Saturday, February 9, 2013

On the ontological argument for god

My Genesis friend was trying to convince me of god’s existence (he would probably claim he’s only trying to explain his position on the matter, but I digress). His belief seems to hinge, at least moderately, upon the ontological proof of god.
The way he described it to me, it goes like this:
Axiom 1: Good and Evil exist.
Axiom 2: God is the sum of all Good, or the greatest possible Good. (can be a mathematical concept, no consciousness required)
Followed by a logic proof showing that if those two concepts are accepted, then the existence of god is a logical requirement.
According to my friend, the logic proof part of the argument is bullet-proof, and nobody ever attacks it; the attacks are always on the axioms. Furthermore, he says that the 2nd axiom is solid, and that the first one is the only real line of attack people take. I had a few problems with his argument, but seeing as how I’m not a good debater (I’m not quick on my feet), I didn’t think of the problems right away, or did not articulate them well. But there are some issues here.
Outside of the ontological argument (which I will get to), he followed the logical proof by “If god exists, then what traits must he have?” And yet, he admitted not a minute beforehand that the “god” defined in the proof was essentially a mathematical concept, not requiring the supernatural. Where did this incredibly large mental leap come from? This is precisely the sort of thing agnostic atheists have problems with when discussing religion. A mathematical construct, like a matrix containing a largest set of Good, is precisely that: a mathematical construct! The existence of a math concept doesn’t mean it exists out in the physical world. Where in the world is the number 5? And I don’t mean 5 apples, or 5 people, but the concept of 5. Where does the concept of happiness exist in the physical world? Where is supercalifragalisticexpialadocious? And more to the point, how is the bridge being crossed from the concept of a mathematical construct called “god”, to the more popular definition of god? Even if such a concept could be shown to physically exist, there’s still a huge leap between it existing and it having consciousness, let alone omnipotence or omniscience. I think probably that he started out with the preconceived notion that a Christian God exists, and then used something that he came across that agreed with that opinion to support said original opinion; that’s bad reasoning, and is explicitly discouraged in science.
Also problematic is that the ontological argument does not seem to be what he claims it is. None of the variations of the ontological argument that I’ve seen seem to match what he says; if it is such a good proof, and so many philosophers out there know it (if they are all attacking Axiom 1, then it must be known), then it stands to reason it would be included in the collection of ontological arguments.
Based upon the content of each ontological argument, he is probably referring either to a variation on Gödel’s or Plantinga’s arguments. Gödel’s argument is the less likely of the two; although it appears to be laid out in the form of a logical proof, it contains 6 Axioms, and at least 4 of them appear (to my eye) to have serious assumptions within them that make any outcome shaky at best.
Axiom 1: If a property is positive, then its negation is not positive.
I can see how this axiom would be tempting to agree with at first; dark is not light, positive numbers are not negative numbers, etc. But the wording is too loose, I think. The wording, as-is, could be used to argue that someone that is not right-handed is not a person, for instance. If you claim that right handed people are positive, then it would follow that left handed people are the opposite of right handed people, and therefore are not positive. Even if you stick to very strict interpretations and uses of this axiom, I’m still not sure that it’s true. In my mind, there is a lot of debate to be had here.
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive.
Here I will simply disagree. Helping others could certainly be viewed as Good, but by this axiom helping Hitler would be good, since he is a person. Or look at the pruning of plants; if either fostering or restricting growth is defined to be Good, then taken to its logical extreme, the results would clearly be something that is not Good. This axiom implies a stark Black-and-White view of the world that I simply do not believe to be the case; most things exist as a spectrum, and “opposites” are not so easily defined within the real world.
Axiom 3: The property of being God-like is positive.
Sure, I’ll let this one slide. That’s not necessarily the definition of God-like that most people use, but outside of that it’s just a definition. Call it what you like.
Axiom 4: If a property is positive, then it is necessarily positive.
Once again, I would disagree. Back to pruning; if promoting growth is Good, then by this axiom promoting growth must always be Good. And yet, there are times when pruning is more helpful than letting the plant run wild. This axiom also implies a stark Black and White view that I don’t often agree with.
