far from clear how.

I propose, then, that the perfection argument opens a new pathway deserving further investigation.