The ontological proof for the existence of God (really “proofs” or perhaps “arguments,” as there are various versions) has popped up in the blogs a few times recently: e.g. Ophelia Benson, Josh Rosenau, Jerry Coyne. You’ve probably heard this one; it was most famously formulated by Saint Anselm, and most famously trashed by Immanuel “Existence is not a predicate” Kant. A cartoon version of it would be something like
- God is by definition a perfect being.
- It is more perfect to exist than to not exist.
- Therefore, God exists.
Now, this is a really cartoonish version of the argument — it’s not meant to be taken seriously. This kind of ontological proof is a favorite whipping-argument for atheists, just because it seems so prima facie silly. Just ask Jesus and Mo.
This kind of mockery is a little unfair (although only a little). What’s important to realize is that the ontological proof is perfectly logical — that is, the conclusions follow inevitably from the premises. It’s the premises that are a bit loopy.
It’s instructive and fun to see this in terms of formal logic, especially because the proof requires modal logic — an extension of standard logic that classifies propositions not only as “true” or “false,” but also as “necessarily true/false” and “possibly true/false.” That is, it’s a logic of hypotheticals.
So here is one formalization of the ontological argument, taken from a very nice exposition by Peter Suber. First we have to define some notation to deal with our modalities. We denote possibility and necessity via:
Just given these simple ideas, a few axioms, and a fondness for pushing around abstract symbols, we’re ready to go. Remember that “~” means “not,” a “v” means “or,” and the sideways U means “implies.” Take “p” to be the proposition “something perfect exists,” and we’re off:
There is something beautiful here, even if it’s somewhat silly as a proof for the existence of God. It’s silly in an illuminating way!
As Suber says, the argument is “valid but unsound.” He pinpoints three premises with which reasonable people might disagree: 1 (“if perfection exists, it necessarily exists”), 2 (“perfection possibly exists”), and 5 (“if something is necessarily true, then it is necessarily necessarily true”). That last one is not a typo.
For me, the crucial mistake is some mixture of 1 and 2, mostly 2. The basic problem is that our vague notion of “perfection” isn’t really coherent. Anselm assumes that perfection is possible, and that to exist necessarily is more perfect than to exist contingently. While superficially reasonable, these assumptions don’t really hold up to scrutiny. What exactly is this “perfection” whose existence and necessity we are debating? For example, is perfection blue? You might think not, since perfection doesn’t have any particular color. But aren’t colors good, and therefore the property of being colorless is an imperfection? Likewise, and somewhat more seriously, for questions about whether perfection is timeless, or unchanging, or symmetrical, and so on. Any good-sounding quality that we might be tempted to attribute to “perfection” requires the denial of some other good-sounding quality. At some point a Zen monk will come along and suggest that not existing is a higher perfection than existing.
We have an informal notion of one thing being “better” than another, and so we unthinkingly extrapolate to believe in something that is “the best,” or “perfect.” That’s about as logical as using the fact that there exist larger and larger real numbers to conclude that there must be some largest possible number. In fact the case of perfection is much worse, since there is not single ordering on the set of all possible qualities that might culminate in “perfection.” (Is perfection sweet, or savory?) The very first step in the ontological argument rests on a naive construal of ordinary language, and the chain is no stronger than its weakest link.
No, the problem is that there is a point before #1. Let us call it point 0, and as such it should be defined as:
0. A being named God is asserted.
Only then can you continue on to point #1. And if you do not accept point #0 then the whole logic chain falls apart.
I don’t take this stuff too seriously. Logicians are still debating the outcome of Zeno’s Paradox and that one is simple by comparison.
I’ve blogged about the modal ontological argument, explaining exactly why the premises do not say what they appear to say. Occasionally I’ve gotten trained philosophers trying to attack my arguments, and every time it becomes apparent that they don’t understand logic. (Come on! It’s just like math!)
Long story short, I once got Plantinga himself to respond to me, and in his response he suggested that the parallel postulate might be necessary. Does he not know about non-euclidean geometries? And thus my respect for “sophisticated” theology dropped to an all-time low.
When I have more time I’ll be happy to jump into the details of above comments.
If Kant were on Facebook, I wonder if he would be expounding on the lolcategorical imperative
Hume’s general objection to this argument is the most important. You can’t prove the existence of a being with an apriori argument.
