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.
I get this one put to me time and again.
Just stop the perpetrator by saying that you don’t accept that “It is more perfect to exist than to not exist.”
Where does that come from?
Moreover you can argue with them that since we can imagine a perfect unicorn that also must exist.
I’m confused by the displayed argument by Prof. Suber. In particular, I don’t think Line 5
~[]P –> []~[]P
is derivable by substituting ‘~[]P’ for ‘P’ in
[]P –> [][]P.
Instead, maybe we are supposed to substitute ‘~P’ for ‘P’ in
~[]~P –> []~[]~P
and then apply double-negation elimination on the resulting sentence.
By the way, Sean, is you interest in logic and metaphysics a new thing? Any interesting connections to your interest in physics?
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I haven’t looked at your proof closely yet, but I think you are being unfair by calling the first version you listed a “cartoon version”. My understanding is that this is the original formulation of the proof and that the idea of “necessary existence” was a later addition. Further, I have seen many instances where the original version of the proof is used to support the idea of God rather than one the later revisions.
So rather than being the strawman you imply, it was originally intended to be take seriously, and still is be many religious people.
Spinoza’s take on the perfection argument is pretty awesome. He gives a definition of perfection: he equates it with with reality. The more perfect something is, the more real it is. He does away with modality in the ontological argument: perfect things necessarily exist; imperfect things necessarily do not. God is (infinitely) perfect and (infinitely) real: thus (and through other arguments too) Spinoza arrives at total pantheism. This appears to be a slightly odd concept of perfection, given that it would appear to be comparative rather than superlative — can things be more or less perfect/real? But the argument concerns knowledge, and knowledge of God, so is better put as:
— God is perfect, therefore God is everything.
— Some things appear imperfect to us.
— Imperfect things cannot exist.
— Imperfect things therefore appear so due to a limited knowledge of God.
— To someone with a full knowledge of God, nothing appears imperfect.
Highly unusually, he argues that a full knowledge of God *is* possible for human minds. Why? Well because they are, of course, part of God, as is everything.
Spinoza is barmily wonderful.
John– I think you’re right. Looks like a ~ and a [] were carelessly commuted. But as you say, I think it can be fixed up.
Not really a new thing, just something that doesn’t come up very often. I went to a Catholic university, and was assured by one of my religious-studies professors that the ontological proof could be cast in terms of formal logic, but only with the help of the internet did I finally get around to looking it up.
I think it is much simpler. The thing is, when you state the premises:
# God is by definition a perfect being.
# It is more perfect to exist than to not exist.
you are already stating the conclusion. Not in a deduction way, but inside the premises. If I ask what is “perfect” according to those, one should say something like:
“Perfect is something that is [bla bla bla] and exists”
Since the second premise states that existing is “more perfect” than not. Then, what the first premise is really saying is:
“God is by definition a being that is [blablabla] and exists”.
Therefore, God exists? Of course, it’s almost (if not entirely) tautological.
Of couse we could just challange the premises (as the article did in a way):
1. Who said God is perfect? If I say an unicorn is perfect, than it exists?
2. Why existing is more perfect than not? What is perfect, for that matter?
The last phrase from the article said it all: “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.”
But my point is that EVEN if we accept the premises, the conclusion is meaninless, since it were already hidden in the premises (not in a good, deduction way). “God exists (is perfect), therefore god exists”.
Just stop the perpetrator by saying that you don’t accept that “It is more perfect to exist than to not exist.”
Even better, argue the converse. It is more perfect not to exist. However good something is in reality, you can always imagine something better – something that goes to eleven. Therefore, God is imaginary.
Put enough fancy clothes on that and you can probably disguise it as a consequence of the diagonal argument.
I agree with Rodrigo. It’s not “almost” but entirely tautological, because under the premise, the concept of “perfection” includes “existing”. 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.”
I found, when thinking about this, that the more you think about “perfection” the loopier it seems, at least in relation to anything actual in the actual familiar world. Very good, very very good, very very very good; those all make sense; but perfection is just absurd.
I wonder if engineers see it differently.
Without being an expert in philosophy I would say the proposition stated in the cartoon is pretty accurate. It also pretty well sums up much of Eastern Philosophy. If you can imagine it then it is perfect. What causes problems is when you try to imagine an entity separate from that system, that does not experience happiness and/or desperation and suffering. People traditionally think of a god or gods that is somehow removed a bit from the experience of the world. If you think of desperation and suffering as the yang to the yin of happiness, then you can’t have either without the other. And if you define the world in that way why would a god be in any way separate and removed from that. A formal separate anthropomorphic God isn’t really necessary. One should just assume a lower case god as the totality of what is, suffering and happiness together. And it is perfect, but only in it’s combined totality.
@Ophelia:
#1: God is perfect
#2: Perfect would be a tolerance to infinite precision
#3: An extra digit of precision (going from .001 to .0001) usually involves a 10 fold increase in modeling or machine time.
#4: God is infinitely expensive
#5: Double the factor of safety and settle for a 90% God
By the way, I noticed that the blog banner changed from a blue ball to a….blue ball. Way to break the mold.
(I know, I know. It wasn’t Sean’s design. Consider yourself lucky that some guy going EVA isn’t relieving himself instead.)
