Zach's Ontological Argument in Predicate Logic

Greetings,

It has been quite some time since my last post, due in part to my attending an investment conference called R.I.S.E. in Dayton, Ohio. While there, I found myself attending a 2-hour panel on corporate governance... not the most exciting material, particularly for a philosophy student. However, I had plenty of time to fiddle around with one of my most favorite arguments: the Ontological Argument for the Existence of God.

As an undergraduate in philosophy, it often seems like logic is like a board game without a board—I know the rules, but want a scenario to try my hand with them. So far, the only “board” I’ve learned of that can be played for hours at a time is the Ontological Argument, which is fairly controversial on several grounds. It’s a fun game to play because it’s a challenges to establish a valid argument with true noncontroversial premises, but seems like something where I can consistently make progress.

So, at the conference, here is what I originally came up with:



Where P = …Is the perfection of…, H = …Has the property…, a= A being with all possible perfections, u= The property of existence in the understanding, and r= The property of existence in reality.

The basic argument is that if x is a perfection of existence in the understanding, a being with all perfections and with existence in the understanding must also possess x. As existence in reality is the perfection of existence in the understanding, and a being with all perfections exists in the understanding, a being with all perfections therefore necessarily exists in reality.

This appeared logically valid to me, but I was not satisfied. Premise 1 appears non-controversial to me—if a being has all perfections and has a property, it must therefore have the perfection of that property. However, Premise 2 and Premise 3 seemed more controversial—that the property of existing in reality is more perfect than the property of existing in the understanding (Premise 2), and that a being with all possible perfections exists in the understanding (Premise 3). Thus, I decided to see if I could find non-controversial ways to express these premises.

After playing around with the possibilities, I came up with this argument for Premise 3:



Where H = …Has the property…, A= Can be rationally debated, u= The property of existing in the understanding, and a=A being with all possible perfections.

The basic argument here is that, if any given x does not exist in the understanding, one cannot rationally debate it—for example, if unicorns do not exist in my understanding, then I cannot debate about unicorns. I feel that this should be fairly non-controversial, and thus should make the argument a bit more generally acceptable.

Therefore, my new version of the Ontological Argument (for those who challenge Hau) is:



Where P = …Is the perfection of…, H = …Has the property…, A= Can be rationally debated, a= A being with all possible perfections, u= The property of existence in the understanding, and r= The property of existence in reality.

However, I feel that the new fourth premise—Pru—is still fairly controversial, and wanted to see if I could express it in a less controversial manner. After a bit more exploration (and with the corporate governance panel drawing to a close), I came up with this:



Where P = …Is the purest possible positive property of…, H = …Has the property…, I=…Is a…, n= Perfection, p=Property, …N=Can have a…, u= The property of existence in the understanding, and r= The property of necessary existence in reality.

This is arguing that there’s nothing that exists that is the perfection of existence in the understanding and is not the property of necessary existence in reality. Now, if existence is a property and the property of necessary existence in reality is not the perfection of existence in understanding, then either there exists something that is more perfect existence than necessary existence or existence cannot have a perfection (but not both of these at the same time). As existence can have a perfection, and existence is a property, necessary existence in reality must necessarily be the perfection of existence in understanding.

Plugging this into the original equation would look like this:



Where P = …Is the purest possible positive property of…, H = …Has the property…, I=…Is a…, n= Perfection, p=Property, …N=Can have a…, a= A being with all purest possible positive properties, A= Can be rationally debated, u= The property of existence in the understanding, and r= The property of necessary existence in reality.


So, there you go: Zach’s version of the Ontological Argument in Predicate Logic, plus further argument on Hau and Pru. Also, you may notice that Iep could just as well be left out… I’m trying to anticipate Kant, though. Once I understand his argument better, it’s structured so I should be able to respond and easily plug it in.

Thoughts/comments/suggestions? Think it’s full of crap, think it’s invalid and I missed something, or think there’s a mistaken premise? Impressed with my leet formatting skills on a blog post? Looking forward to any/all comments!