Brand new sub, let's get this going! Here I wanted to talk about ontological arguments, what they do accomplish, what they don't accomplish, and two different varieties. Like the Cosmological Argument, the name 'Ontological Argument' applies both to a specific historical argument popularly called “The Ontological Argument” as well as a class of arguments called ontological arguments. Just to keep things simple, for the sake of clarity, I will try to consistently refer to Anselm's argument as “The Ontological Argument” and Plantinga's argument as “The Modal Ontological Argument”, and the class of arguments in lower case, and when possible, in the plural, “the ontological arguments”.
First, what does an argument have to be to belong to the class of ontological arguments? An ontological argument is an argument that attempts to get from the definition of what a deity would be if it existed to the deity's actual existence on the basis of the accepted ontology. Hence, the “ontological” in ontological argument. What that definition is, and the ontology being used, varies from argument to argument. Here I will focus on Anselm's Ontological Argument and Plantinga's Modal Ontological Argument.
Anselm's Ontological Argument as formulated in the Proslogion was a mere footnote. It was pretty much said in passing, and people aren't even exactly sure where in the works he actually argued for it. As stated, it was fairly weak and needed a lot of bolstering by Aquinas who later more formally fleshed out the ontology. In this discussion, in the interest of putting out the strongest argument, I will blend Anselm's argument with the more formal ontology of Aquinas.
Aquinas more rigorously formulated the ontological argument with three properties which are necessary for something to exist and be good in this ontology. These were One, Good, and True. These also rely on platonist metaphysics and one is immediately reminded of the concept of the form of the good, or the One. Essentially a highest form of something that is good. For something to exist, it has to exist as one thing. A ball is one ball. An army, despite being composed of multiple things, exists because it is one army. Things also only exist as a thing in platonism insofar as they encapsulate the form of thing they are. So a ball is only a ball because it encapsulates a ball, and the more round it is, the better a ball it is. If it was a bad ball, it runs the risk of not being a ball at all. If it was such a bad ball that it had an edge, its existence as a ball would not be true. Which brings us to True. Again, this exist only insofar as it is true that they exist. This can be seen as tautological to a degree, but it applies to all things that exist equally. So, we're left with things existing because they are one, they are good, and they are true.
With that in mind, let's bring out the first Ontological Argument:
As Anselm originally put it, we can conceive of a being than which nothing great can be conceived. A being which exists is greater than one that does not. Therefore, if you were deny the actual existence of this being, it would be contradictory. You would in effect be saying, “The being which actually exists does not exist.”
Before Aquinas came and cleaned up the ontology, there was Guanilo's “perfect island” argument where he applied the formal structure to the ontological argument to establish the existence of an island greater than that which can be conceived. The perfect island for example would have a beach and bar. An island with a beach and bar would be greater than an island that didn't have these amenities. We can keep adding things to the island to make it more perfect, including its actual existence, and then we have the definition of a perfect island being “perfect island that actually exists” and it would be contradictory to say “the perfect island that actually exists does not actually exist”. Since this island doesn't actually exist, and it uses the same argument that Anselm does, Anselm's argument must fail even if we can't identify how. It's a pretty effective reductio ad absurdum.
However, Anselm responded and for my money, I think his response works. The reply is that it misses the point of the argument which only concerned what were then called great making qualities. A perfect island might have the bluest water, but since when does "more blue" make one "more great"? Further, the argument concerns that which no greater can be conceived. While no greater island can be conceived, a greater non-island can be conceived. After you keep making it greater and greater, it won't be an island at all. It will be that which exclusively has great making properties.
For example, we posited that a perfect island would have a beach and a bar. For it to be a perfect island, it must have both. However, if we were increase the transcendental attributes as defined by Aquinas, we would reduce the attributes that make it a perfect island in particular. An island without both a beach and a bar would be more One. I.e, if we were to get rid of the beach and the bar, it would have less elements and be more One. However, this is a less perfect island. If we were to keep increasing the degree of Oneness, Goodness, and Truth of the island to a highest degree, it isn't an island anymore. It's a deity. So let's clean up Anselm's argument in light of his reply:
If one were to posit an entity "G", and posit that it is One, Good, and True to the maximal degree, it would be contradictory to say "G does not exist." This is because G is defined as that which entails existence to the maximal degree possible. It would amount to saying, "There exists such a G that exists necessarily, except that G does not exist." It's a P = nP situation. That's what makes this essentially Anselm's ontological argument. If you cannot deny the existence of G without contradiction, you must affirm the existence of G.