Axiom 5: Necessary existence is positive.
Bull. I’m not saying that it absolutely is not positive, but to throw out something like that with absolutely no justification is lazy at best, a straight up lie at worst. I could just as easily say, The Color Purple Is Necessarily Positive. It holds no meaning.
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
If helping others is Good, then having to help other is Good. This has two problems. The first is that it relies completely on the premise of axioms 4 and 2; indeed, this is mostly just a rewording of that axiom (Black and White, once again). Second, the “necessarily” part adds huge implications in regards to Free Will. It’s essentially a claim that says that having no choice in the matter does not affect it’s Goodness. To this I would disagree on principle. If free will exists, then removing it can certainly have moral impacts. Whether or not Free Will exists at all is, of course, a whole other can of worms.
Those are arguments that took less then 5 minutes to think up, and this is just in dealing with Gödel’s Axioms, without even delving into the actual logic proof. Needless to say, I’m not particularly impressed.
The other closest argument that I found that seemed similar to my Genesis friend's would be Plantinga’s argument. This one seems even flimsier to me. Here is a version of his argument:
  1. It is possible that there is a being that has maximal greatness. (Premise)
  2. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
  3. Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
  4. Therefore, an omniscient, omnipotent and perfectly good being exists.
Oh, where to begin? Part 3 relies on something called Axiom S5. What this axiom basically says is that if something is possible, then its possibility is necessary. This is far from a solid conclusion, in my opinion. It’s a deep thought, and an argument in support of it could certainly be crafted, but the outcome is far from certain, in my opinion. It strikes me as a very hard to disprove (or prove) opinion, but an opinion nonetheless. Hardly the sort of bullet-proof logic that Proves the existence of the supernatural.
But Plantinga takes S5 even further with part 4, arguing that if something is necessary, then it must exist. When combined with axiom S5, it says that anything that has the possibility of existing must exist. Therefore unicorns are real, as is Harry Potter and magic. It’s possible that I could become a billionaire tomorrow, therefore it must be so. Tomorrow also marks the day we all die from thermonuclear war, since that has the possibility of occurring.  It’s possible that I have cancer right now and don’t know it; therefore, I must have cancer. It's also possible that I don't.
Hopefully these silly examples serve their purpose in pointing out the absurdity of arguments 3 and 4 together. You could certainly try to narrow down where the breakdown of logic occurs, but even without further fine tuning it is clear to see that something has gone horribly wrong; this cannot possibly be true.
And these were the only ontological arguments that even came close to my Genesis friend’s claims. I plan on asking him to look up his argument next time, but I’m not holding my breath. Despite his claims to the contrary, he isn’t truly looking for a rational argument; he just wants to be right. But personally, I have found my best-formed opinions (to date) have come from the result of being proven wrong, and having to take the time and effort to re-evaluate. Not being right, while awkward in the short term, is a good growing tool. I hope he is open to its use, even though I suspect he is often not.
UPDATE: I had a chance to talk to my Genesis friend about my results. He verified that he was referring to Gödel’s ontological argument, but seemed unaware that the argument contained six axioms. He decided that it must have been a modified version of Gödel’s argument that he came across way back when, and expressed interest in how I found "holes" within the axioms. Weeks have passed, and I haven't heard back from him. I rather suspect that his foundation on the ontological argument is similar to the faith he had in the Order of Creation: he heard it once, it sounded good to him, and he never bothered to do his homework before spreading it along. Perhaps I wouldn't be as bothered by that if he weren't about to get a PhD in a hard science field.


  1. I like to refer to the Ontological argument as the "fishes from wishes" argument.

    It sounds an awfully lot like: If it can be, then it must, because I'd much rather it be true than not. I don't have a lot of sympathy for that line of thinking. Engaging with fantasy is fun and interesting, but ultimately our wishes aren't fishes.

  2. I commend you for having and keeping a friend who will actually discuss these things with you... even if it ultimately is driving you slowly mad.

  3. He's certainly still a friend, I just wish that his logic was as sound as he thinks it is. Just because things make sense from your own perspective doesn't mean they are right, or that they even make sense from other perspectives.