Pruss’s clever ontological argument inspired me to offer two ontological arguments of my own:
A Simplicity Ontological Argument
Axiom 1: The simplest determinate of an exemplifiable determinable is itself exemplifiable.
Clearly, if a determinable property can be exemplified, then so can at least one of its determinates. The idea behind axiom 1 is that if some determinates are simpler than others (easier to grasp or analyze, or built out of fewer elements), then the simplest determinates have the greatest epistemic probability of being exemplifiable. (Complexity might result in there being incompatible components.) So, if there is any question as to whether every determinate of an exemplifiable determinable is exemplifiable, the safest assumption is that the simplest of the determinates is exemplifiable.
Axiom 2: Greatness is an exemplifiable determinable
This axiom invites an entire essay devoted to discussing what “greatness” is. Here I simply I propose that we have a primitive, analyzable notion of greatness by which we can recognize instances of greatness of various flavors and degrees.
Axiom 3: Maximal greatness (being the greatest conceivable being) is the simplest determinate of greatness.
I’m assuming that zero greatness is not a determinate of greatness, since if something had zero greatness it wouldn’t even have the determinable, greatness. I’m also assuming that there is no such thing as minimal greatness, since for every degree of greatness near zero, one can conceive of there being something half that great (e.g., if something has 1 unit of power, one could conceive of there being something with .5 units). The final assumption is that there is no other specification of greatness that is as simple (e.g., as easy to grasp or analyze) as maximal greatness.
Therefore, maximal greatness is exemplifiable.
Axiom 4: Maximal greatness entails essential maximal power, essential maximal
knowledge, essential moral perfection, and necessary existence.
This is perhaps controversial, but I think it has some intuitive appeal.
From those axioms plus given S5, it follows that that there is an essentially maximally powerful, good, and perfect being. This argument draws on the apparent simplicity of maximal greatness.
A Causal Ontological Argument
(Disclaimer: This argument may be called ‘ontological’ because all its premises are supposed to be knowable a priori, but it may also be called ‘cosmological’ because it relies on a causal principle.)
Let a ‘causable property’ be a property such that there can be a causal explanation as to why that property has ever been exemplified at all. For example, being an armchair is a causable property because there can be (indeed has been) a causal explanation as to why that property has ever been exemplified.
Let a ‘contingent property’ be one that is exemplifiable, but not necessarily exemplified. I propose the following axiom:
Axiom 1: Every contingent property is causable.
One motivation for this axiom is that it appears to be the simplest axiom that accounts for all known cases of causable properties. There are many known cases of contingent properties that are causable and no known cases that are not. I propose that the simplest explanation for this is that being a contingent property entails being causable. (I suspect the entailment goes the other way, too.)
Axiom 2: being contingent is a contingent property.
This is plausible, though not wholly uncontroversial. It is plausible that there is a world containing no contingent things, for it is plausible that there can be contingent things whose non-existence doesn’t depend upon the existence of other contingent things.
From Axioms 1 and 2, it follows that being contingent is causable. But as you probably already realize, being contingent couldn’t be caused to be exemplified by any contingent thing or things without circularity: contingency would have to already be exemplified by the contingent cause(s) prior to the effect. That is to say:
Axiom 3: No instance(s) of a property P can be the causal explanation(s) as to why P is ever exemplified at all.
Therefore, if being contingent is causable, then it is possible for there to be a necessary being. From S5, there is a necessary being. Call it (or them), N.
Axiom 4: Every degreed determinate within a continuum of possible degrees is itself contingent.
For example, being 400.12 feet long is contingent–it need not be exemplified. The thought here is that for every degree of A among a continuous range of possible degrees, there could have been a slightly higher or lower degree of A exemplified instead.
From here, an argument for N’s being maximally great can go like this. Premise: every non-maximal degree of greatness is a degreed determinate within a continuum of possible degrees [any non-maximal degree can be slightly exceeded]. (Note: it is not clear that there are exemplifiable degrees of greatness infinitesimally close to maximal greatness.) Therefore, every non-maximal degree of greatness is a contingent property (axiom 4). Now if A and B are both contingent, then unless the negation of A entails B or the negation of B entails A, then the disjunction, A or B, is also contingent. Thus, more generally, every disjunction of contingent properties whose negations are compatible is itself contingent. From here, if the negation of every non-maximal degree of greatness is compatible with the negation of any other non-maximal degree [and surely they are: just because there isn’t anything great to degree D doesn’t thereby entail that a certain other contingent degree of greatness is exemplified], then it follows that the disjunction G of every non-maximal degree of greatness is itself contingent. So, G is causable [axiom 1]. G cannot be causally explained by a non-maximal thing given that every non-maximal thing would be an instance of G [axiom 3]. Therefore, G can be causally explained by a maximal being. Therefore, a maximal being is possible. This means that being maximally great is either contingent or necessary. If it were contingent, then it would be causable [axiom 1]. But anything that is dependent for its greatness on another being is not maximally great. Therefore, it’s not possible for a thing to be caused to be maximal great. Therefore, maximal greatness is not causable. Therefore, maximal greatness is not contingent. Therefore, maximal greatness is necessary. Therefore, in a world in which there are no contingent things (recall axiom 2), maximal greatness must be exemplified by N. Then, if maximal greatness entails essential maximal greatness [isn’t that plausible?], then N is maximally great, even today.
This argument draws on the apparent contingency and explicability of the exemplification of non-maximal degrees of greatness.