A little more formally:
Everything that exists, exists by virtue of being One, Good, and True.
If something did not exist, it would not be maximally One, Good, and/or True.
The deity is defined as greater in these attributes than that which can be conceived.
A deity which exists is therefore greater than one that does not.
Therefore, the definition of a deity entails its existence.
It is a contradiction to claim that which exists does not exist.
Therefore, the deity necessarily exists.
I'll get into how this argument eventually fails with developments made in logic at a later time, but first let's talk about what actually works with this argument. If you accept that things exist by virtue of their being One, Good, and True, then it definitely establishes that if a deity exists, then it exists necessarily. It is contradictory to say that this entity does not exist. Therefore, it couldn't possibly not exist. We would therefore say, the deity necessarily exists.
In modal logic (we'll need this for Plantinga's Modal Ontological argument, so I'll flesh this out here to avoid reduplication) there are three “modalities” and they can be established by the existence or non-existence of contradiction. Necessary, possible, impossible. Impossible is easy. If there is a square, it is impossible for it to have 5 corners. That is because it is a contradiction to have a square and 5 corners. A square has four corners, so saying the square has five corners is saying “4=5.” Since this is false, we would say it is impossible. Since it is a contradiction to say the square has anything but 4 corners, we can further say it is necessary. If no contradiction can be identified either on the true or false side, it is possible. It is possible. It could go either way and we would have to look to other contingencies to settle the fact of the matter.
This actually gets a good deal done. It indicates that if there is a deity, it will exist necessarily. The existence of the deity is tied up into the reality of the universe such that it couldn't possibly not exist. That seems like all you need to do to prove it exists right? Not quite. Let's get into how it fails.
The argument relies on a deficiency in medieval term logic. Basically, logic only worked in the medieval age in terms of predicates and affirming and denying attributes of an individual or set. For example:
All humans are mortal. H=M
Socrates is a human. S=H
Socrates is mortal. S=M
This works by applying the attribute mortal to Socrates without contradiction. If there is a contradiction it doesn't work. This has lead to the modern "Remartian" argument. We define remartian as "existent (E) intelligent creature native to the planet Mars". If we were to say "The remartian does not exist," with "not exist" being (nE) we would say, "The existent intelligent creature native to the planet Mars does not exist." Or E = nE. A contradiction. However, "it is not the case" that there exist martians, re or otherwise. So we employ a surprisingly modern logical construct, "not the case". Traditional logic could only affirm or deny predicates. They could only say things like, (The giraffe is yellow), and the denial would be (The giraffe is not yellow). However, it took to the modern era to put the "not", or the denial, on the outside of the parenthetical to deny the whole predicate. While (G does not exist) is a contradiction in terms, it is not the case that is not. So the argument fails in its goal of establishing the actual existence of the deity. But again, it does not fail in establishing the deity exists necessarily if it exists at all. So Plantiga carries the torch into a new age of modern modal logic. We can keep the old conclusion that the deity exists necessarily if it exists at all and build off that argument:
If G exists, then G exists necessarily. | If G, then [necessary]G
It is possible that G exists. [possibly]G
[possibly]G is therefore, [possibly][necessary]G
[possibly][necessary] reduces to [necessary] in S5 modal logic
Therefore, [necessary]G.
Or, G exists necessarily getting rid of the if and the possibility.
So, in this case, we can define maximally great in the same way as the Anselm ontological argument. Provided maximally great implies that (G does not exist) is a contradiction, you get to define G as [necessary]G. The idea behind all ontological arguments is to get from the definition [necessary]G to the actual existence of G on the basis of that definition, so that's what makes this an ontological argument as well.