@Sean #6
The problem is you stated Becker’s postulate incorrectly. It says that if something is necessary, then it is necessarily necessary AND if something is possible then it is necessarily possible. Note that ~[]p is equivalent to <>~p, so Becker’s postulate can be applied to it.
Pingback: An interesting take on the Ontological Proof. « A still more glorious dawn…
I exist.. therefore I must be perfect!
Yes, I think it’s quite clear that the notion of “perfect” is conditional, and therefore irrational per se.
What’s more perfect than god? God with a pizza. What’s more perfect than god with a pizza? God with a pizza and a 6-pack of really good beer. And on and on.
Nothing defined as “perfect” can exist because the concept is necessarily limited to non-existent things. Except Natalie Portman, of course.
But it’s quite possible to redefine god as “not quite perfect”, and then the game’s on again. This notion of god as omni is a fairly recent invention, I think.
For the purposes of Anselm, it borks the argument, however.
Still looking for not-God? Or not-good? Nothing is perfect — Mother Nature is not perfect, but she is harmonic — not by implication, but by operation.
In a similar fashion, but different:
https://secure.wikimedia.org/wikipedia/en/wiki/G%C3%B6del%27s_ontological_proof
It’s a proof for the neccessary existence of god.
If anyone has interest for the details:
http://www.springer.com/philosophy/logic+and+philosophy+of+language/book/978-1-4020-0604-3
I like Dan Dennett’s demonstration of the silliness of the OA: proof of the perfect ice-cream sundae!
But Hume also nailed this one, didn’t he? When he pointed out that nothing ‘necessarily exists’ if it is possible to conceive of it’s non-existence without contradiction: “Nothing is demonstrable, unless the contrary implies a contradiction.” (Dialogues, part IX)
IMO the big problem is line 2. The fact is, that if we talk about something possible being true, we normally imply that it is also possibly false. But that possibility is not explicitly mentioned here.
So what would happen if we introduced line 2a: <>~p or ~[]p which would state that the not perfect was possible.
It would lead via modus tolens of line 1 directly to ~p.
So by line 1 we have introduced a context in which <>p ^ <>~p is a contradiction and in which the choice of <>p or <>~p leads to p or ~p respectively.
Now if I have to choose between the perfect is possible and the not perfect is possible, I’ll choose the second every time. Because that is not only possible, we see it’s existence every minute.
My problem with taking seriously the proofs of existence/non-existence of God is that the idea of existence is not well defined and that one only uses the classical logic, where the rule of the exclusion of the third is valid (i.e. p or not p). Given the ideas from modern physics, i.e. quantum mechanics and parallel universes, it is clear that the outcome of such a proof depends on the context which one assumes. Note that the logic of quantum mechanics does not have the exclusion of the third rule (an electron passes through both slits in the double-slit experiment) but in all profs the validity of classical logic is assumed, and this is not justified, since the ontological features should apply to all domains. Another observation is that existence can be relative, if one accepts multiple universes (i.e. something does not exist in our universe bat it can exist in another universe). If one enlarges the domain of existence even further, one can say that there are abstract ideas outside of the universes, one arrives at the platonic ontology. For me the platonic ontology is the most general context in which various general questions can be analyzed. Then the idea of God exists, so that God exists, but what is interesting is to find out what is the relation between God and our universe.
Things like this are what make me believe that logic is about as far away as you can get from mathematics without actually leaving the subject.
…. even those things that have gone bad or become broke – were once *perfect*
You can break it pretty easily by asking the person to define “existence.” Most things that we think of as “existing” are contingent, temporary configurations of matter. We think about chairs “existing” without taking into account that there’s a definite time at which the chair is constructed and almost certainly a time at which the chair will be destroyed or dismantled.
I have yet to hear of anything that “exists” in any sort of eternal way. Even electrons and other “fundamental particles” can be “destroyed” in nuclear reactions. One might be able to plausibly claim that electrons necessarily exist, but one can’t claim that of any particular electron.
I think that, based on the sample so far investigated by human beings, one could make a pretty good case that anything that exists does so contingently (essentially by definition of “exists”). After all, if something existed necessarily, it would be eternal, and I simply can’t think of an example of ANYTHING that exists eternally.
If the Ontological Argument is correct then the opposite would also be correct.