-Matt (an engineer)
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As a Buddhist, I’ve always felt that non-existence was more perfect than existence.
For a really nice take on what goes wrong with (a version of) the argument, see David Lewis’s “Anselm and Actuality.” Lewis takes an informal version of the argument and claims that there are four different ways we can read: “Something exists in the understanding, than which nothing greater can be conceived”. Under two of those ways, the argument is valid, but the premise in question is not plausible. Under the other two ways, the premises all look true, but the conclusion doesn’t follow. Lewis also nicely avoids using any modal logic at all by quantifying over possible worlds directly. (Don’t read the final section of the paper, though, where Lewis goes off the rails with his idiosyncratic metaphysical views.)
I think I’ll go stare at my navel now.
If we take the notion of something which is perfectly blue, we can claim to conceive of something than which nothing can be more blue: a pure blue, containing not the faintest admixture of any other tint. Do we conceive of a dark blue, or a light blue? Obviously, though the OA claims that we can conceive of the greatest possible something-or-other, we can’t. Perfection is a mere superlative, and as such is something on a scale between “a bit” and “absolutely”. But we cannot conceive of “absolutely”. As Ophelia points out, it’s a case of good, “very good, very very good”……most perfect…even more perfect…(!) So it’s basically just a word, meaningful only in relation to some context, and meaningless as an attempt to describe accurately some sort of “absolute” (whatever that might be).
Clearly, only an entity can be perfect, or at least perfectible (or just improvable), because perfection must be some condition of the properties of an entity. Also, an entity must be a sort of sum total of its properties, otherwise there would be no entity. This means that “perfection” is contingent, so immediately the OA seems to contradict itself, considering that a perfect being isn’t supposed to be contingent. After all, the OA is correct in claiming that something that exists is more perfect than something that doesn’t, for the banal reason that there is no thing that doesn’t exist.
I would further like to posit that everybody goes to Shakey’s pizza, because Shakey’s is the place to go.
I’ve always had a few problems with this argument. Mainly:
1. Existence as an attribute of perfection.
One could make an argument that says something like: God is perfect. Perfection is an ideal. No thing in existence correctly matches it’s ideal. Therefore God does not exist.
2. The vagueness of “perfection”.
People just tend to throw it in there as a catch-all abstract, but what is perfection exactly? What makes a perfect blue, for example, perfect? Now add in the fact that not everyone will agree on what constitutes perfection. Can we ever arrive at an objective definition of perfection?
3. Logically paradoxical.
When people do give some explanation of God’s attributes, they tend to throw in omnipotence, omniscience, omnibenevolence, etc., all of which come with their own internal contradictions. Can God make a rock too heavy for himself to lift? Either answer put limits on his power, and thus his perfection. In fact the very idea of omnipotence is illogical, therefore not possible, hence not perfect.
It seems just sophistry to mask the lack of data on the subject. Like Sherlock Holmes said: can’t make bricks without clay.
Is the crude version of the argument above perfectly logical? Yes, but only in the sense that-
God exists, therefore God exists
-is perfectly logical. Validity occurs when the truth of the premise(s) means that the conclusion must be true, on pain of contradiction. So an argument which “begs the question” can be valid. If one is going start talking about “X” in the premises of an argument, and then conclude with the existence of X, the “X” in the premises has to refer to the “concept of X” not X itself, if it is not to beg the question. If one then admits that the “X” in the premises refers to the “concept of X” then the argument will be equivocating between the “concept of X” and “X”, so it will not be valid. I can’t see how any modal version of the argument would alter this. So the argument seems to be doomed from the beginning. Am I missing something?
The only way I know to decide if something exists is by reasoning about observations. I’m sure that’s not “perfect” but it appears to be “necessarily’ the case.
For that reason I think the Design argument was a better challenge. You really had to think about that one in the days before science began to show that primeval simplicity could lead to levels of complexity you’d need to produce conscious beings.
The only way I know to decide if something exists is by reasoning about observations. I’m sure that’s not “perfect” but it appears to be “necessarily’ the case.
For that reason I think the Design argument was a better challenge. You really had to think about that one in the days before science began to show that primeval simplicity could lead to levels of complexity you’d need to produce conscious beings.
What Rodrigo said, at #7. The conclusion of the ontological argument is contained in its premise. It’s hidden a little more sneakily than in your average circular argument, but that’s all.
Also, to play off what Sean said about perfection not being a well-ordering relation on the set of all objects: Who says the axis of perfection has to run in only one direction? Couldn’t you use the ontological argument to prove the existence of an all-powerful, all-knowing, perfectly evil being – one that’s exactly as powerful as God, but always has the opposite desire in any situation? (You could call this “the Manichaean Reductio”.)
Ebonmuse,
Why even define God as being perfection in the form of good or evil. It seems even western atheists are steeped in the traditions of good and evil. Couldn’t perfection be something altogether different from that? Use some imagination!
I forget who to attribute it to, but back in my undergrad days I remember a discussion of this where someone pointed out that, just as a perfect God who exists is even more perfect than a perfect God who doesn’t, a perfect God who exists and tastes like delicious ice cream is even more perfect still. Mmm, delicious ice cream.