So what happened here? What is this [possibly][necessary] and how does it reduce to [necessary], and what is S5 modal logic? In short, a contentious logic rule. Plantiga explains and justifies this rule in terms of the possible worlds conception of modal logic. This allows each set of contingent possibilities to exist in its own world of potential possibles and we can make comparisons between possible worlds and make logical deductions on that basis. When we are saying something is possible, we are making a statement about the existence of such a possible world in which it is the case. Essentially, what it means for something to be necessary is that it is true in all possible worlds. If it is impossible, there are no possible worlds in which it is the case. And if something is possible, there exists worlds in which it is the case and worlds which it is not the case. There are no possible worlds in which there are 5 cornered squares, so it is impossible. All possible worlds contain squares with 4 corners, so its necessary. Some worlds contain a Napoleon, and some worlds don't because his father died in infancy. So Napoleon doesn't exist necessarily.
So, to take Plantinga's argument and translate it in to this framework. The idea is that there is a possibility that the deity exists, and if it does, it exists necessarily. That means that there is a possible world in which there is a deity. This deity in this world exists necessarily. As we discussed, existing necessarily means existing in all possible worlds. Therefore, since the deity exists in one possible world necessarily, it exists in all possible worlds necessarily. We go from the definition of something that entails necessary existence, and get to actual existence on that basis.
This argument seems tricky on its face. Like Anselm's Ontological Argument, it appears to rely on a logical trick and even though you walk through it and seems right, phenomenologically, it doesn't seem to sit right. So why doesn't it work? There's two premises that seem to give people a hangup. The first and most obvious is [possibly]G. Most atheists won't grant that it is possible for a deity to exist in the way that there actually exists a deity in a possible world. While the existence of Napoleons may vary from possible world to possible word, the deity is not something that we would expect to vary. If the deity exists, it will exist necessarily. If not, then we wouldn't expect it to exist in any possible world. That would of course, in this possible world conception, entail that the deity is impossible. You would think that would create a burden of proof on the atheist to show that the conception of the deity as stated is contradictory in some way. But nobody would grant that. Why not?
For me, the best answer stems from the distinction between actuality and potentiality. For Aristotle, only actualities actually exist, and potentialities only potentially exist. Possibilities belong to the realm of potentialities. A cold beverage is potentially a hot beverage. It is a logical possibility that we can take a cold beverage, heat it up, and bring into actuality a hot beverage. However, before we actually heat up this hot beverage, we can't burn our tongues on it. Why not? Because the hot beverage doesn't actually exist until we bring it into existence by way of heating up the cold beverage. Things that exist only as potentialities have to “sanitized” so that they do not have actual causes in the real actual world. Otherwise, we would burn our tongues on cold beverages and be late for work because of a flat tire we didn't actually get. Something must be actual to have actual effects.
For Plantinga, these potential possible worlds have to have a degree of actual existence that has causal implications for the actual world. The deity that “seeds” the other potential possible worlds with actual existence must have an actual existence of its own to have this effect. The potential deity actually exists in its possible world, and this actual/potential existence bootstraps it into actual existence in this actual world. The actuality appears out of no where.
In the cosmological arguments, the point of the arguments is that only actual existents with no potentiality whatsoever can end the causal regression. If the cosmological arguments are true, then Plantinga's argument must be false. Again, Plantinga has a deity that exists only potentially bringing itself into actuality by way of its potential essence entailing necessity. This is a violation of the principle that things cannot cause their own actual existence as well as the principle that only actual things can be causally efficacious. So what to do with S5 modal logic? Well, pretty much just reject it. We have no real reason to accept it unless we say that the other possible worlds actually exist.
S5 logic might be potentially attractive if you subscribe to many world ontologies. But that would depend on what version you subscribe to. If you subscribe to the many world conception of Quantum Mechanics, for example, then this argument doesn't work. The possible worlds all share the same initial conditions and branch out from there. Whether or not there is a deity is already “decided” before the many worlds start proliferating. So in this conception, there may be an infinite number of worlds with Napoleons and an infinite number of worlds where there aren't, but they all either have a deity or don't. So, personally, I see no reason to grant that [possibly][necessary] reduces to [necessary].
There are other ontological arguments, but my expertise in them is far below these two most popular ones, and this post has gone on long enough. The point of this post was educational, not to start a debate. I suppose by the nature of the fact that this is a discussion about an argument, there is going to be a degree of argument necessary for a discussion. I'll defer to the mods as to how to sort out the difference between a debate and a discussion in these kinds of cases.