1. George W. Bush is by definition an imperfect being.
2. It is more imperfect to not exist than to exist
3. Therefore, George W. Bush does not exist.
Theoretical physics offers a way to define timeless existence: a particle trajectory in the spacetime (worldline) is such an object. The particle worldlines constitute the so called “block universe” interpretation of reality and time. In this interpretation the passage of time is an “illusion”, i.e. the time passage is an emergent phenomenon. Personally I subscribe to the “evolving block universe” interpretation, where the passage of time is identified as a moving Cauchy surface ( a section of the block universe).
I believe it was Woddy Allen who put for the syllogism:
1) Socrates was a man
2) All men are mortal
therefore
3) All men are Socrates
Put that in your pipe and smoke it!
Some responses:
To TheBlackCat
“My understanding is that this is the original formulation of the proof and that the idea of “necessary existence” was a later addition.”
And to
RawheaD:
“I’d also point out the logical instability of the phrase “more perfect”. If something is perfect, it should, by definition, unable to be “more perfect.” ’
The original formulation, that of Anselm in the Proslogion, refers not to perfection but to “something than which nothing greater can be conceived”, aliquid quo nihil maius cogitari possit. This is not a quibble in the present context since everything depends on exactly how the argument is worded.
To Ernie Keller
“The only way I know to decide if something exists is by reasoning about observations.”
There are many cases in which we use other methods to determine existence. In order to determine whether there is an integral square root of 181 we could , for example, try squaring all numbers within a certain range: this would not even require observing a piece of paper and ink marks if you were good at doing math in your head.
To Simon:
“But Hume also nailed this one, didn’t he? When he pointed out that nothing ‘necessarily exists’ if it is possible to conceive of it’s non-existence without contradiction: “Nothing is demonstrable, unless the contrary implies a contradiction.” (Dialogues, part IX)”
It is exactly Anselm’s contention that the non-existence of God involves a contradiction: therefore the quote from Hume here begs the question (I am not presuming in this brief comment to refute Hume’s complete presentation, which see.)
To Dan L.:
“If something existed necessarily, it would be eternal, and I simply can’t think of an example of ANYTHING that exists eternally.”
It is at least arguable that the number three exists necessarily and eternally, that is, timelessly. I would suggest that the burden of proof would be on anyone who thought 3 was temporary and contingent.
To Tom:
“If the Ontological Argument is correct then the opposite would also be correct.
1. George W. Bush is by definition an imperfect being.
2. It is more imperfect to not exist than to exist
3. Therefore, George W. Bush does not exist.”
I cannot tell to what extent this was meant seriously, but in any case this would apply only to the most imperfect being, not merely some imperfect being.
The problem is see is that you can prove anything if you pull your axioms out of thin air. If I assert as an axiom that two perfect things are greater than a single perfect thing, doesn’t that prove there are an infinite number of Gods? And by extension doesn’t that prove that monotheism must be wrong? Those lucky Hindus must have the only valid religion, I just proved it.
If I were to run into old Anselm himself, I would ask him that since I can conceive of a conception of being than which no greater can be conceived that no other conception of that being can be made, that description must be the only true conception of that being and all other conceptions of that being, including Anselm’s are wrong? (He would weasel out, I’m sure, how humans are imperfect, blah, blah, blah)
If god exists then he is perfect
Men are perfectly male.
Black is perfectly colorless
Therefore god is a black male.
The real first line of the argument should read:
1. We will assume that god exists and that he is perfect.
Lines 2 and 3 are thus built upon pure conjecture.
The Greeks made fun of these silly arguments 2000 years ago. And how you can prove or disprove that God is when God is by definition undefinable.
The bottom line is: look around – if it makes sense to you then God is – if it doesn’t then you are another piece of garbage in your own mind. So sorry.
I’ve heard it said that the reason perfection must be possible is that we can imagine it. But that’s silly. We can imagine all sorts of impossible, self-contradictory things, because our minds don’t need a coherent description of something to imagine it. We tend to interpret any sequence of words that *sounds* coherent to be a coherent idea, whether it is or not. For instance, I can imagine “a stone so heavy that an omnipotent God cannot lift it”, even though this is self contradictory (you can’t simultaneously have an omnipotent God and a limit to his power). But because I can imagine it, I could say such a thing is possible. And if an omnipotent God is necessary, and yet it is possible for there to be a limit on his power, then he’s not necessarily omnipotent at all, so we arrive at a contradiction. This is an unsound argument, but the flaw in its premises is much the same as the flaw in this version of the Ontological Argument.